There are two individuals playing repeatedly the game whose payoffs are as specified in Table 11.3. Player ’s admissible strategies _consist of the countable set {γi1, γi2, γi3, . . .} ∪ {γi∞} where each γik (∈ N) is interpreted as follows:


“Switch irreversibly to Bi at kprovided the opponent has not switched to Bj before; in the latter case, remain playing Ai for ever.” and γi∞ is interpreted as

“Never choose Bi .” Let βo stand for the initial beliefs of player over ’s strategy, with βo

Iq (= 12, . . . . ,∞) indicating the subjective probability associated with each γjq . Further assume that βo iq 0 for each and every = 23, . . . ,.Within the theoretical framework proposed in Subsection 11.4.3, answer the following questions.

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(a) Does the setup described satisfy (GT)?

(b) Argue that, if (EPM) holds, some player switches to Bi at some t.

(c) Specify conditions on βo i guaranteeing that both players switch to Bi at

= 1.

(d) Assume that (EPM) holds. Does the process converge to Nash play for the repeated game? and for the stage game? Relate your answer to (a) and Theorem 11.8.