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
(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.