Related papers: ZERO: Playing Mathematical Programming Games

Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…

Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency…

Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…

We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…

We describe an efficient algorithm to compute solutions for the general two-player Blotto game on n battlefields with heterogeneous values. While explicit constructions for such solutions have been limited to specific, largely symmetric or…

The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig (1951) is known to be incomplete. We explain and combine classical…

Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In this…

We investigate a repeated two-player zero-sum game setting where the column player is also a designer of the system, and has full control on the design of the payoff matrix. In addition, the row player uses a no-regret algorithm to…

A core novelty of Alpha Zero is the interleaving of tree search and deep learning, which has proven very successful in board games like Chess, Shogi and Go. These games have a discrete action space. However, many real-world reinforcement…

We propose a new General Game Playing (GGP) system called Regular Games (RG). The main goal of RG is to be both computationally efficient and convenient for game design. The system consists of several languages. The core component is a…

In this paper, we address the problem of a two-player linear quadratic differential game with incomplete information, a scenario commonly encountered in multi-agent control, human-robot interaction (HRI), and approximation methods for…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

Card games are widely used to study sequential decision-making under uncertainty, with real-world analogues in negotiation, finance, and cybersecurity. These games typically fall into three categories based on the flow of control: strictly…

The focus of this paper is a Bayesian framework for solving a class of problems termed multi-agent inverse reinforcement learning (MIRL). Compared to the well-known inverse reinforcement learning (IRL) problem, MIRL is formalized in the…

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious…

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined by hybrid dynamical equations. The game consists of a min-max problem involving a cost functional that depends on the actions and resulting solutions…

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zero-sum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many…

Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no…

Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum…

As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as…