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We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…
In this paper we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information. We start from a continuous-time gradient-play dynamics that converges to an NE…
We study generalized games with full row rank equality constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of 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…
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…
Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
We study network games in which players choose both the partners with whom they associate and an action level (e.g., effort) that creates spillovers for those partners. We introduce a framework and two solution concepts, extending standard…
In this paper, we show the equivalence between a constrained, multi-agent control problem, modeled within the port-Hamiltonian framework, and an exact potential game. Specifically, critical distance-based constraints determine a network of…
We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players'…
Coordination games describe social or economic interactions in which the adoption of a common strategy has a higher payoff. They are classically used to model the spread of conventions, behaviors, and technologies in societies. Here we…
Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…
We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to…
Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
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…
In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition…