O teorii strategických her
On a game of Sierpiński
On a modified game of Sierpiński
On a new solution concept for bargaining problems
The purpose of this paper is to discuss the properties of a new solution of the 2-person bargaining problem as formulated by Nash, the so-called Average Pay-off solution. This solution of a very simple form has a natural interpretation based on the center of gravity of the feasible set, and it is "more sensitive" to changes of feasible sets than any other standard bargaining solution. It satisfies the standard axioms: Pareto-Optimality, Symmetry, Scale Invariance, Continuity and Twisting. Moreover,...
On game ideals
On optimal play in the game of Hex.
On polyhedral games
On smoothing of parametric minimax-functions and generalized max-functions via regularization.
On the best choice of a damping sequence in iterative optimization methods.
Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.
On the optimal strategy in a random game.
On totally bounded games
On two-point Nash equilibria in bimatrix games with convexity properties
This paper considers bimatrix games with matrices having concavity properties. The games described by such payoff matrices well approximate two-person non-zero-sum games on the unit square, with payoff functions F₁(x,y) concave in x for each y, and/or F₂(x,y) concave in y for each x. For these games it is shown that there are Nash equilibria in players' strategies with supports consisting of at most two points. Also a simple search procedure for such Nash equilibria is given.
On ɛ-optimal strategies in discounted Markov games