Consider a repeated game in which the stage game above is re

Consider a repeated game in which the stage game above is repeated twice and there is no discounting. The maximum payoff a player can achieve in a SPNE of the repeated game is _________ (Please, enter a numerical value like: -1, 0, 0.5, 3.5, 4, etc)  

please explain answer

Player lI 6,6 2,7 2,-2 Player B 7,-4 -2,-2 1,-1 C 2,-2 1,1 1,1

Solution

The answer is one. The reason is starting with player 1,he will choose B because that gives him payoff of 7 but player 2 will get F in response to lower his loss( - 1 is greater than - 2,-4).in 2nd round given the choice of F by player 2,player 1 will choose C OR B with equal probability because payoff 1 is highest possible given choice of player 2.In response B will choose C because it provides highest payoff of 1(compared to - 2,-1). Thus CF will be SPNE. Thus Answer is 1. Note by backward induction same conclusion can be reached