(epsilon,k) Equilibria and Well-posedness

The aim of this paper is to discuss a new concept of well-posedness for non cooperative games. Starting from the definition of (e,k)- equilibrium as the point where every player either guarantees at least ''k'' or he (she) does not lose more than ''e'', we introduce an original definition of well-posedness. We study characterizations of this well-posedness and its relations with the more known Tikhonov well-posedness. We prove that this well-posedness is an ordinal property if the payoff functions are bounded from below

An ordinal well posedness property

The aim of this paper is to give, for Nash equilibria, a well posedness criterion in the form of an ordinal property. This property is im- portant for games because it captures the case when players' decisions depend on preferences and not on a special choice of an utility function. The ordinal characteristics of this well posedness criterion comes from considering value bounded approximate equilibria

\u2019\u2019 Value bounded approximations for Nash equilibria\u2019\u2019

The aim of this contribution is to give a well posedness property wich is ordinal

Potential games and well posedness properties

The aim of this paper is to study Potential Games which are a special class of games; in fact their properties are dictated by a single function called the potential function. We consider Tihkonov well-posedness and other well posedness properties introduced by the authors in previous papers. We relate these properties with the Tihkonov well posedness of the potential function as maximum problem

Stackelberg Well-posedness and Hierarchical Potential Games

The aim of this paper is to study Potential Games which are a special class of games; in fact their properties are dictated by a single function called the potential function. We consider Tihkonov well-posedness and Stackelberg well-posedness of these games, the latter in both the optimistic and pessimistic cases

On Tikhonov well-posedness of concave games and Cournot oligopoly

The purpose of this paper is to investigate whether theorems known to guarantee the existence and uniqueness for Nash equilibria, provide also sufficient conditions for the Tikhonov well-posedness. We have considered several hypotheses that ensure existence and uniqueness of a Nash equilibrium These assumptions imply existence and uniqueness of a Nash equilibrium but not all assure the well posedness property. We use the oligopoly Cournot model to apply the obtained resuls

A New Approach to Tikhonov Well-Posedness for Nash Equilibria

It is suggested a new approach to Tihkonov well-posedness for Nash equilibria. The novelty of our approach consists in a suitable definition of what could be considered an approximate solution for a Nash equilibrium problem. Furthermore it can be proved that this property of well-posedness is preserved under monotonic trasformation of the payoffs: a relevant result for economic interpretation