MicroEconomics 5e by besanko braeutigam chapter 14

Chapter 14 Game Theory and Strategic Behavior Chapter Fourteen Overview 1.Motivation: Honda and Toyota 3.Nash Equilibrium 5.The Prisoner's Dilemma 6.Dominant Strategy Equilibrium 7.Limitations of the Nash Equilibrium 8.Sequential Moves Games • The Value of Limiting One’s Opinion Chapter Fourteen Capacity Expansion Game What is the likely outcome of this game? Toyota Honda Chapter Fourteen Capacity Expansion Game Game Elements Players: 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) Chapter Fourteen Capacity Expansion Game Information: 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) Chapter Fourteen Nash Equilibrium Definition: 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 selfinterest") Toyota vs Honda: A Nash equilibrium: Each Firm Builds a New Plant Chapter Fourteen Nash Equilibrium Why? • 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 Chapter Fourteen Prisoner's Dilemma Definition: 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 Ron Chapter Fourteen Other Considerations Nash Equilibrium: both confess Pareto Dominant Point: Neither confesses Definition: 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 Chapter Fourteen Dominant Strategy Equilibrium Definition: A Dominant Strategy Equilibrium occurs when each player uses a dominant strategy Toyota Honda Chapter Fourteen Dominated Strategy Definition: 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 Toyota Honda Chapter Fourteen Dominant or Dominated Strategy Why look for dominant or dominated strategies? A dominant strategy equilibrium is particularly compelling as a "likely" outcome Similarly, 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 Chapter Fourteen Dominated Strategy Game Matrix 4: Dominated Strategies Toyota Honda "Build Large" is dominated for each player By eliminating the dominated strategies, we can reduce the game to matrix #1! Chapter Fourteen Nash Equilibrium Limitations Game Matrix 4: Dominated Strategies Limitations of Nash Equilibrium The Nash Equilibrium need not be unique Slick Luke Chapter Fourteen Nash Equilibrium Limitations In the above example, Nash Equilibriums: (Swerve, Stay) and (Stay, Swerve) Now, compare to the following case: Sirius XM Chapter Fourteen Nash Equilibrium Limitations Example: Bank Runs Depositor Depositor Chapter Fourteen Nash Equilibrium Limitations Nash Equilibrium need not exist Example: Matching Pennies Game Matrix 6: Non-existence of Nash Equilibrium Player Heads Tails Heads 1,-1 -1,1 Tails -1,1 1,-1 Chapter Fourteen Mixed Strategies Pure 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 Chapter Fourteen Repeated Prisoner’s Dilemma Cooperation 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 to your opponent in this period what your opponent did to you in the last period Chapter Fourteen Repeated Prisoner’s Dilemma Likelihood of cooperation increases under these conditions: 1.The players are patient 2.Interactions between the players are frequent 3.Cheating is easy to detect 4.The one-time gain from cheating is relatively small Likelihood of cooperation diminishes under these conditions: 5.The players are impatient 6.Interactions between the players are infrequent 7.Cheating is hard to detect 8.The one-time gain from cheating is large in comparison to the eventual cost of cheating Chapter Fourteen Sequential Move Games Games 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 Chapter Fourteen Sequential Move Games - Terms A 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 Chapter Fourteen Sequential Move Games – Game Tree Game Tree 1: Toyota and Honda, Revisited Chapter Fourteen Sequential Move Games – Game Tree Game 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 flexibility Example: Industry Irreversibility of Business Decisions in the Airline Chapter Fourteen Summary 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 competitors 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 The Nash Equilibrium may be a good predictor when it coincides with the Dominant Strategy Equilibrium When there are multiple Nash Equilibriums, we must appeal to other concepts to choose the "likely" outcome of the game 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 Chapter Fourteen ... first player Chapter Fourteen Sequential Move Games – Game Tree Game Tree 1: Toyota and Honda, Revisited Chapter Fourteen Sequential Move Games – Game Tree Game trees often are solved by starting... (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) Chapter Fourteen Capacity... Equilibrium) Chapter Fourteen Nash Equilibrium Definition: A Nash Equilibrium occurs when each player chooses a strategy that gives him/her the highest payoff, given the strategy chosen by the other