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Full-Text Articles in Social and Behavioral Sciences
Classification Of Two-Person Ordinal Bimatrix Games, Imre Bárány, Jon Lee, Martin Shubik
Classification Of Two-Person Ordinal Bimatrix Games, Imre Bárány, Jon Lee, Martin Shubik
Cowles Foundation Discussion Papers
The set of possible outcomes of a strongly ordinal bimatrix game is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto optimal sets of each cardinality; we establish asymptotic bounds for the number of different convex hulls of the point sets, for the average shape of the set of points dominated by the Pareto optimal set, and for the average shape of the convex hull of the point set. We also indicate the effect of individual rationality considerations on our results. As most …
A Bound Of The Proportion Of Pure Strategy Equilibria In Generic Games, Faruk Gul, David G. Pearce, Ennio Stacchetti
A Bound Of The Proportion Of Pure Strategy Equilibria In Generic Games, Faruk Gul, David G. Pearce, Ennio Stacchetti
Cowles Foundation Discussion Papers
In a generic finite normal form game with 2(α) + 1 Nash equilibria, at least alpha of the equilibria are nondegenerate mixed strategy equilibria (that is, they involve randomization by some players).
-Person Game And Endogenous Coalition Formation, Lin Zhou
-Person Game And Endogenous Coalition Formation, Lin Zhou
Cowles Foundation Discussion Papers
The two most fundamental questions in cooperative game theory are: When a game is played, what coalitions will be formed and what payoff vectors will be chosen? No previous solution concepts or theories in the literature provide satisfactory answers to both questions; answers are especially lacking for the first one. In this paper we introduce the refined bargaining set, which is the first solution concept in cooperative game theory that simultaneously provides answers to both of the fundamental questions.