bài giảng kinh tế vi mô tiếng anh ch14 strategy multistage game

1 Chapter 14 Strategy: Multistage Games Key issues 1. preventing entry: simultaneous decisions 2. preventing entry: sequential decisions 3. creating and using cost advantages 4. advertising Nonprice strategies: Satanism • Procter & Gamble (P&G) sued Amway and 11 of its distributors • P&G accused them of disparaging P&G products and spreading stories about Satanism at P&G in an effort to attract customers from P&G • Amway responded, claiming P&G was engaged in a false public relations campaign of its own Nonprice strategies: Hiring • Volkswagen (VW) settled with General Motors (GM) after GM accused VW of hiring one of its executives who brought with him confidential information • H J Heinz and Campbell Soup Company agreed to mediation over Heinz's attempt to hire away a Campbell executive Preventing entry: Simultaneous decisions • consider a market with either 1 or 2 firms • simultaneous entry decision: neither firm has an advantage that helps it prevent other firm from entering • sequential decision: incumbent (firm already in market) may have an advantage over firm deciding whether to enter Simultaneous decisions • initially no gas stations • physical space for at most 2 gas stations • 2 firms consider opening a gas station at a highway rest stop 2 Room for 2 firms • firms have pure (dominant) strategies: both enter • unique, pure strategy equilibrium Room for only one firm • game is similar to game of chicken • neither firm has a dominant strategy Problem with pure strategies • game has two Nash equilibria in pure strategies: • Firm 1 enters and Firm 2 does not • Firm 2 enters and Firm 1 does not • players don’t know which Nash equilibrium will result • could collude: firm that enters could pay other firm to stay out of market • these pure Nash equilibria are unappealing because identical firms use different strategies Mixed strategies • firms may use same strategies if their strategies are mixed: firm chooses between its possible actions with given probabilities • each firm enters with 50% probability • result: Nash equilibrium in mixed strategies 3 Mixed strategy equilibria • if both firms use this mixed strategy, each of four outcomes in payoff matrix equally likely • Firm 1 has • ¼ chance of earning $1 (upper-right cell) • ¼ chance of losing $1 (lower-right cell) • ½ chance of earning $0 (left cells) • thus, Firm 1's expected profit is ($1 × ¼) + (-1 × ¼) + (0 × ½) = $0 Firm 2’s response • if Firm 1 uses this mixed strategy, Firm 2 cannot do better using a pure strategy • if Firm 2 enters with certainty, it earns • $1 half time • loses $1 other half • so its expected profit is $0 • if Firm 2 stays out with certainty, Firm 2 earns $0 Nash equilibria • firms play mixed strategy • one firm plays pure strategy of entering and other firm plays pure strategy of not entering Games without pure-strategy equilibria • some games have no pure-strategy Nash equilibrium, so mixed strategies must be used • Theorem (Nash, 1950): every game with a finite number of firms and a finite number of actions has at least one Nash equilibrium, which may involve mixed strategies Preventing entry: Sequential decisions • incumbent (monopoly) firm knows potential entrant is considering entering • stage 1: incumbent decides whether to take an action to prevent entry • stage 2: potential entrant decides whether to enter, and firms choose output levels • no entry: incumbent earns monopoly profit • entry: each firm earns duopoly profit • assume potential entrant does not enter if it breaks even or loses money To act or not to act? • incumbent can act strategically to prevent other firm from entering • does it pay to take action? 4 Three possibilities 1. blockaded entry: market conditions make profitable entry impossible so no action necessary 2. deterred entry: incumbent acts to prevent an additional firm from entering because it pays 3. accommodated entry: doesn't pay for incumbent to prevent entry • incumbent does nothing to prevent entry • reduces its output (or price) from monopoly to duopoly level Two-stage game • stage 1: incumbent decides whether to pay rest stop landlord b for exclusive right to be only gas station • stage 2: if incumbent doesn't take this strategic action, potential entrant decides whether or not to enter in second stage Coke vs. Dr Pepper • Coca-Cola wanted McDonald's restaurant owners to carry its drinks exclusively • offered each franchise a payment of enough soda syrup to make from 30,000 to 90,000 drinks • Dr Pepper made a comparable counteroffer Phone companies • regional telephone companies (Baby Bells) lobbied FCC and state regulatory bodies to block potential entrants from providing local phone service • when Teleport Communications announced plans to build fiber-optic network to offer phone services in Houston, Southwestern Bell Corporation (SBC) claimed that Teleport was violating state law and demanded that Texas regulators issue a "cease and desist" order Phone (cont.) • then, when state adopted rules to promote more competition, SBC challenged in court • although federal telecommunication laws were changed to permit entry in 1996, Baby Bells were able to delay entry for years by lobbying and suing Incumbent’s decision • blockaded entry: duopoly profit is negative, Q d < 0 (entry doesn't pay) • deterred or accommodated entry: Q d > 0 (entry occurs unless incumbent acts) • incumbent can prevent entry by paying b, but it may not pay for incumbent to do so 5 Figure 14.1 Whether an Incumbent Pays to Prevent Entry Incumbent Enter Do not enter ( π m , $0) ( π m – b, $0) ( π d , π d = R – F ) Do not pay Second stageFirst stage Pay for exclusive rights (entry is impossible) Entrant ( π i , π e ) Does incumbent pay? • incumbent pays b if monopoly profit minus payment is greater than duopoly profit tQ m – b > Q d • incumbent accommodates entry if Q d > Q m - b Fixed costs and demand • entry is profitable only if Q d > 0 • duopoly profit Q d = R – F • assume firms have no variable costs • fixed cost of entering, F • firm’s revenue is R (depends on demand) Blockaded entry •if R < F, 3 d < 0, and second firm doesn't enter • not enough demand given fixed cost • still possible that 3 m > 0 • entry is blockaded only if a firm must incur a fixed cost to enter • if F = 0, then R > F, then 3 d > 0 • with F > 0 and demand so low there's room for only one firm in market: a natural monopoly Incumbent’s advantage • Because incumbent is already in market, • its fixed entry cost is sunk • so it ignores its sunk cost in deciding whether to operate • potential entrant • views fixed cost of entry as avoidable cost • incurs cost only if entry takes place Commitment and entry prevention • credible threat: rivals must believe that firm's threatened strategy is rational: it is in firm's best interest to use it to prevent entry • commitment makes a threat credible: burning bridges 6 Figure 14.2 Noncredible Threat Incumbent ($300, $300) (–$100, –$100) Cournot output Large output ( π i , π e ) Cournot vs. Stackelberg • these models illustrate role of commitment • Stackelberg model • leader chooses its output level before follower so has first-mover advantage • moving first allows leader to commit to producing a relatively large quantity, q s • Cournot model • firms choose output levels simultaneously • so no firm has an advantage over its rival • no firm can commit credibly to produce large quantity Output commitment • incumbent can commit to large quantity of output before potential entrant decides whether to enter • 3 possibilities 1. no commitment: entry occurs, Cournot equilibrium 2. commit to Stackelberg-leader quantity: entry occurs, Stackelberg equilibrium 3. commit to larger quantity: deters entry, monopoly equilibrium Commitment and fixed cost • incumbent's decision depends on potential entrant's fixed cost of entry, F • illustrate role that F plays in incumbent's decision by looking at demand and cost structure that underlie game tree: Figure 14.3 Game Trees for the Deterred Entry and Stackelberg Equilibria Incumbent Enter Do not enter (b) Entrant ’s Fixed Cost Is $16. ($900, $0) ($450, $209) Accommodate (q i = 30) Accommodate ( q i = 30) Enter Do not enter ($416, $0) ($208, $0) Deter (q i = 52) Entrant Entrant Incumbent Enter Do not enter (a) Entrant ’ s Fixed Cost Is $100. ($900, $0) ($450, $125) Enter Do not enter ($800, $0) ($400, $0) Deter ( q i = 40) Entrant Entrant (π i , π e ) 7 Figure 14.4 Cournot and Stackelberg Equilibria q e , Units per period q i , Units per per iod Entrant’s best-response curve Incumbent’s best-response curve e s e c (a) Best-Response Curves 03020 60 15 20 30 60 π i , $ per period q i , Units per per iod π i (b) Incumbent ’s Profit 03020 60 450 400 F = $0; Stackelberg equilibrium Figure 14.6 Incumbent Loss If It Deters Entry q e , Units per period q i , Units per period Entrant’s best-response curve e s (a) Entrant’s Best-Response Curve 0305260 15 30 π i , $ per period q i , Units per period π i π m π s (b) Incumbent’s Profit 0305260 416 900 450 F = $16 Creating/using cost advantages • incumbent invests to lower its MC (relative to its rivals’) in later periods to deter entry • firm with a lower MC has a larger market share and a higher profit than its higher-cost rival • incumbent with relatively low costs can price low enough to prevent rivals from entering • incumbent may benefit if it lowers its cost relative to that of its rivals (or raises its rivals' costs) Lowering MC but raising C • should monopoly buy new piece of equipment that lowers its MC but raises its total cost, C? • answer depends on whether buying equipment will prevent potential rivals from entering Monopoly manufacturing plant • currently uses many workers to pack boxes with its product • can replace workers with robotic arms that • raise the monopoly's F substantially • lowers MC cost (no longer has to hire as many workers) Should firm buy robots? • monopoly definitely buys robotic arms if labor savings large so that total cost (C) falls • even if C rises (monopoly can't sell enough units that robot arms pay for themselves), might still buy • purchasing robotic equipment is a credible commitment • increases potential entrant's expectations about incumbent's output • thus, could deter entry 8 Figure 14.7 Investment Game Tree Incumbent Enter Do not enter ($900, $0) ($400, $300) Do not invest Enter Do not enter ($500, $0) ($132, – $36) Invest Entrant Entrant ( π i , π e ) Raising rivals' costs • by raising its rivals’ variable costs relative to its own, firm may increase its own profit • firm can raise rivals’ variable costs either directly or indirectly Direct method: Interfere • interfere with production or sales of rival to raise its cost • British Airways vs. Virgin Atlantic Airways • buy up all of a rival's product during periods of heavy advertising and return it later, depriving rival of extra advertising-induced sales Direct method: Signal jamming • firm conducts marketing experiment: introduces new brand at a single location • rival firm disrupts experiment by • offering large discounts • engaging in a massive advertising campaign • or otherwise “jamming the signal” Indirect methods • incumbent lobbies for government regulation that disproportionately affects new firms • many such regulations (e.g., environmental regulations) grandfather (exempt) older firms • incumbent buys up market supplies of scarce resources to prevent rivals from using them Example alleged [in U.S vs. Aluminum Co. of America, 148 F.2d 416 (1945)] that, by certain provisions in its contracts with power companies, Alcoa prevented those companies from supplying power to any other firm for the purpose of making aluminum 9 Essential facility • resource may be an essential facility: scarce resource that rival must use to survive • railroad bridges in St. Louis • owned by group of railroads • railroads could have prevented entry by refusing rivals access to their essential facilities (bridges) • U.S. v. Terminal Railroad Association of St. Louis, 224 U.S. 383 (1912): owning group had to provide access to rival railroads on reasonable terms Preventing customers from switching • incumbent makes it difficult for customers to switch to entrant in future to discourage entry • industrial customers of Pacific Gas and Electric (PG&E) were told that they'd have to pay a fee to stop buying from PG&E Raising all firms' costs • incumbent may raise costs of all firms, including its own • incumbent wants to raise costs if its cost is sunk and potential rivals' entry costs are avoidable Strategic advantage • incumbent derives strategic advantage from its sunk-cost commitment • incumbent is willing to spend more money to keep other firms out of market than they are willing to spend to enter Figure 14.8 Raising-Costs Game Tree Incumbent Enter Do not enter ($10, $0) ($3, $3) Do not raise costs Enter Do not enter ($6, $0) ( – $1, –$1) Raise costs $4 Entrant Entrant ( π i , π e ) cost to all firm rises by $4 Advertising • advertising/promotional activities • ads in newspapers & magazines mailings • free samples • branding • placing cereals on lower shelves • one of many strategic actions firms use to boost their profits 10 Monopoly advertising • successful advertising campaign shifts market demand curve by • changing consumers' tastes • informing them about new products • if advertising convinces some consumers they can't live without product, demand curve may • shift out • become less elastic at new equilibrium • firm charges a higher price for its product Decision whether to advertise • even if advertising shifts demand, it may not pay to advertise • if demand curve shifts out or becomes less elastic, firm's gross profit (ignores cost of advertising) must rise • firm undertakes advertising campaign only if it expects net profit (= gross profit - cost of advertising) to increase Figure 14.9 Advertising Price of Coke, p c , $ per unit B Q c , Units of Coke per year 0 19 17 5 Q 2 =28 68 76Q 1 =24 MR 1 MR 2 D 2 D 1 p 2 = 12 p 1 = 11 e 2 e 1 π 1 MC = AC (unit = 10 cases) Coke example • advertising º Coke's gross profit rises over 36% • if cost of advertising is < B, its net profit rises How much to advertise • How much should a monopoly advertise in order to maximize its net profit? • level of advertising maximizes firm’s net profit if last $1 of advertising increases its gross profit by $1 O J trial effect • O J Simpson's 1995 trial for murder was broadcast by many television and radio stations • O J factor cut take from infomercials on other television stations • marginal benefit (MB) curve for infomercials shifted • estimates of average infomercial sales declines due to the Simpson trial ranged from 10% to 60% across cities [...]... heaviest smokers in the world • • Advertising in Poland • with no antismoking pressures, RJR heavily advertise to persuade Poles to switch to its brands • market researcher for RJR in Poland observes: “We are able to replace something that is very harmful [the unfiltered cigarettes with coarse tobacco and a strong aroma, which Poles currently smoke] with something that is of better quality It's obvious... differentiate its products from those of rivals (possibly spuriously) • • • 6.04% in 1981 4.33% in 1989 (it falls because market power falls) so they should advertise more to maximize profits 11 Empirical evidence • cigarette advertising is cooperative • • increases size of market doesn't change market shares substantially Strategic advertising equilibria whether advertising hurts or helps rivals affects . play mixed strategy • one firm plays pure strategy of entering and other firm plays pure strategy of not entering Games without pure -strategy equilibria • some games have no pure -strategy Nash. enter • unique, pure strategy equilibrium Room for only one firm • game is similar to game of chicken • neither firm has a dominant strategy Problem with pure strategies • game has two Nash equilibria. 1 Chapter 14 Strategy: Multistage Games Key issues 1. preventing entry: simultaneous decisions 2. preventing entry: sequential