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Games in Normal Form
Matrix and Bimatrix Games
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action assume assumption behavior strategy beliefs best reply bimatrix game choose completely mixed condition control costs converges Corollary deﬁned deﬁnition denotes direct ESS dynamic equilibrium concept equilibrium of F equilibrium outcome equilibrium payoff equilibrium strategy equivalent example exists expected payoff extensive form game ﬁnite ﬁtness ﬁxed point follows form game F Furthermore game of Fig game theory Harsanyi hence implies incentive to deviate inﬁnitely information set justiﬁed KM-admissible Lemma Let F matrix minmax mistake mixed strategies monopolist Nash equilibrium noncooperative normal form game optimal Pareto payoff vector perfectness concept perturbed game play probability Proof proper equilibrium pure strategy quasi-strict reduced normal form reﬁnements regular equilibrium renegotiation-proof repeated games resp satisﬁed Sect self-enforcing Selten sequential equilibrium shown shows signalling games speciﬁc stable set strategy combination strategy of player strictly perfect subgame perfect equilibrium sufﬁces symmetric symmetric equilibrium Theorem undominated unique equilibrium weakly proper zero