Related papers: Bridging the Gap Between Single and Multi Objectiv…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

Behavioral diversity, expert imitation, fairness, safety goals and others give rise to preferences in sequential decision making domains that do not decompose additively across time. We introduce the class of convex Markov games that allow…

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…

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…

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…

Training multi-agent systems (MAS) to achieve realistic equilibria gives us a useful tool to understand and model real-world systems. We consider a general sum partially observable Markov game where agents of different types share a single…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

The 2-spin Ising model in statistical mechanics and the 2x2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no…

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…

We present new data structures for representing symmetric normal-form games. These data structures are optimized for efficiently computing the expected utility of each unilateral pure-strategy deviation from a symmetric mixed-strategy…

Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable…

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…

We consider a system of single- or double integrator agents playing a generalized Nash game over a network, in a partial-information scenario. We address the generalized Nash equilibrium seeking problem by designing a fully-distributed…

Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…

We formulate a general framework for competitive gradient-based learning that encompasses a wide breadth of multi-agent learning algorithms, and analyze the limiting behavior of competitive gradient-based learning algorithms using dynamical…

Multiagent learning settings are inherently more difficult than single-agent learning because each agent interacts with other simultaneously learning agents in a shared environment. An effective approach in multiagent reinforcement learning…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…

We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…