Consider the stage game given by the following payoff table:

Suppose 1, so that the game is of the same kind as the prisoner’s

dilemma given in Table 8.1. Now consider the game of incomplete information

R(W(ψ)i=1,2, η) where, for some given and ε, the “alternative reputation” for

each = 12 is associated with payoffs ψthat display the following features:

_ If, at any given period, the opponent has not played before, it is a dominant

strategy to play then.

_ If, at any given period, the opponent has played sometime in the past,

the stage payoffs are given by the above payoff table.

(a) Let η = 0.1 and = 2Determine some parameter configuration for and

such that there exists a sequential equilibrium where the normal type of

either player is indifferent between playing or in the first period of

the game.

(b) Fix the values of and determined in (a) and suppose η = 0.01Determine

some value of for which the normal type of either player decides

to play in the first period at some sequential equilibrium.