Generic finiteness of equilibrium distributions for bimatrix outcome game forms

We provide sufficient and necessary conditions for the generic finiteness of the number of distributions on outcomes, induced by the completely mixed Nash equilibria associated to a bimatrix outcome game form. These equivalent conditions are stated in terms of the ranks of two matrices constructed from the original game form.The first author acknowledges that this work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-1827. The second author acknowledges financial support from the Ministerio Economía y Competitividad (Spain), grant ECO2016-75992-P, MDM 2014-0431, and Comunidad de Madrid, MadEco-CM (S2015/HUM-3444). The third author acknowledges support from the Spanish Ministerio de Economía y Competitividad under project ECO2015-66803-P and from the Danish Council for Independent Research|Social Sciences (Grant-id: DFFD 1327-00097)

On the generic finiteness of outcome distributions for bimatrix game forms

We provide an example of an outcome game form with two players for which there is in an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induce a continuum of outcome distributions. The case for three or more players has been settled by Govindan and McLennan [3]

On the generic finiteness of equilibrium outcome distributions in bimatrix game forms

We provide an example of an outcome game form with two players for which there is an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induces a continuum of outcome distributions.Publicad

On the generic finiteness of outcome distributions for bimatrix game forms

We provide an example of an outcome game form with two players for which there is in an open set of utilities for both players such that, in each of the associated games, the set of Nash equilibria induce a continuum of outcome distributions. The case for three or more players has been settled by Govindan and McLennan [3].

Generic Finiteness of Outcome Distributions for Two Person Game Forms with Three Outcomes

Generic finiteness; game forms; Nash equilibrium

Generic finiteness of equilibrium payoffs for bimatrix games

It is shown that in any affine space of payoff matrices the equilibrium payoffs of bimatrix games are generically finite.Bimatrix Games, Generic Finiteness

Determinacy of equilibrium outcome distributions for zero sum and common utility games

We show the generic finiteness of probability distributions induced on outcomes by the Nash equilibria in two player zero sum and common interest outcome games.We thank an anonymous referee for his/her insightful comments. The authors acknowledge financial support from project No. ECO2010-19596 from the Spanish Ministry of Science and Innovation. Cristian Litan also acknowledges financial support by CNCSIS-UEFISCSU, project number PN II-RU 415/2010.Publicad

How proper is the dominance-solvable outcome?

We examine the conditions under which iterative elimination of weakly dominated strategies refines the set of proper outcomes of a normal-form game. We say that the proper inclusion holds in terms of outcome if the set of outcomes of all proper equilibria in the reduced game is included in the set of all proper outcomes of the original game. We show by examples that neither dominance solvability nor the transference of decision-maker indifference condition (TDI of Marx and Swinkels [1997]) implies proper inclusion. When both dominance solvablility and the TDI condition are satisfied, a positive result arises: the game has a unique stable outcome. Hence, the proper inclusion is guaranteed

Generic Determinacy of Nash Equilibrium in Network Formation Games

This paper shows that the set of probability distributions over networks induced by Nash equilibria of the network formation game proposed by Myerson (1991) is finite for a generic assignment of payoffs to networks. The same result can be extended to several variations of the game found in the literature.Networks; generic finiteness; Nash Equilibrium