Related papers: On the commitment value and commitment optimal str…

We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…

In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…

Prior work has studied the computational complexity of computing optimal strategies to commit to in Stackelberg or leadership games, where a leader commits to a strategy which is observed by one or more followers. We extend this setting to…

In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…

Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these…

Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…

We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…

Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…

Two-vehicle racing is natural example of a competitive dynamic game. As with most dynamic games, there are many ways in which the underlying solution concept can be structured, resulting in different equilibrium concepts. The assumed…

We study games in which a leader makes a single commitment, and then multiple followers (each with a different utility function) respond. In particular, we study ambiguous commitment strategies in these games, in which the leader may commit…

We study best-response type learning dynamics for zero-sum polymatrix games under two information settings. The two settings are distinguished by the type of information that each player has about the game and their opponents' strategy. The…

This paper is an exposition of algorithms for finding one or all equilibria of a bimatrix game (a two-player game in strategic form) in the style of a chapter in a graduate textbook. Using labeled "best-response polytopes", we present the…

In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

We propose a new hierarchical approach to understand the complexity of the open problem of computing a Nash equilibrium in a bimatrix game. Specifically, we investigate a hierarchy of bimatrix games $(A,B)$ which results from restricting…

We develop a constrained bimatrix game framework that can be used to model many practical problems in many disciplines, including jamming in packetized wireless networks. In contrast to the widely used zero-sum framework, in bimatrix games…

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that…

We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically distributed given some hidden…

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…