We present two new notions of evolutionary stability, the truly evolutionarily stable state (TESS) and the generalized evolutionarily stable equilibrium (GESE). The GESE generalizes the evolutionarily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts all nearby trajectories...

We introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global...

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...

We define the axioms of quantum game theory and show that classical, Nashian, game theory is a special case of quantum game theory. In our more general framework, we prove the insufficiency of the von Neumann Morgenstern utility, because it is not uniquely defined. Relating utility to the time...

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to...

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...

This chapter reviews the theory of the voluntary public and private redistribution of wealth elaborated by economic analysis in the last forty years or so. The central object of the theory is altruistic gift-giving, construed as benevolent voluntary redistribution of income or wealth. The theory...

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the...

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best-reply correspondence if it has (1) a product structure, is (2) upper hemi--continuous, (3) always includes a best-reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each...