Related papers: The GameTheory package for Macaulay2

We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem…

We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…

In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…

This paper presents an optimization framework to model Formula 1 racing dynamics, where multiple cars interact physically and strategically. Aerodynamic wake effects, trajectory optimization, and energy management are integrated by means of…

We introduce a new paradigm for game theory -- Bayesian satisfaction. This novel approach is a synthesis of the idea of Bayesian rationality introduced by Aumann, and satisfaction games. The concept of Bayesian rationality for which, in…

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…

In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best…

Quantum game theory is a new interdisciplinary field between game theory and physical research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement…

If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…

We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…

The Nash equilibrium paradigm, and Rational Choice Theory in general, rely on agents acting independently from each other. This note shows how this assumption is crucial in the definition of Rational Choice Theory. It explains how a…

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of…

This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…

The paper studies properties of functional dependencies between strategies of players in Nash equilibria of multi-player strategic games. The main focus is on the properties of functional dependencies in the context of a fixed dependency…

We consider $\epsilon$-equilibria notions for constant value of $\epsilon$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that…

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person…

This paper provides a tutorial overview of game theoretic techniques used for communication over frequency selective interference channels. We discuss both competitive and cooperative techniques. Keywords: Game theory, competitive games,…

The game theory techniques are used to find the equilibrium of a market. Game theory refers to the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents,…

Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into…

A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information…