Related papers: Replicator Equation: Applications Revisited
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
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…
Adaptive dynamics describes a deterministic approximation of the evolution of scalar- and function-valued traits. Applying it to the team game developed by Menden-Deuer and Rowlett [Menden-Deuer & Rowlett 2019], we constructed an…
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…
Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is…
Although learning has found wide application in multi-agent systems, its effects on the temporal evolution of a system are far from understood. This paper focuses on the dynamics of Q-learning in large-scale multi-agent systems modeled as…
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…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
The emergence of complex networks from evolutionary games is studied occurring when agents are allowed to switch interaction partners. For this purpose a coevolutionary iterated Prisoner's Dilemma game is defined on a random network with…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the new approach, individuals have different heritable strategies,…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…
Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products,…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture…
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider symmetric two-player games with two…
We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…
In this paper, we investigate the learnability of the function approximator that approximates Nash equilibrium (NE) for games generated from a distribution. First, we offer a generalization bound using the Probably Approximately Correct…