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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…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…
In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or…
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…
We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…
We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…
We study a complementarity game as a systematic tool for the investigation of the interplay between individual optimization and population effects and for the comparison of different strategy and learning schemes. The game randomly pairs…
Evolutionary game theory is a mathematical toolkit to analyse the interactions that an individual agent has in a population and how the composition of strategies in this population evolves over time. While it can provide neat solutions to…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
We calculate the standard deviation of (N1-N0), the difference of the number of agents choosing between the two alternatives of the minority game. Our approach is based on two approximations: we use the whole set of possible strategies,…
Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no…
We initiate the study of game dynamics in the population protocol model: $n$ agents each maintain a current local strategy and interact in pairs uniformly at random. Upon each interaction, the agents play a two-person game and receive a…
This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemic -- is modeled as a mean-field game with health-related…
In this paper, we present a model of a game among teams. Each team consists of a homogeneous population of agents. Agents within a team are cooperative while the teams compete with other teams. The dynamics and the costs are coupled through…
We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…
The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…