Related papers: Le Chatelier principle in replicator dynamics
We analyze the robustness of (pure strategy) Nash equilibria for network games against perturbations of the players' utility functions. We first derive a simple characterization of the margin of robustness, defined as the minimum magnitude…
This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the payoff function of each player depends on an aggregate of all players' actions. We present a distributed continuous time algorithm such that…
Fudenberg and Harris' stochastic version of the classical replicator dynamics is considered. The behavior of this diffusion process in the presence of an evolutionarily stable strategy is investigated. Moreover, extinction of dominated…
In a society of multiple individuals, if everybody is only interested in maximizing his own payoff, will there exist any equilibrium for the society? John Nash proved more than 50 years ago that an equilibrium always exists such that nobody…
For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither…
We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a…
We study the evolutionary stability of Nash equilibria (NE) in a symmetric quantum game played by the recently proposed scheme of applying `identity' and `Pauli spin flip' operators on the initial state with classical probabilities. We show…
In this study, we analyse the global stability of the equilibrium in a departure time choice problem using a game-theoretic approach that deals with atomic users. We first formulate the departure time choice problem as a strategic game in…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…
The Nash equilibrium paradigm, and Rational Choice Theory in general, rely on agents acting independently from each other. This note shows how this assumption is crucial in the definition of Rational Choice Theory. It explains how a…
Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in…
We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary…
This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…
We analyze the stability of a nonlinear dynamical model describing the noncooperative strategic interactions among the agents of a finite collection of populations. Each agent selects one strategy at a time and revises it repeatedly…
Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement…
The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed…
Evolutionary dynamics experienced by mixed microbial populations of cooperators and cheaters has been examined in experiments in the literature using a protocol of periodic dilution to investigate the properties of resilience and…
In this paper, we discuss the fitness landscape evolution of permanent replicator systems using a hypothesis that the specific time of evolutionary adaptation of the system parameters is much slower than the time of internal evolutionary…
For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this…
Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…