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We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in…
We study the game modification problem, where a benevolent game designer or a malevolent adversary modifies the reward function of a zero-sum Markov game so that a target deterministic or stochastic policy profile becomes the unique Markov…
The generalization of the problem of adaptive competition, known as the minority game, to the case of $K$ possible choices for each player is addressed, and applied to a system of interacting perceptrons with input and output units of the…
Learning in stochastic games is a notoriously difficult problem because, in addition to each other's strategic decisions, the players must also contend with the fact that the game itself evolves over time, possibly in a very complicated…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
We study first-order methods (FOMs) for solving \emph{composite nonconvex nonsmooth} optimization with linear constraints. Recently, the lower complexity bounds of FOMs on finding an ($\varepsilon,\varepsilon$)-KKT point of the considered…
We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a…
We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and…
Autonomous vehicles must balance ranked objectives, such as minimizing travel time, ensuring safety, and coordinating with traffic. Games of ordered preference effectively model these interactions but become computationally intractable as…
We study the computation of Nash equilibria in a two-player normal form game from the perspective of parameterized complexity. Recent results proved hardness for a number of variants, when parameterized by the support size. We complement…
Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…
In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a…
This paper investigates online stochastic aggregative games subject to local set constraints and time-varying coupled inequality constraints, where each player possesses a time-varying expectation-valued cost function relying on not only…
In noncooperative Nash games, equilibria are often inefficient. This is exemplified by the Prisoner's Dilemma and was first provably shown in the 1980s. Since then, understanding the quality of Nash equilibrium (NE) received considerable…
We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions. We show that the canonical utility maximisation is one special case of a quantifier and that our more…
We study Nash equilibria learning of a general-sum stochastic game with an unknown transition probability density function. Agents take actions at the current environment state and their joint action influences the transition of the…
We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow…
We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…
Reinforcement learning from human feedback (RLHF) has become essential for improving language model capabilities, but traditional approaches rely on the assumption that human preferences follow a transitive Bradley-Terry model. This…
In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used,…