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##### Game Theory

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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**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**Game Theory**• Elements of the game • Players • Lapizza • Piecrust LaPizza AdvertiseNot Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• Elements of the game • Strategies • Advertise • Not Advertise LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**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**Game Theory**• Elements of the game • Presentation • Strategic form • Extensive form LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• Elements of the game • Presentation • Strategic form • Extensive form**Game Theory**• Types of Games • Cooperative vs. Non-cooperative • Simultaneous vs. Sequential • Zero Sum vs. Positive Sum • Single Play vs. Repeated**Game Theory**• (a) What strategy should PieCrust choose if LaPizza chooses to advertise? Explain using the dollar value in the payoff matrix. • Payout for Advertise = $250 • Payout for Not Advertise = $180 LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• (b) What is the dominant strategy, if any, for LaPizza? Explain using the dollar values in the payoff matrix. • None for LaPizza • Advertise for Piecrust LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• (c) In the Nash equilibrium, determine each of the following. • i. PieCrust’s daily profit • ii. LaPizza’s daily profit LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• (c) In the Nash equilibrium, determine each of the following. • i. PieCrust’s daily profit • ii. LaPizza’s daily profit LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise**Game Theory**• (d) Suppose that advertising costs increase by $60 per day. Redraw the payoff matrix to reflect the effort of the higher advertising costs. LaPizza Advertise Not Advertise • Advertise • Piecrust • Not Advertise