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The prisoner's dilemma (PD) is a game-theoretic model studied in a wide array of fields to understand the emergence of cooperation between rational self-interested agents. In this work, we formulate a spatial iterated PD as a discrete-event…

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations…

The strategic Go game, known for the tedious mathematical complexities, has been used as a theme in many fiction, movies, and books. Here, we introduce the Go game and provide a new version of quantum Go in which the boxes are initially in…

We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…

This paper presents a new mathematical formalism that describes the quantization of games. The study of so-called quantum games is quite new, arising from a seminal paper of D. Meyer \cite{Meyer} published in Physics Review Letters in 1999.…

A new representation of Game Theory is developed in this paper. State of players is represented by a density matrix, and payoff function is a set of hermitian operators, which when applied onto the density matrix give the payoff of players.…

Learning in games has emerged as a powerful tool for machine learning with numerous applications. Quantum games model interactions between strategic players who have access to quantum resources, and several recent works have studied…

LLMs are increasingly used in applications where they interact with humans and other agents. We propose to use behavioural game theory to study LLM's cooperation and coordination behaviour. We let different LLMs play finitely repeated…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

In game theory, a popular model of a struggle for survival among three competing agents is a truel, or three person generalization of a duel. Adopting the ideas recently developed in quantum game theory, we present a quantum scheme for the…

The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the winning probabilities those correlations offer in cooperation games where…

Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is…

This article uses data from two experimental studies of two-person Prisoner's Dilemma games [1, 2] and compares the data with the theoretic predictions calculated with the use of a quantum game theoretical method. The experimental findings…

We investigate Nash Equilibrium in the quantum Battle of Sexes Game. We find the game has infinite Nash Equilibria and all of them leads to the asymmetry result. We also show that there is no unique but infinite Nash Equilibrium in it if we…

The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative game. In both cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved.

Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the…

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are…

In this work we consider a stochastic linear quadratic two-player game. The state measurements are observed through a switched noiseless communication link. Each player incurs a finite cost every time the link is established to get…

Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the…