Related papers: A Generalization of von Neumann's Reduction from t…

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

Zero-sum asymmetric games model decision making scenarios involving two competing players who have different information about the game being played. A particular case is that of nested information, where one (informed) player has superior…

We study the Maximum Budgeted Allocation problem, i.e., the problem of selling a set of $m$ indivisible goods to $n$ players, each with a separate budget, such that we maximize the collected revenue. Since the natural assignment LP is known…

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To…

Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the…

The Distributional Alignment Game framework provides a powerful variational perspective on Answer-Level Fine-Tuning (ALFT). However, standard algorithms for these games rely on estimating logarithmic rewards from small batches, introducing…

Incomplete cooperative games generalise the classical model of cooperative games by omitting the values of some of the coalitions. This allows to incorporate uncertainty into the model and study the underlying games as well as possible…

Probabilistic timed automata are a suitable formalism to model systems with real-time, nondeterministic and probabilistic behaviour. We study two-player zero-sum games on such automata where the objective of the game is specified as the…

Autonomous agents must often deal with conflicting requirements, such as completing tasks using the least amount of time/energy, learning multiple tasks, or dealing with multiple opponents. In the context of reinforcement learning~(RL),…

The assignment game is a classical model for profit sharing and a cornerstone of cooperative game theory. While an imputation in its core guarantees fairness among coalitions, it provides no fairness guarantee at the level of individual…

In this paper, we extend the Descent framework, which enables learning and planning in the context of two-player games with perfect information, to the framework of stochastic games. We propose two ways of doing this, the first way…

Today's multiagent systems have grown too complex to rely on centralized controllers, prompting increasing interest in the design of distributed algorithms. In this respect, game theory has emerged as a valuable tool to complement more…

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein, charges an agent for doing costly computation; the second, initiated by Neyman, does not charge for…

We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market;…

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…

This paper introduces a notion of weak solution for the coupled system of master equations in mean field games with a major player. It extends the previously introduced notion of Lipschitz solutions in mean field games. By relying on a…

Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…