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...

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...

Using the formalism of quantum theory we prove that the von Neumann entropy satisfies the conditions of the von Neumann--Morgenstern utility. We extend the entropy observable using the ensemble of statistical physics to derive a number of important functional relationships. The ensemble is then...

At each moment in time, some alternative from a finite set is selected by a dynamic process. Players observe the alternative selected and sequentially cast a yes or a no vote. If the set of players casting a yes-vote is decisive for the alternative in question, the alternative is accepted and...

Stochastic games offer a rich mathematical structure that makes it possible to analyze situations with heterogeneous and interacting economic agents. Depending on the actions of the economic agents, the economic environment changes from one period to another. We focus on stationary equilibrium,...

This paper presents a simple Ramsey-type model example where two infinitely-living agents have same utility function except for time preference, and shows that equilibrium is indeterminate that is to be interpreted as being non-existent. The issues regarding New Keynesian transversality...

This paper presents a complete survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection theories. We present all...

We study games with almost perfect information and an infinite time horizon. In such games, at each stage, the players simultaneously choose actions from finite action sets, knowing the actions chosen at all previous stages. The payoff of each player is a function of all actions chosen during...

In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously degenerated system, when only one agent is involved. The...

Generalization of the minority game to more than one market is considered. At each time step every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of utility then market occupancies become inhomogeneous...