Related papers: Ising model versus normal form game

We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…

We study the problem of learning a Nash equilibrium (NE) in an imperfect information game (IIG) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular IIG under the perfect-recall assumption where the only…

We train two neural networks adversarially to play static games. At each iteration, a row and column network observe a new random bimatrix game and output individual mixed strategies. The parameters of each network are independently updated…

We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to…

Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria…

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…

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program…

We propose a new type of state sum model for two-dimensional surfaces that takes into account topology and spin. The definition used - new to the literature - provides a rich class of extended models called spin models. Both examples and…

In this note, we present a compatibility test based on John Nash's game-theoretic notion of equilibrium strategy. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. The…

Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect…

A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…

Behavioral diversity, expert imitation, fairness, safety goals and others give rise to preferences in sequential decision making domains that do not decompose additively across time. We introduce the class of convex Markov games that allow…

We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case,…

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 --…

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…

The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past…

We address the problem of mechanism design for two-stage repeated stochastic games -- a novel setting using which many emerging problems in next-generation electricity markets can be readily modeled. Repeated playing affords the players a…

This paper investigates the strategic concealment of environment representations used by players in competitive games. We consider a defense scenario in which one player (the Defender) seeks to infer and exploit the representation used by…