Consider the stage game W given by the following payoff table:

Suppose b > a > 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

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

each i = 1, 2 is associated with payoffs ψi that display the following features:

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

strategy to play C then.

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

the stage payoffs are given by the above payoff table.

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

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

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

the game.

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

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

to play C in the first period at some sequential equilibrium.