《管理經(jīng)濟學》研究生課件IPPTChap010

1、Chapter 10Game Theory: Inside OligopolyMcGraw-Hill/IrwinCopyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.Chapter OutlineOverview of games and strategic thinkingSimultaneous-move, one-shot gamesTheoryApplication of one-shot gamesInfinitely repeated gamesTheoryFactors affecting co

2、llusion in pricing gamesApplication of infinitely repeated gamesFinitely repeated gamesGames with an uncertain final periodGames with a known final period: the end-of-period problemMultistage gamesTheoryApplications of multistage games10-2Chapter OverviewIntroductionChapter 9 examined market environ

3、ments when only a few firms compete in a market, and determined that the actions of one firm will impact its rivals. As a consequence, a manager must consider the impact of her behavior on her rivals.This chapter focuses on additional manager decisions that arise in the presence of interdependence.

4、The general tool developed to analyze strategic thinking is called game theory.10-3Chapter OverviewGame Theory FrameworkGame theory is a general framework to aid decision making when agents payoffs depends on the actions taken by other players.Games consist of the following components:Players or age

5、nts who make decisions.Planned actions of players, called strategies.Payoff of players under different strategy scenarios.A description of the order of play.A description of the frequency of play or interaction.10-4Overview of Games and Strategic ThinkingOrder of Decisions in GamesSimultaneous-move

6、gameGame in which each player makes decisions without the knowledge of the other players decisions.Sequential-move gameGame in which one player makes a move after observing the other players move.10-5Overview of Games and Strategic ThinkingFrequency of Interaction in GamesOne-shot gameGame in which

7、players interact to make decisions only once.Repeated gameGame in which players interact to make decisions more than once.10-6Overview of Games and Strategic ThinkingTheoryStrategyDecision rule that describes the actions a player will take at each decision point.Normal-form gameA representation of a

8、 game indicating the players, their possible strategies, and the payoffs resulting from alternative strategies.10-7Simultaneous-Move, One-Shot GamesNormal-Form Game10-8Simultaneous-Move, One-Shot GamesPlayer APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 10Set of playersPlayer As strategiesPl

9、ayer Bs strategiesPlayer As possible payoffs from strategy “down”Player Bs possible payoffs from strategy “right”Possible StrategiesDominant strategyA strategy that results in the highest payoff to a player regardless of the opponents action.Secure strategyA strategy that guarantees the highest payo

10、ff given the worst possible scenario.Nash equilibrium strategyA condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy, given the other players strategies.10-9Simultaneous-Move, One-Shot GamesDominant Strategy10-10Simultaneous-Mov

11、e, One-Shot GamesPlayer APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 10Player A has a dominant strategy: UpPlayer B has no dominant strategyPlayer APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 10Secure StrategySimultaneous-Move, One-Shot GamesPlayer APlayer BStrategyLeftRightUp10, 2

12、015, 8Down-10 , 710, 10Player As secure strategy: Up guarantees at least a $10 payoff Player Bs secure strategy: Right guarantees at least an $8 payoffPlayer APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 10Player APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 1010-11Nash Equilibrium S

13、trategySimultaneous-Move, One-Shot GamesPlayer APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 10A Nash equilibrium results when Player As plays “Up” and Player B plays “Left”Player APlayer BStrategyLeftRightUp10, 2015, 8Down-10 , 710, 1010-12Application of One-Shot Games: Pricing Decisions Si

14、multaneous-Move, One-Shot GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -10High price-10 , 5010, 10A Nash equilibrium results when both players charge “Low price”Firm AFirm BStrategyLow priceHigh priceLow price0, 050, -10High price-10 , 5010, 10Payoffs associated with the Nash equilib

15、rium is inferior from the firms viewpoint compared to both “agreeing” to charge “High price”: hence, a dilemma.10-13Application of One-Shot Games: Coordination Decisions Simultaneous-Move, One-Shot GamesFirm AFirm BStrategy120-Volt Outlets90-Volt Outlets120-Volt Outlets$100, $100$0, $090-Volt Outlet

16、s$0 , $0$100, $100There are two Nash equilibrium outcomes associated with this game:Equilibrium strategy 1: Both players choose 120-volt outletsFirm AFirm BStrategy120-Volt Outlets90-Volt Outlets120-Volt Outlets$100, $100$0, $090-Volt Outlets$0 , $0$100, $100Equilibrium strategy 2: Both players choo

17、se 90-volt outletsFirm AFirm BStrategy120-Volt Outlets90-Volt Outlets120-Volt Outlets$100, $100$0, $090-Volt Outlets$0 , $0$100, $100Ways to coordinate on one equilibrium:1) permit player communication2) government set standard10-14Application of One-Shot Games: Monitoring EmployeesSimultaneous-Move

18、, One-Shot GamesManagerWorkerStrategyMonitorDont MonitorMonitor-1, 11, -1Dont Monitor1, -1-1, 1There are no Nash equilibrium outcomes associated with this game.Q: How should the agents play this type of game?A: Play a mixed (randomized) strategy, whereby a player randomizesover two or more available

19、 actions in order to keep rivals from being able to predict his or her actions.10-15Application of One-Shot Games: Nash BargainingSimultaneous-Move, One-Shot GamesManagementUnionStrategy05010000, 00, 500, 1005050 , 050, 50-1, -1100100, 0-1, -1-1, -1There three Nash equilibrium outcomes associated wi

20、th this game:Equilibrium strategy 1: Management chooses 100, union chooses 0Equilibrium strategy 2: Both players choose 50Equilibrium strategy 3: Management chooses 0, Union chooses 10010-16TheoryAn infinitely repeated game is a game that is played over and over again forever, and in which players r

21、eceive payoffs during each play of the game.Disconnect between current decisions and future payoffs suggest that payoffs must be appropriately discounted.Infinitely Repeated Games10-17Present Value Analysis ReviewInfinitely Repeated Games10-18Supporting Collusion with Trigger StrategiesInfinitely Re

22、peated GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -40High price-40 , 5010, 10The Nash equilibrium to the one-shot, simultaneous-move pricing game is: Low, LowWhen this game is repeatedly played, it is possible for firms to collude without fear of being cheated on using trigger stra

23、tegies.Trigger strategy: strategy that is contingent on the past play of agame and in which some particular past action “triggers” a differentaction by a player.10-19Supporting Collusion with Trigger StrategiesInfinitely Repeated GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -40High p

24、rice-40 , 5010, 10Trigger strategy example: Both firms charge the high price, providedneither of us has ever “cheated” in the past (charge low price). If one firm cheats by charging the low price, the other player will punish the deviator by charging the low price forever after.When both firms adopt

25、 such a trigger strategy, there are conditionsunder which neither firm has an incentive to cheat on the collusive outcome.10-20Trigger Strategy Conditions to Support Collusion10-21Infinitely Repeated GamesSupporting Collusion with Trigger Strategies10-22Infinitely Repeated GamesFirm AFirm BStrategyL

26、ow priceHigh priceLow price0, 050, -40High price-40 , 5010, 10Suppose firm A and B repeatedly play the game above, and the interest rate is 40 percent. Firms agree to charge a high price in each period, provided neither has cheated in the past.Q: What are firm As profits if it cheats on the collusiv

27、e agreement?A: If firm B lives up to the collusive agreement but firm A cheats,firm A will earn $50 today and zero forever after.Supporting Collusion with Trigger Strategies10-23Infinitely Repeated GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -40High price-40 , 5010, 10Q: What are fi

28、rm As profits if it does not cheat on the collusive agreement?Supporting Collusion with Trigger Strategies10-24Infinitely Repeated GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -40High price-40 , 5010, 10Q: Does an equilibrium result where the firms charge the high pricein each period

29、?Factors Affecting Collusion in Pricing Games10-25Infinitely Repeated GamesSustaining collusion via trigger strategies is easier when firms know:who their rivals are, so they know whom to punish, if needed.who their rivals customers are, so they can “steal” those customers with lower prices.when the

30、ir rivals deviate, so they know when to begin punishment.be able to successfully punish rival.Factors Affecting Collusion in Pricing GamesInfinitely Repeated GamesNumber of firms in the marketFirm sizeHistory of the marketPunishment mechanisms10-26TheoryFinitely Repeated GamesFinitely repeated games

31、 are games in which a one-shot game is repeated a finite number of times.Variations of finitely repeated games: games in which playersdo not know when the game will end;know when the game will end.10-27Games with Uncertain Final PeriodFinitely Repeated GamesFirm AFirm BStrategyLow priceHigh priceLow

32、 price0, 050, -40High price-40 , 5010, 10An uncertain final period mirrors the analysis of infinitely repeated games. Use the same trigger strategy.No incentive to cheat on the collusive outcome associated with a finitely repeated game with an unknown end point above, provided:10-28Repeated Games wi

33、th a Known Final Period: End-of-Period ProblemFinitely Repeated GamesFirm AFirm BStrategyLow priceHigh priceLow price0, 050, -40High price-40 , 5010, 10When this game is repeated some known, finite number of timesand there is only one Nash equilibrium, then collusion cannot work.The only equilibrium

34、 is the single-shot, simultaneous-move Nashequilibrium; in the game above, both firms charge low price.10-29TheoryMultistage GamesMultistage games differ from the previously examined games by examining the timing of decisions in games.Players make sequential, rather than simultaneous, decisions.Repr

35、esented by an extensive-form game.Extensive form gameA representation of a game that summarizes the players, the information available to them at each stage, the strategies available to them, the sequence of moves, and the payoffs resulting from alternative strategies.10-30Theory: Sequential-Move Ga

36、me in Extension FormMultistage GamesBBAUpUpUpDownDownDownDecision node denoting the beginning of the gamePlayer Bs decision nodesPlayer A payoff Player B payoff Player A feasible strategies:Player B feasible strategies:UpDownUp, if player A plays Down and Down, if player A plays DownUp, if player A

37、plays Up and Down, if player A plays Up10-31Equilibrium CharacterizationMultistage GamesBBAUpUpUpDownDownDownNash Equilibrium Player A: Down Player B: Down, if player A chooses Up, and Down if Player A chooses DownIs this Nash equilibrium reasonable? No! Player Bs strategy involves a non-credible threat since if A plays Up, Bs best response is Up