A.Prove that, given any stage game W, *ˆδ such that if δ ≤ ˆδ and γ is a Nash equilibrium of Rδ (W), then for every history ht−1 that has positive ex ante probability (according to γ ), γ (ht−1) = α * for some Nash equilibrium α * of W (possibly dependent on ht−1). Is this conclusion also true if ht−1 has zero ex ante probability?
B. Consider the chain-store game with an infinite horizon, as described in Section 8.4. Compute the minimum discount rate¯δ that is consistent with the fact that the (constant) strategies described in (8.10) and (8.11) define a Nash equilibrium of the repeated game. Is the lower bound ¯δ affected if those strategies are required to define a subgame-perfect equilibrium?
