Related papers: The Replicator Dynamic, Chain Components and the R…
In this paper we characterise the long-run behaviour of the replicator dynamic in zero-sum games (symmetric or non-symmetric). Specifically, we prove that every zero-sum game possesses a unique global replicator attractor, which we then…
Characterizing the limit behavior -- that is, the attractors -- of learning dynamics is one of the most fundamental open questions in game theory. In recent work on this front, it was conjectured that the attractors of the replicator…
The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a…
In this paper we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc…
Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when…
We propose a simple model of network co-evolution in a game-dynamical system of interacting agents that play repeated games with their neighbors, and adapt their behaviors and network links based on the outcome of those games. The…
A partial differential equation is derived, describing the replicator dynamics with mutations of games with a continuous strategy space. This equation is then applied to continuous versions of symmetric 2x2 games, such as the Prisoners…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Replicator dynamics, the continuous-time analogue of Multiplicative Weights Updates, is the main dynamic in evolutionary game theory. In simple evolutionary zero-sum games, such as Rock-Paper-Scissors, replicator dynamic is periodic…
An important feature of a dynamic game is its monitoring structure namely, what the players effectively see from the played actions. We consider games with arbitrary monitoring structures. One of the purposes of this paper is to know to…
Recently, a new model extending the standard replicator equation to a finite set of players connected on an arbitrary graph was developed in evolutionary game dynamics. The players are interpreted as subpopulations of multipopulations…
Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals…
Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms…
We study the convergence properties of a payoff-based higher-order version of replicator dynamics, a widely studied model in evolutionary dynamics and game-theoretic learning, in contractive games. Recent work has introduced a…
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…
A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes…
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of…
A growing number of machine learning architectures, such as Generative Adversarial Networks, rely on the design of games which implement a desired functionality via a Nash equilibrium. In practice these games have an implicit complexity…
Replicator equation -- a paradigm equation in evolutionary game dynamics -- mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the…
The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator…