We consider nonzero-sum semi-Markov games with a countable state space and compact metric action spaces. We assume that the payoff, mean holding time and transition probability functions are continuous on the action spaces. The main results concern the existence of Nash equilibria for nonzero-sum discounted semi-Markov games and a class of ergodic semi-Markov games with the expected average payoff criterion.
We give a formalization of the ?knowledge games? which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the ?common knowledge? in these games may be incomputable,...
Noncooperative games with systems governed by nonlinear differential equations remain, in general, nonconvex even if continuously extended (i. e. relaxed) in terms of Young measures. However, if the individual payoff functionals are “enough” uniformly convex and the controlled system is only “slightly” nonlinear, then the relaxed game enjoys a globally convex structure, which guarantees existence of its Nash equilibria as well as existence of approximate Nash equilibria (in a suitable sense) for...
En este artículo revisamos los conceptos de equilibrio perfecto y propio para juegos en forma normal y obtenemos un refinamiento del equilibrio perfecto.
En este trabajo introducimos la extensión generalizada de un jungo n-personal finito en forma normal y, en dicho contexto, damos un concepto de equilibrio y algunos refinamientos estables de él. Se indican casos particulares de notable interés.
This review paper gives a characterization of non-coalitional zero-sum and non-zero-sum games with finite strategy spaces and payoff functions having some concavity or convexity properties. The characterization is given in terms of the existence of two-point Nash equilibria, that is, equilibria consisting of mixed strategies with spectra consisting of at most two pure strategies. The structure of such simple equilibria is discussed in various cases. In particular, many of the results discussed can...
A special class of generalized Nash equilibrium problems is studied. Both variational and quasi-variational inequalities are used to derive some results concerning the structure of the sets of equilibria. These results are applied to the Cournot oligopoly problem.