? E XERCISE 275.1 (Expected payoffs in a variant of BoS with imperfect information) Construct…

? EXERCISE 275.1 (Expected payoffs in a variant of BoS with imperfect information) Construct tables like the one in Figure 276.1 for type n1 of player 1, and for types y2 and n2  of player 2.

I claim that ((B, B), (B, S)) and ((S, B), (S, S)) are Nash equilibria of the game, where in each case the first component gives the actions of the two types of player 1

(B, B)     (B, S)     (S, B)     (S, S)

B S

 

Figure 276.1 The expected payoffs of type y1 of player 1 in Example 274.2. Each row corresponds to a pair of actions for the two types of player 2; the action of type y2 is listed first, that of type n2 second.

 

 

and the second component gives the actions of the two types of player 2.    Using

Figure 276.1 you may verify that B is a best response of type y1 of player 1 to the pair (B, S) of actions of player 2, and S is a best response to the pair of actions   (S, S). You may use your answer to Exercise 275.1 to verify that in each of the claimed Nash equilibria the action of type n1 of player 1 and the action of each type of player 2 is a best response to the other players’ actions.