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

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

each *i *= 1*, *2 is associated with payoffs *ψ**i *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.