Chapter 14 - Game theory and strategic behavior. This chapter presents the following content: Motivation: Honda and Toyota, nash equilibrium, the prisoner''s dilemma, dominant strategy equilibrium, limitations of the nash equilibrium, sequential moves games.
ld Large 0,0 12,8 18,9 Build Small 8,12 16,16 20,15 Do Not Build 15,20 18,18 Build Large 9,18 "Build Large" is dominated for each player By eliminating the dominated strategies, we can reduce the game to matrix #1! Chapter Fourteen 13 Copyright (c)2014 John Game Matrix 4: Dominated Strategies Toyota Nash Equilibrium Limitations Game Matrix 4: Dominated Strategies Limitations of Nash Equilibrium The Nash Equilibrium need not be unique Luke Swerve Stay Swerve 0,0 10,10 Stay 10,10 100,100 Copyright (c)2014 John Slick Chapter Fourteen 14 Nash Equilibrium Limitations In the above example, Nash Equilibriums: (Swerve, Stay) and (Stay, Swerve) Now, compare to the following case: Sirius Stay Exit Stay 200, 200 300,0 Exit 0,300 Copyright (c)2014 John XM 0,0 Chapter Fourteen 15 Nash Equilibrium Limitations Example: Bank Runs Depositor Depositor Don't Withdraw Withdraw 25,25 50,0 Don't Withdraw 0,50 110,110 Copyright (c)2014 John Withdraw Chapter Fourteen 16 Nash Equilibrium Limitations Nash Equilibrium need not exist Example: Matching Pennies Game Matrix 6: Non-existence of Nash Equilibrium Heads Tails Heads 1,1 1,1 Tails 1,1 1,1 Chapter Fourteen Copyright (c)2014 John Player 17 Mixed Strategies Mixed Strategy – A choice among two or more pure strategies according to prespecified probabilities Chapter Fourteen 18 Copyright (c)2014 John Pure Strategy – A specific choice of a strategy from the player’s possible strategies in a game Repeated Prisoner’s Dilemma “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 19 Copyright (c)2014 John Cooperation can result from self-interested behavior on the part of each player under certain circumstances: Repeated Prisoner’s Dilemma Likelihood 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 Chapter Fourteen 20 Copyright (c)2014 John Sequential Move Games Chapter Fourteen Copyright (c)2014 John 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 21 Sequential Move Games - Terms Backward induction is a procedure for solving a sequentialmove 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 22 Copyright (c)2014 John A game tree shows the different strategies that each player can follow in the game and the order in which those strategies get chosen Sequential Move Games – Game Tree Copyright (c)2014 John Game Tree 1: Toyota and Honda, Revisited Chapter Fourteen 23 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 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 24 Copyright (c)2014 John Keeps analysis manageable Ensures optimality at each point Summary 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 Chapter Fourteen 25 commitment Copyright (c)2014 John 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 ... The one-time gain from cheating is large in comparison to the eventual cost of cheating Chapter Fourteen 20 Copyright (c)2 014 John Sequential Move Games Chapter Fourteen Copyright (c)2 014 John... 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 19 Copyright (c)2 014 John Cooperation... Tails 1,1 1,1 Chapter Fourteen Copyright (c)2 014 John Player 17 Mixed Strategies Mixed Strategy – A choice among two or more pure strategies according to prespecified probabilities Chapter Fourteen