(a) In a repeated game, show that if for each player there is a subgame-perfect equilibrium where…

(a) In a repeated game, show that if for each player there is a subgame-perfect equilibrium where that player's payoff is his minmax value, then any payoff of a Nash equilibrium is also the payoff of a subgame-perfect equilibrium.

(b) Suppose that, for each player i and each  Show that the sets of Nash-equilibrium and perfect-equilibrium payoffs are identical for sufficiently large discount factors. Give an economic example where the condition is plausible, and an example where it is not. Show that the sets can differ for small discount factors.

(c) Suppose that the minmax profile is in pure strategies, that the vector where all players simultaneously receive their minmax payoff is in the interior of the feasible set, and that for each player i there is an di such that  Show that the sets of Nash-equilibrium and perfect-equilibrium payoffs are identical for large enough discount factors. Give an example of a game where the feasible set has full dimension yet the in-feriority condition used here does not apply. (Answers are given in Fuden-berg and Maskin 1990b.)