Abstract: Since in a noncooperative game the players are not allowed to make commitments, any solution should be self-enforcing i.e. once it is agreed upon, nobody is interested to deviate. The Nash equilibrium (equilibrium point) is the most important solution concept of the noncooperative game theory and it is defined in terms of the normal form of a game, as a strategy combination with the property that no player can gain by unilaterally deviating from it. In the original definition of J.F.Nash, the players options were expressed by utility functions de.ned on the product of the individual strategy spaces, and the most significant existence results refer to this formalization. Later, the original definition was extended to cover more general situations met in the noncooperative competitions. This is the case of the equilibrium of abstract economies (Shafer and Sonnenschein, where the individual preferences are represented as correspondences. Particularly, such correspondences can be derived from the normal form of a game, but as primary elements of the model they generalize the earlier representations of individual preferences. Motivated by the problem of the implementation in noncooperative solutions of the voting operators, a new concept of equilibrium, called Nash equilibrium in choice form, has been introduced (Stefanescu and Ferrara). Rephrased in terms of game strategies and renamed as equilibrium in choice, this concept is discussed in the present paper. The formal framework for the definition of equilibria in choice is the game in choice form, represented as the family of the sets of individual strategies and a choice profile. Intuitively, a choice profile speci.es the desirable outputs of each player, and since each output of the game is associated to a game strategy, it can be represented as a collection of subsets of the set of all game strategies. Particularly, when the players options are represented by utility functions or by preference relations, a choice profile may be the family of the graphs of players best reply mappings, and then the set of equilibria in choice coincides with the set of Nash equilibria. So that, the definition of the equilibrium in choice captures the main idea of the "best reply" from the definition of the Nash equilibrium, but the new concept is more general, responding to various representations of the players options. Two variants of this concept are proposed here. The basic one presumes a relaxation of the best reply principle and has obvious counterparts for classical solutions, if this relaxation is accepted. The stronger form of the equilibrium in choice can be considered as a generic notion of noncooperative solution and several usual versions of such solutions are produced when the choice profile is designed indifferent particular ways.

Brief Biography of the Speaker:
Massimiliano Ferrara is Professor of Mathematical Economics at "Mediterranea" University of Reggio Calabria where he was also Dean of the degree in Economics. Actually he is the Director of Culture, Education, Research and University Department at Regione Calabria. He was the Founder and Director of MEDAlics and Vice Rector at "Dante Alighieri" University of Reggio Calabria. He was also Visiting Professor at Harvard University, Cambridge (USA), Morgan State University in Baltimore (USA), Western Michigan University (USA), New Jersey Institute of Technology in Newark (NJ) (USA). He was a speaker at several WSEAS international conferences. He is editor of several international journals: Advances in Management and Applied Economics (AMAE), African Journal of Science, Technology, Innovation and Development Applied Sciences (APPS), International Journal of Functional Analysis, Operator Theory and Applications (IJFAOTA), Far East Journal of Mathematical Sciences (FJMS), Journal of Indian Academy of Mathematics (Jiam), Journal of the Calcutta Mathematical Society and Universal Journal of Mathematics and Mathematical Sciences. His main research interests are: dynamical systems, patterns of growth and sustainable development, mathematical economics, game theory, optimization theory, applied Economics.