An experimental study of the impact of product differentiation on collusive behaviour

... measurement of the Introduction degree of product differentiation The closer is γ to zero, the higher the degree of product differentiation With this demand function, suppose the production cost... cost and the monopoly price as the degree of product differentiation changes Furthermore, the most distinct conclusion in this paper is the establishment of monotonic relationship between collusive. .. profit by defecting collusive (monopoly) agreement, on the condition that the degree of product differentiation √ is in the interval [ − 1, 1) As known, the maximized collusive profit is the monopoly

AN EXPERIMENTAL STUDY OF IMPACT OF PRODUCT DIFFERENTIATION ON COLLUSIVE BEHAVIOR YU JUAN (Econ Dept, NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SOCIAL SCIENCE DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2008 Acknowledgements The essays in this dissertation would not have seen the light of day without the help of numbers of individuals and institutions. First, I would like to express my sincere appreciation to my supervisor A/P Julian Wright for his insightful ideas, patience and support throughout my Master program. Secondly, special gratitude is also expressed to Prof. Li Jianbiao in Nankai University, China, who has made great contribution to the field work for the data collection. Besides, I have had many fruitful discussions about the experimental design and dissertation process with fellow students. Hence, I would like to thank all of them for their help, especially Zhang Yongchao, Gu Jiaying, Ju Long and Wang Guangrong. Next, I would like to acknowledge the Graduate Research Support Scheme of Faculty of Arts and Social Science for the financial support of the field work in this dissertation. Finally, I am excited to express great thanks to my parents for instilling in me the importance of education, and for always providing motivation, encouragement and love. ii Contents Acknowledgements ii List of Tables v List of Figures vi Introduction 2 1 Theoretical Models 5 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 The Setup of Differentiated Product . . . . . . . . . . . . . . . . . . 6 1.3 Nash Reversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 T-Period Punishment . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Optimal Punishments . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.6 Price Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Experimental Literature Review 19 iii Contents iv 2.1 The Role of Information and Communication . . . . . . . . . . . . . 19 2.2 Experimental Tests of the Standard Theory . . . . . . . . . . . . . 21 3 Experimental Design and Research Procedures 23 3.1 Main Experimental Issues . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Institutional Formulation . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Research Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Experimental Results and Predication 28 4.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Comparison Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2.1 Comparison with One Shot Game and Repeated Game . . . 31 4.2.2 Estimation of δ . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2.3 Non-parametric Analysis . . . . . . . . . . . . . . . . . . . . 36 5 Conclusion 41 Bibliography 43 A Instruction and Test(EN) 48 A.1 Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 A.2 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 B Instruction and Test (CN) 52 B.1 Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 B.2 Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 C Computer Screen and Payoff Table 56 List of Tables 4.1 Statistical Measurements for Each Treatment. . . . . . . . . . . . . 29 4.2 Estimate δ of the Theoretical Models . . . . . . . . . . . . . . . . . 35 4.3 Wilcoxon Signed Ranks Test for 13th period . . . . . . . . . . . . . 37 4.4 Wilcoxon Signed Ranks Test for 15th period . . . . . . . . . . . . . 38 4.5 Wilcoxon Signed Ranks Test for 17th period . . . . . . . . . . . . . 38 A.1 Payoff Table(EN). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 A.2 Payoff Table for Test(EN). . . . . . . . . . . . . . . . . . . . . . . . 51 v List of Figures 1.1 Critical Discount Factor for NR Model . . . . . . . . . . . . . . . . 12 1.2 Maximum collusive price for NR Model . . . . . . . . . . . . . . . . 13 1.3 Critical Discount Factor for TP Model . . . . . . . . . . . . . . . . 17 1.4 Critical Discount Factor for OP Model . . . . . . . . . . . . . . . . 17 1.5 Maximum collusive price for PM Model . . . . . . . . . . . . . . . . 18 4.1 Descriptive Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.2 Comparison with One Shot game and Repeated Games . . . . . . . 39 4.3 Price Estimations for the Theoretical Models . . . . . . . . . . . . . 40 C.1 Main Computer Screen . . . . . . . . . . . . . . . . . . . . . . . . . 56 C.2 Example Payoff Table 57 . . . . . . . . . . . . . . . . . . . . . . . . . vi Abstract We will study the relationship between product differentiation and price in a setting where collusion can arise. The standard theory of tacit collusion predicts an ambiguous relationship between the price supported and product differentiation under linear demands. Other theories such as the price matching punishment’s theory of collusion predict a monotonic relationship. We wish to discover the relationship between product differentiation and prices in an experimental setting where tacit collusion can arise. Despite the obvious interest both from a theory point of view and from a policy perspective, this has not been tested before. Keywords: Tacit Collusion, Product Differentiation, Experimental Design. Introduction Even though explicit collusion among firms is illegal and prohibited in many countries, it is our position that collusion may still be possible to achieve due to many relevant factors, such as signalling by price, long-standing repeated interactions and so on. This is so called “tacit collusion”, which means firms in a market could collude without explicit communication and agreement. In this paper, we are interested in price collusion of symmetric duopoly markets with different degrees of product differentiation, but with no money transfers and no communication. According to Friedman(1971), firms are able to achieve non-cooperative subgame perfect equilibrium, which enables them to obtain higher profits than Nash profits in a one-shot game. However, the price under implicit collusion should be in the interval of one-shot price and monopoly price. Therefore, given some theoretical assumptions, we aim to investigate whether such collusive price is sustainable in the long run competition. From this prospective, we want to experimentally clarify the relationship between collusion behavior and product differentiation in duopoly markets. 2 Introduction In general, there are two kinds of product differentiation. One refers to “vertical differentiation”; another is “horizontal differentiation”. Vertical differentiation means that firms focus on developing a ”better product”, thus resulting in different level of quality and even cost for the similar product(Mussa, Rosen, 1978). Therefore, all consumers agree over the most preferred mix of characteristics and, more generally, over the preference ordering. Chang (1991) has concluded that collusion is more difficult when firms are differentiated by levels of quality. Horizontal differentiation refers to different combinations of characteristics, possibly at comparable prices but targeted at different types of customers(Hotelling, 1929). Such differentiation aims at segmenting customers and maximizing the market share by creating customer loyalty, thus there is no ranking among consumers based on their willingness to pay for the product. Tirole (2003) concluded that this kind of segmentation strategy affects the effect of collusion in two ways. First, it limits the short-term profit from undercutting rivals due to customer loyalty; second, it also restricts the severity of price wars and thus the firm’s power to punish a potential deviation. Hence the relation seems contradictive. Moreover, the standard theory of tacit collusion predicts a non-monotonic relationship between the price supported and product differentiation under linear demands. Other theories such as the price matching punishment’s theory of collusion predict a monotonic relationship. Overall, theoretically the impact of horizontal differentiation on collusive price seems quite ambiguous. We are the first research to test the relationship between collusive behavior and product differentiation by using economic experiments. In order to simplify the experimental procedures and figure out the clear relationship, we restrict the experimental design into a duopoly market (Firm i and j), where we create conditions for tacit collusion to emerge. Within this market, the inverse demand functions are pi = α − β(qi + γqj ), where γ ∈ (0, 1) is considered as the measurement of the 3 Introduction degree of product differentiation. The closer is γ to zero, the higher the degree of product differentiation. With this demand function, suppose the production cost is 0, we fix α, β, vary γ with five different values, and then calculate five different payoff tables. Subjects in each market will choose price according to the payoff table in each treatment. Therefore, data availability on different combination of prices depends on the value of γ. Our results show that price is decreasing as the γ shifts up, but the probability of collusion is increasing at the same time, which indicates that the more collusion has been achieved on lower price as γ becomes bigger. Moreover, we compare the experimental with theoretical models, and conclude that Price Matching Model is the best model to explain the experimental data. 4 Chapter 1 Theoretical Models 1.1 Introduction Most discussion in the traditional industrial organization literature has regarded product differentiation as one of the primary characteristics in market structure, which has powerful effect on the performance of firms in the market. Due to the complexity of product differentiation, it is difficult to discover the relationship between this kind of market structure and its consequent firm performance. In this chapter, we will introduce some basic models related to this topic and some theoretical models with different frameworks in duopoly market. In reality, even in the duopoly market, two firms probably cannot produce homogenous commodity. Therefore, the revenue of the two firms not only depends on the price and pricing strategy they choose, but also on the product differentiation. However, the effect of product differentiation on price collusion is more complicated. Due to the product differentiation, on one side, a firm maybe cannot take the entire market by lowering its price in an infinitesimal amount of a single period. That is to say, higher degree of product differentiation reduces the benefits of defecting from a collusive agreement, thus, collusion will be easy to support; 5 1.2 The Setup of Differentiated Product on the other hand, if they defect, the punishment may not be very severe, thus, collusion should be hard to sustain. Overall, the effect of product differentiation on collusive outcome is ambiguous. In a differentiated-products market, the pricing decision of a firm depends not only on its own product (quality, quantity), but also on the substitutability of its rival’s product, because the high price for its product is strictly restricted when there are substitutive products in the market. On the other hand, in such kind of market, firms have strong intensive to coordinate their pricing strategies in order to avoid price wars. Meanwhile, the intention to deviate from collusive agreement is also aggressive if the products are differentiated too much, since in this case, the slight deviation will result in large increase in demand. Therefore, the effect of product differentiation on the collusive behavior is far from straightforward. In the subsections, we want to clarify how collusive price is affected by horizontal product differentiation in the theoretical framework. 1.2 The Setup of Differentiated Product Suppose two firms are competing in the market, and selling similar products. The marginal production cost for both firms is constant, and it is normalized to zero. Each firm faces the following linear demand curve expressing the price , pi , in terms of demand quantity qi and qj : pi = α − β(qi + γqj ), i, j = 1, 2 where γ(0 < γ < 1)1 denotes the measurement of product differentiation.The smaller of γ means the higher of product differentiation. In a price competition 1 If γ < 0, this demand function is associated with product complements, rather than substi- tutes. If γ > 1, it means in the pricing stage,the effect of rival’s demand is larger than its own demand, which is also not allowed 6 1.2 The Setup of Differentiated Product 7 market, we assume the monopoly profit, deviation profit and one-shot Nash Equilibrium profit are represented by π M , π D , π N , respectively. We also denote that firms are willing to collude at the Pareto Frontier of joint profit maximization, thus splitting the profit equally. Therefore, the highest collusive price should be the monopoly price. However, whether it is sustainable depends on the deviation profit and the punishment strategy of the rival. As for price competition, the demand function is piecewise linear: When the prices of the two firms are sufficiently close, both firms will have positive demands, and we can easily get firm i’s demand function in terms of pi and pj by inverting the inverse demand functions. However, when the prices of the two firms strongly diverge, the high price firm will receive no demand, while the low price firm captures the entire market. Specifically, according to Lu and Wright(2007), in order to ensure the demand is non negative, firm i’s demand function is as follows,  −α(1−γ)+pj α(1−γ)−pi +γpj   , < pi < α(1 − γ) + γpj ;  γ  β(1+γ)(1−γ) −α(1−γ)+pj α−pi qi = , 0 < pi < ; β γ     0, p ≥ α(1 − γ) + γp . i j With this kink demand function, we can easily solve the best response functions for the two firms. For example, given any pj set by firm j, firm i’s best response function is as follows:      pi =     α(1−γ)+γpj , 2 pj −α(1−γ) , γ α , 2 0 < pj < α(1−γ)(2+γ) 2−γ 2 α(1−γ)(2+γ) ; 2−γ 2 < pj < α(1 − γ2 ). pj ≥ α(1 − γ2 ). Obviously, the corresponding constrain conditions for each portion represent different competitive status. For example, if the rival’s price is low, the best response function for the two firms is linear upward sloping with γ as the endogenous variable; when the rival’s price is higher, firm i will quote a lower price and try to capture the whole market; in the case that the rival’s price is very high, firm i’s 1.3 Nash Reversion 8 price will be independent of its rival’s price, and also it could achieve the whole market by setting the monopoly price. With the best response function above, we calculate the monopoly prices, quantities and profits, which are pm i = α m α α2 , qi = , πim = , 2 2β(1 + γ) 4β(1 + γ) respectively. Similarly, the Nash Equilibrium prices, quantities and profits are pni α(1 − γ) n α α2 (1 − γ) n = , , qi = , π = 2−γ β(1 + γ)(2 − γ) i β(1 + γ)(2 − γ)2 respectively. In order to simplify the calculation in the experiment to follow, we choose the control variables as α = 46, β = 1. Hence, we have πm = 529 462 (1 − γ) ; πn = ; 1+γ (1 + γ)(2 − γ)2 In Bertrand Competition, the two firms will try to collude on price if possible. Obviously, the collusive price should be within the interval of monopoly price and one-shot Nash equilibrium price, that is to say, pn ≤ pc ≤ pm . However, whether the collusion can be supported in repeated games depends on the punishment rules applied when one firm deviates. In the next few sections, we will discuss the relationship between collusive price and product differentiation under some different punishment rules separately, such as Nash Reversion Model(noted as “NR”), Price Matching Model(noted as “PM”), T-Period Model (noted as“TP”). 1.3 Nash Reversion Nash Reversion, as so-called trigger strategy, is the standard punishment strategy in most models about tacit collusion, which assumes that if any firm defects 1.3 Nash Reversion from the collusive agreement, the other firm will reverse to the one-shot Nash equilibrium as soon as the defect is detected. Thus, a small cut in prices results in the same severe punishment as does a large cut in prices. The threat of this punishment strategy is somewhat credible since the defection will results in zero profit. Therefore, this approach facilitates price collusion and makes it even easier to support monopoly outcomes. In supergames, the price or quantity depends on the interaction between the two firms and the discount factor δ. In a related paper, Friedman (1971) introduced a dynamic reaction function for both firms within the repeated framework. He concludes that when static games are infinitely repeated, it is possible that firms set a cooperative price with trigger strategy, even though not explicitly colluding. Friedman (1968) analyzed the firm’s reaction functions that depend on the past behavior of the rival in a repeated duopoly game. Based on the assumptions, which are almost aline with those of Cournot Model, this kind of reaction functions could be considered as ”tacit collusion”. He has proved the existence of equilibrium points within this framework, that is to say, in the non-cooperative subgame, firms can achieve higher profit in repeated game than that in one-shot game, if the discount rate is high enough. Because the firms’ interaction about reaction functions, they may be able to implicitly collude to maximize their joint profits with no incentive to defect and thus increase profits. A firm that defects is possible to suffer adverse effect- Nash Reversion- in the future, as this will likely lead to a breakdown of the cartel. Hence, the firm will not defect unless the short-term benefits by doing so outweigh the long-term costs caused by the breakdown of the cartel. Furthermore, although explicit collusion is prohibited in many countries, firms are still able to obtain higher profits by tacit collusion. The simplest possible version of grim trigger strategy is as follows. Suppose the 9 1.3 Nash Reversion 10 collusive profit per period for each firm is π c , the deviation profit2 is π d , the oneshot Nash Equilibrium profit3 is π n , and the discount factor is δ . Therefore, each firm will stick to the collusive agreement on the condition that π c +δπ c +δ 2 π c +· · · ≥ π d + δπ n + δ 2 π n + · · · . thus it implies δ> πd − πc . πd − πn If the inequality above is satisfied, the collusive profit should be sustainable. It also shows some interesting comparative static results (see Tirole, 1998 or Motta, 2004). First, from the right side, it is shown that the more firms in the market, the less likely to sustain collusion; secondly, from the left side, in order to ensure the collusion stable, the discount rate should be large enough. Additionally, if the asymmetric information exists among the firms, i.e., they can not observe each other’s behavior quite often, collusion is also difficult to sustain. Moreover, we consider δ ∗ as the critical value of the discount factor. We will try to explain relationship between collusive profit and discount factor, and furthermore, we will explore the relationship between collusive price and the degree of product differentiation. Provided that pdi and qid denote the deviation price and quantity respectively, when firm i defect from the collusive agreement, while firm j insist on monopoly strategy, the demand curve is shown as follows,  46(1−γ)−pdi +γpm −46(1−γ)+pm j j   , < pi < 46(1 − γ) + γpm j ;  (1+γ)(1−γ) γ  m −46(1−γ)+p j qid = ; 46 − pdi , 0 < pi < γ     0, p ≥ 46(1 − γ) + γpm . i j Thus firm i’s profit is πid = pdi qid = pdi · 2 46(1 − γ) − pdi + γpm j , (1 + γ)(1 − γ) The current period profit that the firm receives if it deviate when all other firms take the collusive actions. 3 The profit that firm receives following a deviation. 1.3 Nash Reversion 11 d d since pm j = α/2, with first order condition, we have ∂πi /∂pi = 0, which yields pdi = 23(2 − γ) d 23(2 − γ) 462 (2 − γ)2 , qi = , πid = . 2 2(1 − γ)(1 + γ) 16(1 − γ)(1 + γ) We now consider the incentive of deviation from monopoly strategy, when competition is repeated infinitely, i.e., compare π m with π d . Take the competing behavior of firm i as an example, based on the calculation above, it is easy to verify pdi − pm i = − πid − πim = [ 23γ ≤0 2(1 + γ) 23γ 2 ] ≥0 2(1 + γ) Obviously, in repeated game, firms have strong incentive to lower the price and earn more profits, which means collusive agreement has been destroyed. In this case, as the cheated firm, firmj’s profit should decrease, however, no matter how low the profit is, it cannot be below zero, as we calculate below. qjch = d 46(1 − γ) − pm 23(2 − 2γ − γ 2 ) j + γpi = , (1 + γ)(1 − γ) 2(1 + γ)(1 − γ) 462 (2 − 2γ − γ 2 ) ≥ 0, 8(1 + γ)(1 − γ) √ ≥ 0 for all γ ∈ (0, 3 − 1], while negative for all πjch = qjch pm j = It is easy to check that πjch √ γ ∈ ( 3 − 1, 1). This is due to the quantity of cheated firm has been fallen below √ zero. Hence, if γ ∈ ( 3 − 1, 1), the optimal deviation price and profit for firm i should be calculated with the constraint of qj = 0. With qj = [46(1 − γ) − pm j + γpdi ]/(1 + γ)(1 − γ), we have 23(2γ − 1) d 462 (2γ − 1) , π˜i = γ 4γ 2   529(2−γ)2 , γ ∈ (0, √3 − 1); 4(1−γ)(1+γ) d π = √  529(2γ−1) , γ ∈ ( 3 − 1, 1). p˜i d = γ2 Till now, we have discussed the collusive and deviation behavior in one shot game and repeated games. Based on the analysis above, we conclude that for 1.3 Nash Reversion 12 Bertrand Model, firms could successfully achieve higher profit by defecting collusive (monopoly) agreement, on the condition that the degree of product differentiation √ is in the interval [ 3 − 1, 1). As known, the maximized collusive profit is the monopoly profit in Bertrand Competition, thus in this case π c = π m , which yields the critical value of discount factor as follows: πd − πm δ = d π − πn ∗ It is easy to calculate the critical value of discount factor based on the calculation of π d , π m , π n in previous section:  (γ−2)2  2 −8γ+8 , γ δ∗ =  (γ−2)2 (γ 2 +γ−1) , 2γ 4 −3γ 3 −γ 2 +8γ−4 √ γ ∈ (0, 3 − 1); √ γ ∈ ( 3 − 1, 1). From figure 1.1, we can see that monopoly is possible to sustain provided δ Figure 1.1: Critical Discount Factor for NR Model is greater than 0.5, which means it is easy to achieve collusion for NR Model. Furthermore, if δ > 0.61, the monopoly price is always supported for any degree of 1.3 Nash Reversion 13 product differentiation; if 0.5 < δ ≤ 0.61, the stability of monopoly price depends on γ; if δ < 0.5, monopoly price cannot be sustained for any γ. In order to discover the relationship for collusive price and product differentiation when 0.5 < δ < 0.61, we suppose the maximized collusive price is pc , the corresponding collusive profit and deviation profit is π c and π dd : πc = (46 − pc )pc 1+γ With the kink demand function, we induce the deviation function as follows.  √  [46(1−γ)+γpc ]2 , γ ∈ (0, 3 − 1]; 4(1+γ)(1−γ) dd π =  (46−pc )(pc −46(1−γ)) , γ ∈ [√3 − 1, 1). γ2 Regarding δ > π dd −π c , π dd −π n it is easy to plot the graph for pc and γ when δ = 0.4, 0.55, 0.9, respectively( See Figure1.2). However, in this model, the Nash Equilibrium solution is not unique. Because Figure 1.2: Maximum collusive price for NR Model from the inequity above, it is easy to conclude that any agreement that yields 1.3 Nash Reversion collusive profits π c > π n sustainable should be considered as Nash equilibrium of the repeated game, if the inequity above is satisfied. And also here the one shot Nash Equilibrium is not Pareto optimal, since firms could obtain more profits if they choose collusive price. Therefore, it should be a multiple non-cooperative equilibria model. Based on this concept, Abreu (1986) predicts that other forms of punishment may sustain collusive price with a larger range of δ . We will discuss it in the next section. In a related paper, Deneckere(1983)discovers the collusive behavior in duopoly supergames with trigger strategies as defined by Friedman(1971). He calculates the critical discount factor that could sustain collusion on the monopoly outcome for both Bertrand and Cournot competition with product differentiation. Furthermore, he finds that as for a low degree of product differentiation, collusion in quantities is more ”stable” than in price if discount factor is high; as for a high degree of product differentiation, collusive price is more sustainable. Deneckere also shows that if the collusion could be sustained, the discount rate in Bertrand supergame is non monotone regarding product differentiation. Chang(1990)examines the relationship between the degree of substitutability and the ability for firms to collude on price. He concludes that in the Hotelling Model of product differentiation, collusion is easier to sustain as the degree of product differentiation becomes larger. Furthermore, one crucial assumption is that the game is repeated infinitely. However, if the game is finite and known in advance, then the story should be different. With the backwards induction, both firms exactly know that they will defect in the penultimate period, and results in the Nash Equilibrium in the final period. Thus, they will play Nash Equilibrium for every period and collusion cannot be sustained. In the next chapter, we will discuss how the experimental design deal with this problem. 14 1.4 T-Period Punishment In a related paper, Tyagi (1999) also concludes that with a linear demand function, high degree of product differentiation hinders tacit collusion in Cournot Competition Model. 1.4 T-Period Punishment T -period punishment is defined that the punishment period lasts T periods after either of firm deviates from the collusion, and convert to collusive price afterwards. Thus it could be regarded as the Nash Reversion punishment if T is infinite. However, if T is finite, it means the collusive price will return back after a certain periods, thus it indicates that this kind of punishment rule is not as severe as Nash Reversion. Collusion should be easier to sustain when the number of periods in the punishment phase increases. Hence, the conditions for sustaining the collusive price in this model should be revised from that of Nash Reversion as follows: π c + δπ c + · · · + δ T π c > π d + δπ n + · · · + δ T π n Based on the condition above, it is figure out the relation between δ and γ as well, provided the number of punishment periods T . For simplicity, we fix T = 1. From Figure 1.3, we could conclude that monopoly price can not be supported any more. Thus in general, TP punishment rule is not as “credible” as Nash Reversion. 1.5 Optimal Punishments Abreu (1986,1988)first explores the optimal punishment in infinitely repeated games with discounting. He defines the optimal penal code, and a strategy profile as a rule specifying an initial path and punishments for any deviation from the initial path. If a deviation is detected in period t, then in next period, t + 1, 15 1.6 Price Matching firms switch to a punishment phase where both firms adopt the punishment action ap irrespective of which firm is punishing the other. Finally he concludes that the optimal punishment strategy exists in the discounted repeated games, and it maybe highly un-stationary, especially in the early stage, the deviation firm will be punished by a lower payoff than the subsequent stages. Lambson (1987)investigates the relationship between the optimal penal codes and the discounted profits with the consideration of participation constraint. They derived optimal punishment price and the associated critical discount factor for both Bertrand and Cournot competition in a duopoly supergame with differentiated products, and concluded that the critical discounted factor to sustain collusive price is as follows(See Figure 1.4). From figure 1.4, it is clear that the discount rate to support collusive price is lower than NR model, thus resulting that collusion is easier to arrive for OP Model, compared with that of NR Model. Hence, as for optimal punishment Model, the monopoly price is able to be supported as well.  √ (2−γ)2  , γ ∈ (0, 3 − 1];  16(1−γ)   √ √ (2−γ)2 (γ 2 +γ−1) √ 3 − 1, (3 5 − 5)/2]; , γ ∈ ( δ∗ = (γ 2 +2 −1+2γ−γ 3 )2    √  γ 2 +γ−1 γ ∈ ((3 5 − 5)/2], 1). 2γ 2 +γ−1 1.6 Price Matching Price matching, as a punishment strategy in tacit collusion, indicates that if a customer receives a lower price offered by another seller, the current seller will match that price. Starting from some collusive price, any price cut is matched by the other seller but not a price increase. According to Wright and Lu (2007), increased product differentiation makes collusion easier to sustain. They also provide some conditions that credibly support collusive outcomes under this punishment strategy and predict a unique collusive price which continuously varies between 16 1.6 Price Matching Figure 1.3: Critical Discount Factor for TP Model Figure 1.4: Critical Discount Factor for OP Model 17 1.6 Price Matching 18 marginal cost and the monopoly price as the degree of product differentiation changes. Furthermore, the most distinct conclusion in this paper is the establishment of monotonic relationship between collusive price and product differentiation, which is given by the following formula.(See Figure 1.5 as well) pc = 1−γ 2 − (1 + δ)γ Figure 1.5: Maximum collusive price for PM Model Chapter 2 Experimental Literature Review In this chapter, we will review some experimental literature related to this topic. And also, we will try to find some clues about the design of our experiments, such as how to choose parameters, how to restrict other factors in order to effectively achieve our target. 2.1 The Role of Information and Communication Experiments regarding collusion differ in many subtle ways, for example, the amount of information that subjects will receive during the experiments, such as, the market environment, the actions and performances of their rivals. In this section, we try to find out the effect of such variables on the extent of collusion. Haan, Schoonbeek and Winkel (2005) reviewed a large variety of experimental literature on collusion, particularly focusing on the roles of information and communication. They pointed out that as for the competition model, some researchers prefer Cournot Model, while others prefer Bertrand Model. The choice of the two 19 2.1 The Role of Information and Communication competition models is a contentious issue. Holt(1995) argues that Cournot competition is subject to a rather mechanical market-clearing assumption, thus the experimental results with this competition mode is not efficient. However, Kreps and Scheinkman (1983)notes that if firms first choose production capacities and then set prices, the result should be Cournot Equilibrium. Unfortunately, the experimental evidence on this issue is rather weak. Davis (1999) runs the experiments in triopoly markets with two treatments. In the treatment of a posted offer market, he concludes that prices decline slowly toward the competitive level.In the treatment of a posted offer market with advance production, he finds that prices are somewhat higher, while quantities are somewhat lower. Overall, there is no convergence to Cournot Equilibrium. Anderhub et al. (2003) focus on the duopoly markets with heterogeneous goods, in which players first make decision on capacity, and then set the price. Given the capacity choices, subjects set prices at or close to the equilibrium price most of time, and the capacity choices are clustered around the competitive equilibrium. Therefore, Anderhub et al. (2003) also find that capacity-price competition does not result in Cournot outcomes. Dolbear et al. (1968) experimentally investigate the role of information regarding the Bertrand Model with differentiated products, in which the firm’s demand function only depends on its own price and the average price of its rivals. Regarding their experimental design, in general, player were not informed about the number of periods in each session (actually 15 market periods), but after each period, they will be informed about the price their rival has chosen. Specifically, there are two scenarios: one with complete information, another with incomplete information. Complete information means that the profits of the payoff tables are derived from different combinations of the firm’s own price and the average rival’s price; while incomplete information indicates the profits of the payoff tables are composed of different values of it own price and a range of possible values of its 20 2.2 Experimental Tests of the Standard Theory own demand. Moreover, each subject knows that all the subjects will receive the same payoff tables within one session. After running the experiments with 2, 4, and 6 firms separately, they found that the number of firms adversely affects the stability of collusion. However, more information increases price stability within certainty markets, as measured by the variation of the average price. 2.2 Experimental Tests of the Standard Theory In this section, we consider some experiments with a close set-up to the theoretical model outlined in Chapter 2. We try to figure out some issues, such as, whether firms in experiment are able to collude without communication, achieve profits that are consistently above Nash equilibrium profits of one shot game, and reach the price that maximizes their joint profits. Huck et al.(2004) find some experimental evidence for Cournot Model without communication. After each period, firms receive the aggregate information about the choice of other firms. All subjects are well informed about their own payoff function, and firms are symmetric. With the experimental results, they find that in the tow firms market, total output falls below the Cournot predication by about 7% on average. Thus, the duopoly markets manage to collude to some extent. With a linear demand function, which is commonly used in experiments, perfect collusion implies that total output falls below the Cournot prediction by 25%. As for the markets with more than two firms, however, the effect disappears entirely. Wellford (2002) concludes that experimental price-setting duopolies are sometimes able to achieve collusive outcomes, but with more than two firms, the competition is more fierce, and it is very hard to collude, thus leading to competitive outcomes. It is important to note that in all the experiments considered so far, subjects 21 2.2 Experimental Tests of the Standard Theory are not allowed to communicate. Hence, these were all tests of real tacit collusion. From their reading of the literature, Haan, Schoonbeek and Winkel (2005) summarize the economic experiments that test the standard tacit collusion model as follows. Duopoly markets are able to collude on price. Yet, they are not able to achieve perfect collusion: average output is still much closer to Cournot equilibrium than it is to monopoly equilibrium. Markets with more than two firms are are not able to collude on price at all. 22 Chapter 3 Experimental Design and Research Procedures 3.1 Main Experimental Issues It is not always straightforward how to implement economic theory into experiments, because the assumptions of the theories are somewhat difficult to imitate in the experimental design. In the following two sections, we will investigate some experimental issues related with experimental design to achieve our target. In order to test the relationship between product differentiation and collusive price, we shall (i) fix other variables in the demand function except γ, and consider γ as the independent variable; (ii) try to facilitate collusion on price without communication. In this section, we will discuss how to meet these requirements in our experiment. There are five treatments in our experiment, with five different levels of product differentiation. Note that the standard theory about product differentiation with collusive behavior describes a situation in which firms compete infinitely in 23 3.1 Main Experimental Issues 24 a duopoly market. Therefore, we randomly paired the participants for each treatment. After the ending period of each treatment, all the subjects will be rematched for the next treatment. The randomization of pairs was intended to avoid reputation and path-dependence phenomenon. Thus in our experiment, we recruit participants to attend the five treatments subsequently, but randomly rematched before each treatment. Another difference between theory and experiment is that it is impossible to play an infinitely repeated game in the laboratory. Selten and Stoecker (1986) find that the behavior in a treatment with a long finite horizon is similar to that in an infinitely repeated game, except an end-game effect. Therefore, some researchers try to fix this problem by inserting a fixed probability of continuation after certain rounds. Another alternative approach is that subjects are not informed about the exact rounds of each treatment, but only know that the experiment will end with the instructor’s notice. To some extent, both the two methods above intend to make the ending round filled with uncertainty to the subjects. In order to make the experimental process well controlled, we choose the second one to end each treatment. Another important issue is the trading institution. Holt(1995)describes an exhaustive explanation for all possible trading rules in economic experiments. For our purpose to search the behavior of sellers, in order to avoid the interaction between buyers and sellers, we only consider the seller market and select a posted offer auction as the trading rule. Thus, each seller independently quotes a price in each round and the profit will be calculated with the linear demand function. In order to compare the experimental results with theoretical predications, our experimental design exactly follow the assumptions of the theoretical models (Bertrand competition Model in duopoly markets). Therefore, in our experiments, subjects were paired as the rules described above, and we derived the five payoff tables from 3.2 Institutional Formulation the model above according to the five values of γ(5/22, 9/22, 13/22, 17/22, 21/22) and δ = 0.9. 3.2 Institutional Formulation This experiment was computerized, and the software was initially designed by the author with the platform of ZTree. All the computers (24) were connected through a local network and isolated into different cubicles. One computer installed a master program was assigned as the server to control the whole experiment. We calculate the five payoff tables with the linear demand function and distribute one by one before each treatment randomly. 48 students were recruited at Nankai University, half from economic and business department, half from science faculty. The whole process of this experiment involves two parts: first is the briefing session taken in the reading room, including the instructions, test and computer screen. Instructions (see Appendix A) were translated into Chinese, distributed and read out to all the participants in the reading room by the instructors. The purpose of the test sheet is to clarify whether the participants have fully understood the instruction. After briefing, participants were sequently exposed to cubicles of the computer lab and the experiment started with no communication. During the experiment, subjects were randomly matched before each treatment, and their identities and histories are private information. Based on the design of the computer program, each participate will independently make his/her choice and submitted in every round given the payoff table, and they will be informed about their previous payoff and the rival’s previous price in the subsequent round on the screen. Besides, the participants are informed that their payoffs will be discounted by 0.9 from 11th round and afterwards until this treatment ends. The quoting price page also displays both his/her own price and profit, 25 3.3 Research Procedures the other seller’s price of the previous round. No other information about the seller is made public. The ending round is randomly controlled by the programmer after 20 rounds of each treatment, and then all the participants are required to hand in the payoff tables, meanwhile, we will distribute another table to all participants for the next treatment. Therefore, in aggregate, a player made decision for the price of his/her product more than 100 times. At the end of the experiment, each player was paid by cash according to his/her cumulative profit. After dividing by 500, the final payoff for each player was quite close, from maximum RMB72 to minimum RMB60, and average payoff is RMB65 , which is very close to the local average hourly salary (RMB30) for undergraduates. The detailed experimental instruction , computer screen and payoff table are shown in the Appendix C. 3.3 Research Procedures There are a qualitative predications regarding the maximized collusive price with differentiated products. Based on our model, we will illustrate some of them below. According to the values of the parameters in the model for the experiment, we could calculate the average price of experimental data, Nash Equilibrium and Monopoly price. On the other hand, based on the three models discussed above, we could also figure out the collusive prices given different values of γ, and compare with the experimental results to find out which model best explains the experimental data. In order to investigate the relationship between collusive price and product differentiation, we will try to statistically run some regressions, and compare the collusive prices we define with those of the theoretical models, to see whether they are significantly different or not. The detailed discussion about the results will be 26 3.3 Research Procedures shown in the next chapter. 27 Chapter 4 Experimental Results and Predication The following sections in this chapter report on the experimental results and compare them with the theoretical predications discussed in the previous chapters. We will present the descriptive statistic analysis for the selected rounds of each treatment and predicate the relationship between price and product differentiation. Furthermore,the comparison between experimental data and the three theoretical models will be fulfilled by non-linear regression and non parametric analysis. 4.1 Descriptive Statistics As noted in Chapter 3, the first ten periods without discounting in each treatment are regarded as the learning process for players in each market, in order to achieve the collusive path. Hence, the data for these periods is not suitable to be counted in the collusive behavior analysis. Moreover, experimental data generated from repeated games with discount rate is exactly what the standard theory did. Therefore, we select the experimental results of 11-20 periods, which could avoid the ending effect. Hence, our database for analysis is based on 24 markets for ten periods in each session. A total of 2400 observations of prices was recorded during 28 4.2 Comparison Analysis 29 the experiment, with 480 observations in each treatment. Descriptive statistics for the data pooled by treatment is given in figures 4.1, and table 4.1, where ”mean” is the average price for each treatment, ”Std.D” is the standard deviation. From the figures, we can see that the growth of γ significantly increases the dispersion of prices among sessions, and within given sessions as well, as measured by the variance of the average price in given treatment. The range of price posted in treatment 1 and 2 is restricted in the interval of [13, 24], while the price disperses among all the given choices for the rest three treatments. Table 4.1: Statistical Measurements for Each Treatment. 4.2 Comparison Analysis With the intuitions we have from descriptive statistics above, we further explore this relationship by comparison analysis. First, we will compare the average price in each treatment with one shot Nash equilibrium and monopoly price; secondly, we differentiate the collusive price from the aggregate data1 , and estimate δ of the three theoretical models (NR,TP and PM) with these two series of data separately; finally, in order to further explore which model is the best to fit the 1 We define“collusive price” as the prices for each market are greater than corresponding Nash Equilibrium price. And, 1,700 observations meet this requirement. 4.2 Comparison Analysis (a) γ = 5/22, N E = 20, M ean = 20.88 30 (b) γ = 9/22, N E = 17, M ean = 19.5 (c) γ = 13/22, N E = 13.4, M ean = 18.8 (d) γ = 17/22, N E = 8.5, M ean = 15.2 (e) γ = 21/22, N E = 2, M ean = 13.6 Figure 4.1: Descriptive Analysis 4.2 Comparison Analysis 31 experimental data, we compare these two categories of experimental data with the data series of three models, which are generated by certain reasonable values of δ. The detailed discussions and results are shown in the next few sections. 4.2.1 Comparison with One Shot Game and Repeated Game Figure 4.2(a) shows a clear relationship between average price, Nash Equilibrium and monopoly price, and evolution of these t prices regarding different degree of γ as well, where “AvP” is defined as the average price of the pooled data, “NE” means the Nash Equilibrium price, “Av(NE:MP)” means the average level of Nash equilibrium and monopoly price in order to deeply discover the trend of average experimental price, in other words, to check average price is closer to NE or Monopoly price. It is easy to find that both the average experimental price and “NE” are declining as γ increasing. On the other hand, regarding between-group analysis, we find that the average price is always greater than the corresponding ”NE”, but undoubtedly lower than the monopoly price. Furthermore, we figure out that the average output is very close to the middle of NE and Monopoly price(“Av(NE:MP)”). Hence, we conclude that the collusion on price has been successfully achieved with discount rate, and the collusive price is downwards as γ becomes bigger. Till now, we have some intuitions about the tendency of price as γ increases. However, since the posting price action by subjects is continuously conducted, as time went by, besides the impact factor γ, the learning effect may have some extent of influence on the collusive price. Therefore, it is necessary to distinguish the impact of γ and time trend on the quoting price separately. The variable of time trend is defined into two categories, which TD1 means the time slot by each treatment, that is , all rounds for treatment 1 equals 1, those of treatment 2 equals 2· · · ; TD2 refers to the real time slot happened during the experiment, such as, the 4.2 Comparison Analysis 32 11th round of treatment 1 is 11, 12th round of treatment 1 is 12, the 11th round of treatment 2 is 34, the 11th round of treatment 3 is 58 · · · . After generating the series of TD1 and TD2, we run the linear regressions as follows: P rice = 23.794 − 10.425γ (4.1a) P rice = 23.18 − 12.394γ + 0.591T D1 (4.1b) P rice = 23.42 − 12.219 + 0.023T D2 (4.1c) All the coefficients in the equations above are significantly different from zero. In the equation 4.1a, we can see that as γ increases by 0.2, prices will decreases by 5; In the equation4.1b, the effect of time trend on price is 0.59, which means prices will climb up by 0.59 after each treatment. As the coefficient of γ becomes smaller in equation4.1b, compared that of equation 4.1a. The same analysis could be conducted from equation 4.1c. Thus we statistically conclude that prices are a decreasing function of γ, but this effect is somewhat offset a little by learning effect as time goes by. Regarding this result, two steps are necessary to carry out in order to obtain some deep insight. How to measure the extent of price decreasing. We try to measure the mark-up of experimental price on NE, that is, the ratio of (EX-NE)/NE. Hence regarding this ratio as the dependent variable, we have the estimations in equations 4.2. It is easy to induce that roughly, the mark-up of experimental price on NE will increase by 12% as γ jump up from 5/22 to 21/22. This percentage should be higher if we analyze the effect of γ and time trend separately(see equations 4.2b and 4.2c). Ratio = −2.54 + 6.75γ (4.2a) Ratio = −1.59 + 0.8γ − 0.92T D1 (4.2b) Ratio = −1.928 + 9.757γ − 0.038T D2 (4.2c) 4.2 Comparison Analysis How the tendency of collusive price 33 2 evolves as γ increases. We run a Probit Regression, regarding the probability of collusion as the dependent variable. The regression results are showed in equations 4.3, in which all the coefficients are significant. From 4.3a, we find a very interesting story that collusion increases as γ value goes up, and this effect is offset by some extent as games played as well (see equation 4.3b and 4.3c). Therefore, we conclude that more markets could collude on price as γ increases, even though collusive price is lower. 4.2.2 Collusion = −0.394 + 1.675γ (4.3a) Collusion = −0.56 + 0.876γ + 0.216T D1 (4.3b) Collusion = −0.478 + 0.925γ + 0.008T D2 (4.3c) Estimation of δ In this section we report on the parametric approach to estimate the discount rate for the three theoretical models3 we discussed in Chapter 1 as listed below. NR Model c P =    46(4−8γ+5γ 2 −γ 3 +4γδ−5γ 2 δ) , (γ−2)(γ 2 δ−γ 2 +4γ−4) √ 23(N 1+N 2∗δ− N 3+N 4∗δ+N 5∗δ 2 ) , N 6+N 7∗δ √ γ ∈ (0, 3 − 1]; √ γ ∈ ( 3 − 1, 1). where N 1 = −8 + 4 γ + 10γ 2 − 9γ 3 + 2γ 4 ; N 2 = 8 − 4γ − 6γ 2 + 5γ 3 − γ 4 ; N 3 = 16γ 2 − 32γ 3 + 24γ 4 − 8γ 5 + γ 6 ; N 4 = 16γ 3 − 12γ 4 + 16γ 5 − 10γ 6 + 2γ 7 ; N 5 = 16γ 3 − 12γ 4 − 8γ 5 + 13γ 6 − 6γ 7 + γ 8 ; N 6 = −4 + 7γ 2 − 5γ 3 + γ ; N 7 = 4 − 3γ 2 + γ 3 . 2 3 As defined before. we refer to NR, PM, and TP Model because OP model is easier to sustain monopoly price than NR model given δ = 0.9, thus we will not discuss it any more. 4.2 Comparison Analysis 34 T-Period Model:  √   f or γ ∈ (0, 3 − 1],     46(γ−1)(−4+4γ−γ 2 −4γδ+γ 2 δ+4δ t+1 )  ; (γ−2)(−4+4γ−γ 2 +γ 2 δ+4δ t+1 −4γδt+1) c P = √   f or γ ∈ ( 3 − 1, 1),   √    M 1+M 2∗δ+M 3∗δt+1 − −(M 1+M 2∗δ+M 3∗δt+1 )−4(M 4+M 5∗δ+M 6∗δt+1 )(M 7+M 8∗δ+M 9∗δt+1 ) . 2(M 7+M 8∗δ+M 9∗δ t+1 ) where M 1 = 368 − 184γ − 460γ 2 + 414γ 3 − 92γ 4 ; M 2 = −368 + 184γ + 276γ 2 − 230γ 3 + 46γ 4 ; M 3 = 184γ 2 − 184γ 3 + 40γ 4 ; M 4 = 8464 − 8464γ − 6348γ 2 + 8464γ 3 − 2116γ 4 ; M 5 = −8464 + 8464γ + 4232γ 2 − 6348γ 3 + 2116γ 4 ; M 6 = 2116γ 2 − 2116γ 3 ; M 7 = 4 − 7γ 2 + 5γ 3 − γ 4 ; M 8 = −4 + 3γ 2 − γ 3 ; M 9 = 4γ 2 − 4γ 3 + γ 4 . Price Matching Model: Pc = 46(γ − 1) 2 − (1 + δ)γ (4.4) As mentioned before, we run the non-linear regressions with aggregate data and collusive data separately(see table ).In table 4.2, the columns of PM, NR and TP refer to the estimation of aggregate data, while those of PM(a), NR(a) and TP(a) refer to the estimation of collusive data, which is composed of 1,700 observations. With respect to the aggregate data, the estimation results, δ N R = 0.502, δ T P = 0.78, δ P M = 0.869, reveal that price matching model is comparatively the best model to explain the aggregate data according to AIC value, and the estimation of price matching model is closest to the actual discount rate used in experiment. As for the collusive data, we could draw the same conclusion as the aggregate data. However, the estimation of δ = 0.927 for price matching model differs from that of aggregate data larger than other models,and it is around the actual value. Hence, 4.2 Comparison Analysis 35 the collusive price is tracking the price matching model, and the estimation for Nash Reversion is around 0.5, which is far away from the actual discount rate, thus Nash Reversion punishment rule is not realistic in practice. Parameter Delta PM(a† ) PM Estimate AIC Estimate AIC 0.869 15313.39 0.927 10446.14 (PM Model) Parameter Delta NR(a† ) NR Estimate AIC Estimate AIC 0.502 16434.60 0.534 11470.92 (NR Model) Parameter Delta TP(a† ) TP Estimate AIC Estimate AIC 0.78 18815.38 0.843 13972.71 (TP Model) a† represents the collusive data. Table 4.2: Estimate δ of the Theoretical Models With the estimation of δ for collusive data above, we compute the equations for each model and draw the graph together with the average collusive price(see figure 4.2(b)). It is clear that price matching model is closest to the experimental data, however, they are differed in the right tail, as γ close to 1, PM Model predicates 4.2 Comparison Analysis the price of zero , while the average collusive price is around 14 in this case, which is much higher than predication. 4.2.3 Non-parametric Analysis Based on the estimation of δ above, we first select some reasonable values of δ = 0.75, 0.8, 0.85, 0.9, and generate the prices series of theoretical models, respectively. In order to avoid autocorrelation during the comparisons of difference between experimental results and theoretical models, we pick up the data of some particular rounds(13th, 15th and 17th rounds for each treatment) instead of the aggregate data. Tables 4.3, 4.4 and 4.5 present the Wilcoxon Signed Ranks Test results of selected data, in which sub-table (a) refers to the regression for aggregate data, while sub-table (b) refers to that of collusive data. The Z Values of ”EX-NR” indicate that the both aggregate data and collusive data are significantly different with the predications of NR Model. The values in bold predicate the acceptance of hypothesis that no significant difference between measurements, such as for the aggregate data of 13th round, “EX-TP” of δ = 0.75, “EX-PM” for δ = 0.75 & 0.8; for the collusive data “EX-TP” of δ = 0.8, 0.85 & 0.9, “EX-PM” of δ = 0.85 & 0.9. It is clear that the reasonable values of δ for the models have shifted up from aggregate data to collusive data. The same property and trend happened in 15th round and 17th round. Hence, we conclude that both TP Model and PM Model with δ = 0.9 can well fit the collusive data. 36 4.2 Comparison Analysis Aggr.Data delta 13th period 37 EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 0.75 -11.738 0 -1.96 -0.05 -0.348 0.7276 0.8 -11.738 0 -3.108 0.0019 -1.391 0.1643 0.85 -11.738 0 -3.876 0.0001 -2.916 0.0035 0.9 -11.738 0 -4.42 1E-05 -4.811 1E-06 (a) Collu.Data delta 13th period EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 0.75 -10.758 0 -2.841 -0.004 -4.85 0 0.8 -10.758 0 -1.493 0.136 -3.407 0.002 0.85 -10.758 0 -0.615 0.539 -1.66 0.077 0.9 -10.758 0 -0.154 0.878 -0.279 0.78 (b) Table 4.3: Wilcoxon Signed Ranks Test for 13th period Aggr.Data delta EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 15th period 0.75 -11.832 0 -1.781 0.075 -0.408 0.683 0.8 -11.832 0 -2.907 0.004 -1.259 0.208 0.85 -11.832 0 -3.741 0 -2.718 0.007 0.9 -11.832 0 -4.263 0 -4.842 0 (a) 4.2 Comparison Analysis Collu.Data delta 38 EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 15th period 0.75 -10.856 0 -3.174 0.002 -4.889 0.36 0.8 -10.856 0 -1.814 0.07 -3.349 0.001 0.85 -10.856 0 -0.733 0.464 -2.08 0.037 0.9 -10.856 0 -0.055 0.956 -0.315 0.753 (b) Table 4.4: Wilcoxon Signed Ranks Test for 15th period Aggr.Data delta EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 17th period 0.75 -12.116 0 -3.068 0.002 -0.915 0.36 0.8 -12.116 0 -4.111 0 -2.414 0.016 0.85 -12.116 0 -4.854 0 -4.001 0 0.9 -12.116 0 -5.309 0 -5.801 0 (a) Collu.Data delta EX-NR EX-TP EX-PM Z-value Prop. Z-value Prop. Z-value Prop. 17th period 0.75 -9.546 0 -2.265 0.023 -4.208 0 0.8 -9.546 0 -1.028 0.304 -2.598 0.009 0.85 -9.546 0 -0.028 0.977 -1.225 0.221 0.9 -9.546 0 -0.562 0.563 -0.811 0.418 (b) Table 4.5: Wilcoxon Signed Ranks Test for 17th period 4.2 Comparison Analysis (a) Average price, NE price and Monopoly price (b) Compare average price with theoretical data Figure 4.2: Comparison with One Shot game and Repeated Games 39 4.2 Comparison Analysis Figure 4.3: Price Estimations for the Theoretical Models 40 Chapter 5 Conclusion In this paper, our target is to experimentally explore the relationship between product differentiation and collusive behavior. In chapter 2, we present four theoretical models and their predications with Bertrand Competition in duopoly markets, which indicate the ambiguous relationship between product differentiation and collusive behavior. After deriving the equations of collusive price as the dependent variable, gamma as the independent variable, we find out a non-monotonic relationship for NR Model, a decreasing monotonic relationship for PM and TP Model. Then the experiment was designed upon the assumptions of the theoretical models, and we chose five values of γ ∈ (0, 1) , thus resulting five treatments. Briefly, the main findings of the experimental analysis can be summarized as follows: price is decreasing as γ increases, but the collusion also increases as γ becomes bigger, which indicates that sellers may achieve more collusion on lower prices as products converge to homogenous. Furthermore, regarding the comparison with three theoretical modes, we clarify that price matching model best explains the experimental data. There are several directions for future research by relaxing some of the restrictions in our models and experimental design, or by exploring the experimental data 41 42 in some other ways. First, instead of price competition, future research can also study on the framework of Cournot competition. Second, in our experimental design, the γ value for each treatment is T1=5/22, T2=9/22, T3=21/22, T4=17/22, T5=13/22, this sequence should have some influence on the posting prices of subjects since the learning effect shall increase as time goes by, which will definitely shift the price up. Hence, another possible extension is to figure out some ways to minimally control the learning effect. Finally, in the analysis of experimental data, we don’t consider the option of non-linear regression of price on γ, which maybe another way to test our hypothesis. Bibliography [1] Abreu, D. 1986, ”Extremal Equilibria of Oligopolistic Supergames”, Journal of Economic Theory 39, 191-225. [2] Abreu, D.,1988, ”On the Theory of Infinitely Repeated Games with Discounting”, Econometrica, 56: 383-396. [3] Albaek, S. and L. 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[27] Ross, T.W., 1992, ”Cartel Stability and Product Differentiation”, International Journal of Industrial Organization, 10: 1-13. [28] Rothschild, R., 1992, ”On the Sustainability of Collusion in Differentiated Duopolies”, Economics Letters, 40, pp.33-7. [29] Selten, R., and Stoecker, R., 1986, ”End behavior in finite prisoner’s dilemma supergames”, Journal of Economic Behavior and Organization, 7, 47-70. [30] Singh, N. and X. Vives , 1937. ”Price and Quantity Competition in a Differentiated Duopoly”, Rand Journal of Economics, 15: 546-554. [31] Slade, 1989, ”Price Wars in Price-Setting Supergames”, Economica, 56: 295-310. [32] Standford.W, 1986, ”Subgame-perfect reaction-function equilibria in discounted duopoly supergames are trivial”, Journal of Economic Theory, 39: 226-232. [33] Tirole J., 1992, ”The Theory of Industrial Organization”, MIT Press: Cambridge, MA. [34] Tyagi, R. K., 1999, ”A Characterization of Retailer Response to Manufacturer Trade Deals”, Journal of Marketing Research, 36, 510-516. 46 Bibliography [35] Wellford, C.P., 2002, ”Antitrust: results from the laboratory”, in Experiments Investigating Market Power, ed, by R.M. Isaac, and C.A.Holt, pp. 1-215. JIA Elsevier, Amsterdam. [36] Urs Fischbacher, 2007, z-Tree: Zurich Toolbox for Ready-made Economic Experiments, Experimental Economics 10(2), 171-178. 47 Appendix A Instruction and Test(EN) A.1 Instruction Welcome to this economics experiment. The participation fee is 10, and you will be privately paid at the end of the experiment together with you your accumulated payoffs. Please note that any communication among participants is strictly forbidden. Please raise your hands to ask any questions regarding these instructions. There are five sections in this experiment. Each period contains several periods, which are randomly determined by the computer program. In this experiment, you act as a seller. At the beginning of each section, you will be randomly matched with another subject into groups of two subjects. In each period, you have to decide the price of the only product you produce with no cost based on the payoff tables. To make decisions, you should take into account that: 1) You can choose any integer price between 1 and 25 ECU (an experimental currency unit). We call this price the posed price. 2) Your payoff depends both on your price and the other seller’s price. The table below illustrates the interaction of your price and the other seller’s price on your payoff. The first column is your price, the first row is the other seller’s 48 Instruction 49 price, and the cells show your payoff. Pay attention that the other seller in your group also endowed the same payoff table as yours, but the difference is that in his payoff table, the first column is his/her price, and the first row is your price. Thus, given a price combination, you can easily find your payoff and the other seller’s payoff. E.g., if your price is 3ECU and the other seller’s price is 5ECU, then your payoff should be 35ECU, and the other seller’s payoff should be 0; if your price is 6ECU, the other seller’s price is 3ECU, then your payoff should be 76ECU, the other seller’s payoff is 45 the other seller’s price and your payoff in this round will be shown in the next round on the screen. (Note: the payoff table below is just an example, not the real table in the experiment.) 3) The payoff Table A.1: Payoff Table(EN). table will be distributed to everyone before the start of each section and it will not change within this section. After each section ends, we will go to your cubicles to collect the payoff tables for previous section while distributing the other payoff tables for next section. There is no relation between outcomes in one section and A.2 Test 50 the payoff tables in subsequent sections. 4) Your payoff will be discounted with the discount rate of 0.9, starting from the 11th period in each section. For example, your final payoff for the 11th period is the corresponding payoff in the table multiplied my 0.9; your final payoff for round 12 is the corresponding payoff in the table multiplied by 0.92 your final payoff for 20th period is the corresponding payoff in the table multiplied by 0.92 . The same calculation path will be followed for other sections. 5) In this experiment, you have to input the price you choose and click ”OK” on the computer screen. The time slot for making decision of each period is one minute. Except the requirement above, please don’t execute any other commands on the computer, such as refreshing the webpage, Backspace, etc. 6) At the end of the experiment, you will receive a monetary reward with 10 participation fee plus your accumulated payoffs for the five sections exchanged at a rate of 500 ECUs for 1. If you have any questions about the instruction above, please raise your hand. Otherwise, I would like to show the main WebPages to you. Please look at the projector screen. A.2 Test 1. Look at the payoff table below and find the right answer. 1)If your price is 6, the other seller’s price is 7, thus your payoff is ; 2)If your price is 8, the other seller’s price is 5, thus the other seller’s payoff is ; 3) If your price is 4, the other seller’s price is 9, thus your payoff is ; 4) If your price is 5, the other seller’s price is 4, thus the other seller’s payoff is Instruction 51 . 2. In period 14, your payoff should be . a. the payoff corresponding to the table; b. the payoff in the table multiplied by 0.9; c. the payoff in the table multiplied by 0.93 ; d. the payoff in the table multiplied by 0.94 . Table A.2: Payoff Table for Test(EN). Appendix B Instruction and Test (CN) B.1 Instruction 你现在参加的是一个有真实货币报酬的经济学实验，本次实验是通过计算机局 域网进行的。实验结束后，我们将根据你在整个实验过程中所获得的总点数按 照500点=1.00元人民币的比例现场支付给你现金。报酬的高低取决于你在实验中 所做的决策。此外，每位实验参加人还将另外得到10元人民币的出场费。请不要 相互交流，以下是实验说明，请大家仔细阅读，如对实验说明和要求不理解的 地方请举手向实验主持人示意。 本实验共进行5局，计为S1, S2, S3, S4, S5，每局内部，又分为n个时段，每局的 时段数是随机决定的。在每局开始之前，计算机程序将自动对你们进行随机分 组，每组两人。 在本实验中你（实验参加人）是一个厂商，生产成本为零。你的决策是为你生 产的产品选择定价，以获得收益。你小组中的另一人与你一样，也是一个厂 商，生产成本为零，他也要为自己的产品作出定价。你们面临同一市场。你们 各自获得收益取决于你的定价和对方的定价。在决策过程中，你要注意以下具 体规则： 1. 你可以在1-25个数中选择你产品的定价，称之为报价，报价必须是整数； 52 B.1 Instruction 2. 你的收益取决于你的报价和对方的报价，如下表（价格-收益表）所示，第一 列是你的报价，第一行是对方的报价，表格中其他的数字就是你的收益。对方 也将面对相同的表格，但是不同的是，在他的表格中，第一列是他的报价，第 一行才是你的报价。例如，如果你的报价是3，对方的报价是5，那么对应到表 中，你的收入就是35，但是对方的价格组合却是（5，3），对应到表中，对方 的收入是0；如果你的报价是6，对方的报价是3，那么对应到表中，你的收入就 是76，但是对方的价格组合是（3，6），对应到表中，他的收入就是45；如果你 的报价是2，对方的报价是4，那么对应到表中，你的收入就是23，但是对方的价 格组合是（4，2），对应到表中，他的收入就是53……当每组实验参加者分别选 择报价并点击提交之后，在电脑屏幕上每个人都会看到自己本次实验的收益以 及对方的报价。（注意：下面的价格-收入表只是个例表，实验中的价格-收入表 的报价范围是1-25，而不是1-6。） 3. 在整个实验过程中，我们将在每局开始之前发给每个人一张价格－收益表， 五局则是五张表，分别编号为1-5。每局的价格-收益表之间是没有联系的。实验 开始后，每对实验参加者在本局中，都会根据同样的表格进行决策。 53 B.2 Test 4. 我们将从每局的第11时段开始对实验参加者的收益进行折现，一直到本局结 束。也就是说，在每局的第11时段开始，实验参加者的最终收益将根据表中收益 进行折现，折现率是0.9。例如，你在第11段实验中的最终收益是表中对应的收 益乘以0.9；你在第12时段实验中的最终收益是表中对应的收益乘以0.92……一直 到本局结束。第二局到第五局亦是如此。 5. 在整个实验过程中，实验参与人需要在计算机页面上输入所选报价并点 击OK，每个时段的决策时间为1分钟。除此之外，请大家不要在键盘上点击任 何其他命令，例如”退出”，”后退”，”刷新”等。 如果对以上实验说明的解释有不理解的地方，请大家举手示意。如果没有疑 问，我来介绍一下程序界面，请大家看大屏幕。 B.2 Test 1、请对照下表，填空。 1）如果你的报价是6，对方的报价是7，那么你的收入是 ； 2）如果你的报价是9，对方的报价是5，那么对方的收入是 ； 3）如果你的报价是4，对方的报价是6，那么你的收入是 ； 4）如果你的报价是5，对方的报价是8，那么对方的收入是 。 2、你在每局第13时段的收入应该是 . A. 价格-收入表中对应的收入； B. 价格-收入表中的收入乘以0.9； C. 价格-收入表中的收入乘以0.93 ； D. 价格-收入表中的收入乘以0.94 。 54 B.2 Test 55 Appendix C Computer Screen and Payoff Table Figure C.1: Main Computer Screen 56 Payoff Table 57 AN EXPERIMENTAL STUDY OF IMPACT OF PRODUCT DIFFERENTIATION ON COLLUSIVE BEHAVIOR YU JUAN NATIONAL UNIVERSITY OF SINGAPORE 2008 [...]... that if the collusion could be sustained, the discount rate in Bertrand supergame is non monotone regarding product differentiation Chang(1990)examines the relationship between the degree of substitutability and the ability for firms to collude on price He concludes that in the Hotelling Model of product differentiation, collusion is easier to sustain as the degree of product differentiation becomes... extent of collusion Haan, Schoonbeek and Winkel (2005) reviewed a large variety of experimental literature on collusion, particularly focusing on the roles of information and communication They pointed out that as for the competition model, some researchers prefer Cournot Model, while others prefer Bertrand Model The choice of the two 19 2.1 The Role of Information and Communication competition models... firms are willing to collude at the Pareto Frontier of joint profit maximization, thus splitting the profit equally Therefore, the highest collusive price should be the monopoly price However, whether it is sustainable depends on the deviation profit and the punishment strategy of the rival As for price competition, the demand function is piecewise linear: When the prices of the two firms are sufficiently... 5 1.2 The Setup of Differentiated Product on the other hand, if they defect, the punishment may not be very severe, thus, collusion should be hard to sustain Overall, the effect of product differentiation on collusive outcome is ambiguous In a differentiated-products market, the pricing decision of a firm depends not only on its own product (quality, quantity), but also on the substitutability of its... products The marginal production cost for both firms is constant, and it is normalized to zero Each firm faces the following linear demand curve expressing the price , pi , in terms of demand quantity qi and qj : pi = α − β(qi + γqj ), i, j = 1, 2 where γ(0 < γ < 1)1 denotes the measurement of product differentiation .The smaller of γ means the higher of product differentiation In a price competition... where ”mean” is the average price for each treatment, ”Std.D” is the standard deviation From the figures, we can see that the growth of γ significantly increases the dispersion of prices among sessions, and within given sessions as well, as measured by the variance of the average price in given treatment The range of price posted in treatment 1 and 2 is restricted in the interval of [13, 24], while the. .. product differentiation However, the effect of product differentiation on price collusion is more complicated Due to the product differentiation, on one side, a firm maybe cannot take the entire market by lowering its price in an infinitesimal amount of a single period That is to say, higher degree of product differentiation reduces the benefits of defecting from a collusive agreement, thus, collusion will... case, the slight deviation will result in large increase in demand Therefore, the effect of product differentiation on the collusive behavior is far from straightforward In the subsections, we want to clarify how collusive price is affected by horizontal product differentiation in the theoretical framework 1.2 The Setup of Differentiated Product Suppose two firms are competing in the market, and selling... informed about the price their rival has chosen Specifically, there are two scenarios: one with complete information, another with incomplete information Complete information means that the profits of the payoff tables are derived from different combinations of the firm’s own price and the average rival’s price; while incomplete information indicates the profits of the payoff tables are composed of different... ∗ as the critical value of the discount factor We will try to explain relationship between collusive profit and discount factor, and furthermore, we will explore the relationship between collusive price and the degree of product differentiation Provided that pdi and qid denote the deviation price and quantity respectively, when firm i defect from the collusive agreement, while firm j insist on monopoly