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handoutaps - Recursive Solution Methodology Abreu D D...

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Recursive Solution Methodology Abreu, D., D. Pearce, and E. Stacchetti (1990), “Toward a Theory of Discounted Repeated Games with Imperfect Monitoring,” Econometrica , 58, 1041-63. 1 Environment 1.1 Stage Game N player stage game denoted G. Each player i has a f nite strategy set S i and payo f function Π i : S R where S = S 1 × ... × S N . For q S, Π i ( q ) is an expected value. Realization or payo f actually received is stochastic and denoted π i ( p, q i ) depending on realization of random variable P which takes values p . Distribution of P given by Ψ ( · ; q ) . Realized payo f s π i depend on q i =( q 1 , ..., q i 1 ,q i +1 , ..., q N ) only through their e f ect on only Ψ . Π i ( q )= R π i ( p, q i ) Ψ ( dp ; q ) . 1.2 Repeated Game G ( δ )denotesthein f nitely repeated game with stage game G and dis- count factor δ (0 , 1) . Let p t and q t denote t period signal and action histories. Information Structure: Players can observe (and therefore condition on) only their own past actions q t i and past realizations of

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