Web Appendix Examples, Applications and Additional Results Definition of MPE Consider a general n-person infinite-stage game, where each individual can take an action at every stage. Let the action profile of each individual be a i = a 1 i , a 2 i ,. .. for i = 1,. .. , n, with a t i ∈ A t i and a i ∈ A i = ∞ t=1 A t i. Let h t = a 1 ,. .. , a t be the history of play up to stage t (not including stage t), where a s = (a s 1 ,. .. , a s n), so h 0 is the history at the beginning of the game,

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... let H t be the set of histories h t for t : 0 ≤ t ≤ T − 1. We denote the set of all potential histories up to date t by H t = t s=0 H s. Let t-continuation action profiles be a i,t = a t i , a t+1 i ,. .. for i = 1,. .. , n, with the set of continuation action profiles for player i denoted by A i.t. Symmetrically, define t-truncated action profiles as a i,−t = a 1 i , a 2 i ,. .. , a t−1 i for i = 1,. .. , n, with the set of t-truncated action profiles for player i denoted by A i,−t. We also use the standard notation a i and a −i to denote the action profiles for player i and the action profiles of all other players (similarly, A i and A −i). The payoff functions for the players depend only on actions, i.e., player i's payoff is given by u i a 1 ,. .. , a n. A pure strategy for player i is σ i : H ∞ → A i. A t-continuation strategy for player i (corresponding to strategy σ i) specifies plays only after time t (including time t), i.e., σ i,t : H ∞ \ H t−2 → A i,t , where H ∞ \ H t−2 is the set of histories starting at time t. We then have: Definition 6 (Markovian Strategies) A continuation strategy σ i,t is Markovian if σ i,t (h t−1) = σ i,t ˜ h τ −1 1