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A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
In this discussion draft, we explore different duopoly games of players with quadratic costs, where the market is supposed to have the isoelastic demand. Different from the usual approaches based on numerical computations, the methods used…
In this discussion draft, we investigate five different models of duopoly games, where the market is assumed to have an isoelastic demand function. Moreover, quadratic cost functions reflecting decreasing returns to scale are considered.…
We present a new framework for creating a quantum version of a classical game, based on Fine's theorem. This theorem shows that for a given set of marginals, a system of Bell's inequalities constitutes both necessary and sufficient…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
A quantum version of the Minority game for an arbitrary number of agents is considered. It is known that when the number of agents is odd, quantizing the game produces no advantage to the players, but for an even number of agents new Nash…
We study the three-player Prisoner's Dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off over the classical players. It is also seen that the game's Nash equilibrium…
Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
In this paper we are discussing the question how a continuous quantum system can be simulated by mean field fluctuations of a finite number of qubits. On the kinematical side this leads to a convergence result which states that…
The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum…
The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potential to play games in a unique way:…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…
Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent…
A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…