Question

5. (General Extensive Form Game IID Suppose the following general extensive-form game. Note that denotes the belief that the player 2's decision node after Player 1 chooses Ais reached. Player 1 (2, 2) Player 2 a, 0) (3, 1 (a) Find the conditions on parameter values (a and b) such that (B,X) witlh 0 is the perfect Bayesian equilibrium, if any (b) Find the conditions on parameter values (a and b) such that (C,Y) is the strategy profile of the perfect Bayesian equilibrium, if any. Find also the value of u in this perfect Bayesian equilibrium

Answer 1

The connected doted line of player 2's two nodes shows that this is a simultaneous move game

a) So,

b <1, because if b=1, then Player 2 will be indifference to the choice, he will randomly select between X and Y to maximize payout because expected pay off of that node will be same and if b>1 expected pay off will be higher.

a's value won;t be restricted because if the payoff of that node is zero Player 2's belief to select that node will be 0.

b)

a<=3, in this case expected pay off of Player 1 will be 2 or less than 2

b>=2, so that Player 2 always have higher expected pay off on choosing Y

u will be 0.33, if all three decisions are taken into account, if two nodes of Player 2 are taken then u=0.5

Simplified pay off matrix

		Player 2
		X	Y
Player 1	A	a,0	1,b
	B	3,1	1,0
	C	2,2	2,2