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Commitment devices are powerful tools that can influence and incentivise certain behaviours by linking them to rewards or punishments. These devices are particularly useful in decision-making, as they can steer individuals towards specific…

While Nash equilibria are guaranteed to exist, they may exhibit dense support, making them difficult to understand and execute in some applications. In this paper, we study $k$-sparse commitments in games where one player is restricted to…

Multi-agent policy-gradient methods have been shown to converge locally near stable Nash equilibria. Local convergence, however, does not determine which equilibrium is reached. We study this question through basin-entry probability with…

In the digital age, resources such as open-source software and publicly accessible databases form a crucial category of digital public goods, providing extensive benefits for Internet. This paper investigates networked public goods games…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate…

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…

We study risk-sensitive multi-agent reinforcement learning under general-sum Markov games, where agents optimize the entropic risk measure of rewards with possibly diverse risk preferences. We show that using the regret naively adapted from…

In this paper, a multi-cluster game with high-order players is investigated. Different from the well-known multi-cluster games, the dynamics of players are taken into account in our problem. Due to the high-order dynamics of players,…

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff…

Human behavioural patterns exhibit selfish or competitive, as well as selfless or altruistic tendencies, both of which have demonstrable effects on human social and economic activity. In behavioural economics, such effects have…

We consider the problem of designing distribution rules to share "welfare" (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this…

In this work, we investigate a security game between an attacker and a defender, originally proposed in \cite{emadi2019security}. As is well known, the combinatorial nature of security games leads to a large cost matrix. Therefore,…

In many game-theoretic settings, agents are challenged with taking decisions against the uncertain behavior exhibited by others. Often, this uncertainty arises from multiple sources, e.g., incomplete information, limited computation,…

We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players and the noise level. In the case of…

Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple…

There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have…

In this paper we propose a Bayesian game to allocate resources. In this game, there are $c$ units of resources to be allocated to $n$ players. Agent $i$ has a demand of $V_i$ units of resources and takes action $X_i$ according to a strategy…

We study interactions with uncertainty about demand sensitivity. In our solution concept (1) firms choose seemingly-optimal strategies given the level of sophistication of their data analytics, and (2) the levels of sophistication form best…