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Handbook of Game Theory by Shmuel Zamir, Petyon Young

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k=1τEP˜[1EP˜[σ2(h2t+k)(a^2)|h1T1,B]0 as t

si408_e

This implies [4.9], since convergence in probability implies subsequence a.e. convergence (Chung, 1974, Theorem 4.2.3).

Using Lemma 4.4, we next argue that on B∩F, player 1 believes that player 2 is eventually ignoring her history while best responding to α^1si409_e. In the following lemma, ε2 is from [4.6]. The set At(τ)si410_e is the set of player 2 t-period histories such that player 2 ignores the next τ signals ...

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