Equilibrium in Choice of Generalized Games

Abstract

Introduced in earlier papers of these authors, the equilibrium in choice is a solution concept for noncooperative games defined in a general framework – the game in choice form. There are two leading ideas of the new definition. One is that the players’ preferences need not be explicitly represented, but earlier accepted solution concepts should be formally derived as particular cases. Secondly, the choice of a player need not be a best reply to the strategy combination of the others, if the choices of the other players are motivated for themselves and a best reply does not exist. Now the definitions are extended to cover the case of noncooperative games with restricted individual strategies. The main technical results of the paper concern the existence of the equilibrium in choice. As particular cases, known results on the existence of equilibria in some classical game models are found. Thus, our approach can be also seen as a general method for proving the existence of different solutions for noncooperative games.