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action profile approximately information proof Bayesian equilibrium bidder choose computer complete information game computer choices Consider convergence convex combination coordinatewise combination coordination game defined deviations discussed empirical distribution equilibrium is information example expected play extensive form game game G game theorist high probability incentive to unilaterally information set information-proof equilibrium instantaneous one-shot irrational action Kalai and Lehrer large games large numbers laws of large Lemma mis/matching game n game node normal form games number of players optimal outcome paper play path poet Postlewaite prior probability distribution Private Information profile of compositions proof equilibrium proportion pure strategy equilibria pure strategy Nash random rational-expectations equilibrium realized types repeated game selected actions sequential game sequential play sequential revisional form set of composition set of possible si(M signals simultaneously strategic interdependence strategy Nash equilibrium strategy profile subgame perfect equilibrium switch types and actions uniformly equicontinuous universal set vector of strategies voting zero strategic dependence