Generic finiteness of outcome distributions for two-person game forms with three outcomes

A two-person game form is given by nonempty finite sets S1, S2 of pure strategies, a nonempty set [Omega] of outcomes, and a function [theta]:S1xS2-->[Delta]([Omega]), where [Delta]([Omega]) is the set of probability measures on [Omega]. We prove that if the set of outcomes contains just three elements, generically, there are finitely many distributions on [Omega] induced by Nash equilibria.

[1]  Robert Wilson,et al.  Direct proofs of generic finiteness of nash equilibrium outcomes , 2001 .

[2]  J. Mertens,et al.  ON THE STRATEGIC STABILITY OF EQUILIBRIA , 1986 .

[3]  Generic finiteness of equilibrium payoffs for bimatrix games , 2010 .

[4]  A. McLennan,et al.  On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms , 2001 .

[5]  J. Harsanyi.  Oddness of the number of equilibrium points: A new proof , 1973 .

[6]  Francesco De Sinopoli,et al.  Costly network formation and regular equilibria , 2010, Games Econ. Behav..

[7]  Francesco De Sinopoli,et al.  Undominated (and) perfect equilibria in Poisson games , 2009, Games Econ. Behav..

[8]  In-Uck Park.  Generic Finiteness of Equilibrium Outcome Distributions for Sender–Receiver Cheap-Talk Games , 1993 .

[9]  Giovanna Iannantuoni,et al.  On the generic strategic stability of Nash equilibria if voting is costly , 2003 .

[10]  Nikolai S. Kukushkin,et al.  On the generic finiteness of equilibrium outcome distributions in bimatrix game forms , 2008, J. Econ. Theory.

[11]  Gérard Debreu.  Economies with a Finite Set of Equilibria , 1970 .

[12]  Carlos Pimienta.  Generic determinacy of Nash equilibrium in network-formation games , 2009, Games Econ. Behav..

[13]  Lawrence E. Blume,et al.  The Algebraic Geometry of Perfect and Sequential Equilibrium , 1994 .

[14]  Francesco De Sinopoli,et al.  On the Generic Finiteness of Equilibrium Outcomes in Plurality Games , 2001, Games Econ. Behav..