# Game Theory John R. Swinton, Ph.D. Center for Economic Education

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Game Theory John R. Swinton, Ph.D. Center for Economic Education
Georgia College & State University

Game Theory Question Take from 2013 AP Free Response Section:
There are two pizza restaurants in College Town, Piecrust and LaPizza. Each company must decide whether to advertise or to not advertise. In the payoff matrix below, the first entry in each cell indicates PieCrust’s daily profit, and the second entry indicates LaPizza’s daily profit. Both firms have complete information. Lapizza Advertise Not Advertise Advertise Piecrust Not Advertise \$250, \$200 \$450, \$300 \$180, \$500 \$390, \$400 I am going to work my way through one of the more recent game theory questions asked in the AP Micro exam. While the answer itself is fairly simple, what makes it simple is an understanding of what the game theory presentation tells you. So as I work my way through the problem I will try to decode the various questions.

Game Theory Why Game Theory?
When markets are neither perfectly competitive nor monopolistic models become more complicated Agents must consider reactions to their actions (strategy) Game theory provides a framework to help study strategy First, game theory is just another tool economists use to analyze market behavior. The perfectly competitive and monopoly models have fairly straightforward implications if all of the underlying assumptions hold. But, in many markets there are not either a sufficiently large number of buyers and sellers to assume perfect competition or only one seller (or one buyer) to assume a monopoly (or monopsony). The area in between these two market structures is host to a wide array of possible types of interactions. One area of interest is that of strategic interactions. We assume agents have an objective – such as maximizing profits. We assume that they will rationally set out to achieve that objective. We also assume that they will have to interact with another agent who has similar objectives. Game theory provides a way to assess the value of different reactions individuals will have when they choose to interact in different ways.

Game Theory Elements of the game Players Lapizza Piecrust
Advertise Not Advertise Advertise Piecrust Not Advertise \$250, \$200 \$450, \$300 \$180, \$500 \$390, \$400 Elements: Every game is defined by who is a player in the game – that is who is allowed to make a decision in the game. At the introductory level it is typical to have two players in the game. But games can have many more players. It is also possible to introduce chance into the game is some results are subject to some random element. In this case “Nature” becomes a “player” in the game and represents the random element. In this problem our two players are Piecrust (which I will represent with the color green) and LaPizza (which I will represent with the color red).

LaPizza Advertise Not Advertise Advertise Piecrust Not Advertise \$250, \$200 \$450, \$300 \$180, \$500 \$390, \$400 Elements: Every game is also defined by the strategies that players may choose. Again, simple games often limit the choices to two options. But, there is no theoretical limit to the number of strategies available. The key idea is that each strategy one player chooses will have a payout associated with it that depends both on that player’s strategy and the strategy that the other player(s) chooses. Notice that in this case, if player Lapizza chooses to advertise its payout will depend on whether Piecrust chooses to advertise or not advertise. The same is try for Piecrust.

Game Theory Elements of the game Payouts
Lapizza -- \$200, \$300, \$500, or \$400 Piecrust -- \$250, \$180, \$450 or \$390 LaPizza Advertise Not Advertise Advertise Piecrust Not Advertise \$250, \$200 \$450, \$300 \$180, \$500 \$390, \$400 Elements: Every game is also defined by the strategies that players may choose. Again, simple games often limit the choices to two options. But, there is no theoretical limit to the number of strategies available. The key idea is that each strategy one player chooses will have a payout associated with it that depends both on that player’s strategy and the strategy that the other player(s) chooses. Notice that in this case, if player Lapizza chooses to advertise its payout will depend on whether Piecrust chooses to advertise or not advertise. The same is try for Piecrust.

Game Theory Elements of the game Presentation Strategic form
Extensive form LaPizza Advertise Not Advertise Advertise Piecrust Not Advertise \$250, \$200 \$450, \$300 \$180, \$500 \$390, \$400 Elements: Games can be presented in a variety of ways. The two most common are Strategic form such as the one we are working with. The other is Extensive form (following slide). The strategic form is preferable for games where both players have to move (enact their strategy) at the same time. Games like this include rock-paper-scissors. We refer to these games as simultaneous games.

Game Theory Elements of the game Presentation Strategic form
Extensive form Elements: Here is a picture of a simple extensive form game. It represents a game where players move one at a time such as tic-tac-toe. Player 1 moves first and can choose strategy up (U) or down (D). Player 2 responds with either U’ of D’ . The final node of the tree indicates the payouts that result from the various strategies.

Game Theory Types of Games Cooperative vs. Non-cooperative
Simultaneous vs. Sequential Zero Sum vs. Positive Sum Single Play vs. Repeated There are many types of games that game theorists have modeled: Cooperative (Cartel) vs. Non-cooperative (Most games) Simultaneous (rock-paper-scissors) vs. Sequential (Tic-Tac-Toe) Zero Sum (Rock-Paper-Scissors) vs. Positive Sum (Trade) Single Play vs. Repeated (Reputation) Bring up Crazy Eddie for Mike