488 PART • Market Structure and Competitive Strategy • game Situation in which players (participants) make strategic decisions that take into account each other’s actions and responses • payoff Value associated with a possible outcome • strategy Rule or plan of action for playing a game • optimal strategy Strategy that maximizes a player’s expected payoff for the bidders at the auction, the winner’s payoff is her consumer surplus—i.e., the value she places on the artwork less the amount she must pay A key objective of game theory is to determine the optimal strategy for each player A strategy is a rule or plan of action for playing the game For our pricesetting firms, a strategy might be: “I’ll keep my price high as long as my competitors the same, but once a competitor lowers his price, I’ll lower mine even more.” For a bidder at an auction, a strategy might be: “I’ll make a first bid of $2000 to convince the other bidders that I’m serious about winning, but I’ll drop out if other bidders push the price above $5000.” The optimal strategy for a player is the one that maximizes the expected payoff We will focus on games involving players who are rational, in the sense that they think through the consequences of their actions In essence, we are concerned with the following question: If I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behavior into account when making my decisions? In real life, of course, you may encounter competitors who are irrational, or are less capable than you of thinking through the consequences of their actions Nonetheless, a good place to start is by assuming that your competitors are just as rational and just as smart as you are.1 As we will see, taking competitors’ behavior into account is not as simple as it might seem Determining optimal strategies can be difficult, even under conditions of complete symmetry and perfect information (i.e., my competitors and I have the same cost structure and are fully informed about each others’ costs, about demand, etc.) Moreover, we will be concerned with more complex situations in which firms face different costs, different types of information, and various degrees and forms of competitive “advantage” and “disadvantage.” Noncooperative versus Cooperative Games • cooperative game Game in which participants can negotiate binding contracts that allow them to plan joint strategies • noncooperative game Game in which negotiation and enforcement of binding contracts are not possible The economic games that firms play can be either cooperative or noncooperative In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies In a noncooperative game, negotiation and enforcement of binding contracts are not possible An example of a cooperative game is the bargaining between a buyer and a seller over the price of a rug If the rug costs $100 to produce and the buyer values the rug at $200, a cooperative solution to the game is possible: An agreement to sell the rug at any price between $101 and $199 will maximize the sum of the buyer’s consumer surplus and the seller’s profit, while making both parties better off Another cooperative game would involve two firms negotiating a joint investment to develop a new technology (assuming that neither firm would have enough know-how to succeed on its own) If the firms can sign a binding contract to divide the profits from their joint investment, a cooperative outcome that makes both parties better off is possible.2 An example of a noncooperative game is a situation in which two competing firms take each other’s likely behavior into account when independently When we asked, 80 percent of our students told us that they were smarter and more capable than most of their classmates We hope that you don’t find it too much of a strain to imagine competing against people who are as smart and capable as you are Bargaining over a rug is called a constant sum game because no matter what the selling price, the sum of consumer surplus and profit will be the same Negotiating over a joint venture is a nonconstant sum game: The total profit that results from the venture will depend on the outcome of the negotiations (e.g., the resources that each firm devotes to the venture)