Maximin Strategies Maximin Strategies-Strategy that maximizes the minimum gain that can be earned Firm 2 Don't invest Invest Don't invest 0,0 -10,10 Firm 1 Invest -100,0 20,10
0, 0 -10, 10 -100, 0 20, 10 Firm 2 Firm 1 Don’t invest Invest Don’t invest Invest Maximin Strategies Maximin Strategies — Strategy that maximizes the minimum gain that can be earned
If both firms used maximin strategies the outcome would be that Firm 1 does not invest and Firm 2 does. Suppose that Firm 1 thinks that there is only a 10-percent chance that Firm 2 will not invest. In that case,Firm 1's expected payoff from investing is 0.1×(-100)+0.9×(20)=8 Its expected payoff if it doesn't invest is 0.1×(0)+0.9×(-10)=-9. In this case,firm 1 should invest
If both firms used maximin strategies the outcome would be that Firm 1 does not invest and Firm 2 does. Suppose that Firm 1 thinks that there is only a 10-percent chance that Firm 2 will not invest. In that case, Firm 1’s expected payoff from investing is 0.1×(-100) + 0.9 ×(20) = 8 Its expected payoff if it doesn’t invest is 0.1×(0) + 0.9 ×(-10) = -9. In this case, firm 1 should invest
Suppose Firm 1 thinks that there is a 30-percent chance that Firm 2 will not invest.In this case,Firm 1's expected payoff from investing is 0.3×(-100)+0.7×(20)=-16 Its expected payoff if it doesn't invest is 0.3×(0)+0.7X(-10)=-7. In this case,firm 1 will choose not to invest
Suppose Firm 1 thinks that there is a 30-percent chance that Firm 2 will not invest. In this case, Firm 1’s expected payoff from investing is 0.3×(-100) + 0.7 ×(20) = -16 Its expected payoff if it doesn’t invest is 0.3×(0) + 0.7 ×(-10) = -7. In this case, firm 1 will choose not to invest
Prisoners'Dilemma Prisoner B Confess Don't confess Confess -5,-5 -1,-10 Prisoner A Don't confess -10,-1 -2,-2
-5, -5 -1, -10 -10, -1 -2, -2 Prisoner B Prisoner A Confess Don’t confess Confess Don’t confess Prisoners’ Dilemma
13.4 Repeated Games Repeated game-Game in which actions are taken and payoffs received over and over again. Tit-for-tat strategy -Repeated-game strategy in which a player responds in kind to an opponent's previous play, cooperating with cooperative opponents and retaliating against uncooperative ones
13.4 Repeated Games Repeated game - Game in which actions are taken and payoffs received over and over again. Tit-for-tat strategy - Repeated-game strategy in which a player responds in kind to an opponent’s previous play, cooperating with cooperative opponents and retaliating against uncooperative ones