Related papers: Equilibria of Replicator Dynamics in Quantum Games

In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…

The quasi-static evolution of steady states far from equilibrium is investigated from the point of view of quantum statistical mechanics. As a concrete example of a thermodynamic system, a two-level quantum dot coupled to several reservoirs…

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and…

Evolutionary game theory assumes that players replicate a highly scored player's strategy through genetic inheritance. However, when learning occurs culturally, it is often difficult to recognize someone's strategy just by observing the…

In this paper we address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric (or bimatrix) replicator equations, and some…

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…

We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…

In the Eisert protocol for 2 X 2 quantum games [Phys. Rev. Lett. 83, 3077], a number of authors have investigated the features arising from making the strategic space a two-parameter subset of single qubit unitary operators. We argue that…

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been…

Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\sigma^2I$. The…

Various formulations of counterfactual general equilibrium in economies -- systems of actors manipulating economic goods -- are logically and mathematically analyzed. Evenly-rotating economies are systems whose evolution is stable, steady,…

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some…

We consider three distinct discrete-time models of learning and evolution in games: a biological model based on intra-species selective pressure, the dynamics induced by pairwise proportional imitation, and the exponential / multiplicative…

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…

The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for…

Understanding the evolution of human social systems requires flexible formalisms for the emergence of institutions. Although game theory is normally used to model interactions individually, larger spaces of games can be helpful for modeling…

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of…

We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…