In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player...

We show that the playing sequence-the order in which players update their actions-is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random...

We show that the playing sequence-the order in which players update their actions-is a crucial determinant of whether the best-response dynamic converges to a Nash equilibrium. Specifically, we analyze the probability that the best-response dynamic converges to a pure Nash equilibrium in random...

ROC curves from the signal detection literature are used in an evolutionary analysis of one-shot and repeated prisoners' dilemmas: showing if there is any discounting of future payoffs, or any cost of searching for an additional partner, then cooperative players who contingently participate - in...

ROC curves from the signal detection literature are used in an evolutionary analysis of one-shot and repeated prisoners' dilemmas: showing if there is any discounting of future payoffs, or any cost of searching for an additional partner, then cooperative players who contingently participate - in...

We develop topological analysis of social-network effect on game equilibrium in the context of two- player asymmetric normal-form games and also in evolutionary sense. Firstly, it is confirmed that the game equilibrium in many social networks cannot be established through that in a well-mixed...

It is well known that an upper semi-continuous compact- and convex-valued mapping fi from a nonempty compact and convex set X to the Euclidean space of which X is a subset has at least one stationary point, being a point in X at which the image fi(x) has a nonempty intersection with the normal...

In this paper the well-known minimax theorems of Wald, Ville and Von Neumann are generalized under weaker topological conditions on the payoff function f and/or extended to the larger set of the Borel probability measures instead of the set of mixed strategies.

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In this paper we present two general results on the existence of a discrete zero point of a function from the n-dimensional integer lattice Zn to the n-dimensional Euclidean space Rn. Under two different boundary conditions, we give a constructive proof using a combinatorial argument based on a...