QUESTION 5 Player Player l Player II A 111 444 B 757 163 A 3

QUESTION 5 Player Player l Player II A 1,1,-1 4,4,4 B 7,5,7 -1,6,3 A 3,3,0 3,1,7 B 1,1,8 3,1,4 Player I Player I Consider the stage game above and suppose it is repeated twice without discounting. Consider all possible SPNE in pure strategies for the twice repeated game. The highest payoff Player 1 can get in a SPNE is |. The highest payoff Player 2 can get in a SPNE is Finally, the highest payoff Player 3 can get in a SPNE is . (Please, enter only numerical answers like: 1,2, 3.)

Solution

If we consider player 3 he will have better expected payoff if he plays strategy F because Expected value of E=3.25< Expected value of F=4.75

(7+4+3-1)÷4=3.25 and (8+7+4+0)/4=4.75

And for player 1 and 2 we have 2 NE independent of what player 3 plays

Therefore Pure NE are ADE, ACF and BD

This game is repeated twice we have just to double the payoffs

Here in this game we have 3 SPNE namely ADE, ACF and BDF

Out of these SPNE we have highest payoff for player 1 in ADE that is 8(4×2)

Highest payoff for player 2 in SPNE is ADE 8 and similarly for player 3 is ADE 8