On bargaining in games
On Bellman systems without zero order term in the context of risk sensitive differential games
Bellman systems corresponding to stochastic differential games arising from a cost functional which models risk aspects are considered. Here it leads to diagonal elliptic systems without zero order term so that no simple -estimate is available.
On best proximity pair theorems and fixed-point theorems.
On Bilevel Variational Inequalities Arising in the Analysis of Improper Optimization Problems
On convex combinations of two values
We study values for cooperative TU-games which are convex combinations of the Shapley value and the solidarity value, introduced in our recent paper [1]. First, we axiomatize the convex combination of the two values in the case when the coefficients are given exogenously. Next, we give an axiomatic description of the whole family of such values.
On cooperative games connected with markets
On determining sets for the class of somewhat continuous functions
On existence of equilibrium pair for constrained generalized games.
On game ideals
On games of Topsoe.
On Generalized Bellman 's Functional Equation.
On generalized games in -spaces
We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in -spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.
On heuristic optimization.
On knowledge games.
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,...
On Nash theorem
On Nonadaptive Search Problem
2000 Mathematics Subject Classification: 91A46, 91A35.We consider nonadaptive search problem for an unknown element x from the set A = {1, 2, 3, . . . , 2^n}, n ≥ 3. For fixed integer S the questions are of the form: Does x belong to a subset B of A, where the sum of the elements of B is equal to S? We wish to find all integers S for which nonadaptive search with n questions finds x. We continue our investigation from [4] and solve the last remaining case n = 2^k , k ≥ 2.
On noncooperative nonlinear differential games
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...
On one algorithm finding all bimatrix game equilibria
On optimal play in the game of Hex.
On order locally finite and closure-preserving covers