Quản trị kinh doanh - Chapter 14: Game theory and strategic behavior

1Game Theory and Strategic BehaviorChapter 14Copyright (c)2014 John Wiley & Sons, Inc.2Chapter Fourteen OverviewMotivation: Honda and ToyotaNash EquilibriumThe Prisoner's DilemmaDominant Strategy EquilibriumLimitations of the Nash EquilibriumSequential Moves GamesThe Value of Limiting One’s OpinionChapter FourteenCopyright (c)2014 John Wiley & Sons, Inc.3HondaToyotaChapter FourteenCapacity Expansion GameWhat is the likely outcome of this game?Copyright (c)2014 John Wiley & Sons, Inc.4Chapter FourteenCapacity Expansion GameGame ElementsPlayers: agents participating in the game (Toyota, Honda)Strategies: Actions that each player may take under any possible circumstance (Build, Don't build)Outcomes: The various possible results of the game (four, each represented by one cell of matrix)Payoffs: The benefit that each player gets from each possible outcome of the game (the profits entered in each cell of the matrix)Copyright (c)2014 John Wiley & Sons, Inc.5Chapter FourteenCapacity Expansion GameInformation: A full specification of who knows what when (full information)Timing: Who can take what decision when and how often the game is repeated (simultaneous, one-shot)Solution concept of the game: "What is the likely outcome"? (Dominant Strategy Equilibrium, Nash Equilibrium)Copyright (c)2014 John Wiley & Sons, Inc.6Chapter FourteenNash EquilibriumDefinition: A Nash Equilibrium occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategy chosen by the other player(s) in the game. ("rational self-interest")Toyota vs. Honda: A Nash equilibrium: Each Firm Builds a New Plant Copyright (c)2014 John Wiley & Sons, Inc.7Chapter FourteenNash Equilibrium Given Toyota builds a new plant, Honda's best response is to build a new plant. Given Honda builds a new plant, Toyota's best response is to build a plant. Why is the Nash Equilibrium plausible? It IS "self enforcing” Even though it DOES NOT necessarily maximise collective interest.Why?Copyright (c)2014 John Wiley & Sons, Inc.8RonChapter FourteenPrisoner's DilemmaDefinition: A game situation in which there is a tension between the collective interest of all of the players and the self-interest of individual players is called a Prisoner's Dilemma. Copyright (c)2014 John Wiley & Sons, Inc.9Chapter FourteenOther ConsiderationsNash Equilibrium: both confess Pareto Dominant Point: Neither confessesDefinition: A dominant strategy is a strategy that is better than any other strategy that a player might choose, no matter what strategy the other player follows.Note: When a player has a dominant strategy, that strategy will be the player's Nash Equilibrium strategy.Copyright (c)2014 John Wiley & Sons, Inc.10Chapter FourteenDominant Strategy EquilibriumDefinition: A Dominant Strategy Equilibrium occurs when each player uses a dominant strategy.HondaToyotaCopyright (c)2014 John Wiley & Sons, Inc.11Chapter FourteenDominated StrategyDefinition: A player has a dominated strategy when the player has another strategy that gives it a higher payoff no matter what the other player does.HondaToyotaCopyright (c)2014 John Wiley & Sons, Inc.12Chapter FourteenDominant or Dominated StrategyWhy look for dominant or dominated strategies?A dominant strategy equilibrium is particularly compelling as a "likely" outcomeSimilarly, because dominated strategies are unlikely to be played, these strategies can be eliminated from consideration in more complex games. This can make solving the game easier.Copyright (c)2014 John Wiley & Sons, Inc.13HondaChapter FourteenDominated StrategyToyotaGame Matrix 4: Dominated Strategies "Build Large" is dominated for each playerBy eliminating the dominated strategies, we can reduce the game to matrix #1!Copyright (c)2014 John Wiley & Sons, Inc.14SlickLukeChapter FourteenNash Equilibrium LimitationsGame Matrix 4: Dominated Strategies Limitations of Nash EquilibriumThe Nash Equilibrium need not be uniqueCopyright (c)2014 John Wiley & Sons, Inc.15SiriusXMChapter FourteenIn the above example, Nash Equilibriums: (Swerve, Stay) and (Stay, Swerve). Now, compare to the following case:Nash Equilibrium LimitationsCopyright (c)2014 John Wiley & Sons, Inc.16Depositor 1Depositor 2Chapter FourteenNash Equilibrium LimitationsCopyright (c)2014 John Wiley & Sons, Inc.17Chapter FourteenNash Equilibrium need not existExample: Matching Pennies Game Matrix 6: Non-existence of Nash EquilibriumNash Equilibrium LimitationsPlayer 1Copyright (c)2014 John Wiley & Sons, Inc.18Chapter FourteenMixed StrategiesPure Strategy – A specific choice of a strategy from the player’s possible strategies in a game.Mixed Strategy – A choice among two or more pure strategies according to pre-specified probabilities.Copyright (c)2014 John Wiley & Sons, Inc.19Chapter FourteenRepeated Prisoner’s DilemmaCooperation can result from self-interested behavior on the part of each player under certain circumstances:“Grim Trigger” Strategy – one episode of cheating by one player triggers the grim prospect of a permanent breakdown in cooperation for the remainder of the game.“Tit-for-Tat” Strategy – A strategy in which you do to your opponent in this period what your opponent did to you in the last period.Copyright (c)2014 John Wiley & Sons, Inc.20Chapter FourteenRepeated Prisoner’s DilemmaLikelihood of cooperation increases under these conditions:The players are patient.Interactions between the players are frequent.Cheating is easy to detect.The one-time gain from cheating is relatively small.Likelihood of cooperation diminishes under these conditions:The players are impatient.Interactions between the players are infrequent.Cheating is hard to detect.The one-time gain from cheating is large in comparison to the eventual cost of cheating.Copyright (c)2014 John Wiley & Sons, Inc.21Chapter FourteenSequential Move GamesGames in which one player (the first mover) takes an action before another player (the second mover). The second mover observes the action taken by the first mover before deciding what action it should take.Copyright (c)2014 John Wiley & Sons, Inc.22Chapter FourteenSequential Move Games - TermsA game tree shows the different strategies that each player can follow in the game and the order in which those strategies get chosen.Backward induction is a procedure for solving a sequential-move game by starting at the end of the game tree and finding the optimal decision for the player at each decision point.Strategic moves are actions that a player takes in an early stage of a game that alter the player’s behavior and the other players’ behavior later in the game in a way that is favorable to the first player.Copyright (c)2014 John Wiley & Sons, Inc.23Chapter FourteenSequential Move Games – Game TreeCopyright (c)2014 John Wiley & Sons, Inc.24Chapter FourteenGame trees often are solved by starting at the end of the tree and, for each decision point, finding the optimal decision for the player at that point. Keeps analysis manageable. Ensures optimality at each point.The solution to the revisited game differs from that of the simultaneous game. Why – the first mover can force second mover's hand Illustrates the value of commitment (i.e. limiting one's own actions) rather than flexibilityExample: Irreversibility of Business Decisions in the Airline Industry.Sequential Move Games – Game TreeCopyright (c)2014 John Wiley & Sons, Inc.25Chapter Fourteen1. Game Theory is the branch of economics concerned with the analysis of optimal decision making when all decision makers are presumed to be rational, and each is attempting to anticipate the actions and reactions of the competitors2. A Nash Equilibrium in a game occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategies chosen by the other players in the game.3. The Nash Equilibrium may be a good predictor when it coincides with the Dominant Strategy Equilibrium.4. When there are multiple Nash Equilibriums, we must appeal to other concepts to choose the "likely" outcome of the game.5. An analysis of sequential move games reveals that moving first in a game can have strategic value if the first mover can gain from making a commitment.SummaryCopyright (c)2014 John Wiley & Sons, Inc.