相关论文: Bayesian Nash Equilibria and Bell Inequalities

Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…

Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…

The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…

Auctions are modeled as Bayesian games with continuous type and action spaces. Determining equilibria in auction games is computationally hard in general and no exact solution theory is known. We introduce an algorithmic framework in which…

In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…

We use techniques from the statistical mechanics of disordered systems to analyse the properties of Nash equilibria of bimatrix games with large random payoff matrices. By means of an annealed bound, we calculate their number and analyse…

The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…

As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the…

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…

Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game…

A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…

Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.

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 an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the computation of Nash equilibria in such games as…

We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum Bayesian games with continuous types and finite actions under the conditions that the utility functions and the prior type distributions are continuous concerning the…

A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…

We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob and…

Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…

Game theory relies heavily on the availability of cardinal utility functions, but in fields such as matching markets, only ordinal preferences are typically elicited. The literature focuses on mechanisms with simple dominant strategies, but…