Related papers: Many-player entangled state solutions in game theo…

In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…

We present an efficient algorithm to compute the explicit open-loop solution to both finite and infinite-horizon dynamic games subject to state and input constraints. Our approach relies on a multiparametric affine variational inequality…

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.…

The absent-minded driver's problem illustrates that probabilistic strategies can give higher pay-offs than deterministic ones. We show that there are strategies using quantum entangled states that give even higher pay-offs, both for the…

Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…

We present a new approach to solving games with a countably or uncountably infinite number of players. Such games are often used to model multiagent systems with a large number of agents. The latter are frequently encountered in economics,…

In the present work we deal with set-valued equilibrium problems for which we provide sufficient conditions for the existence of a solution. The conditions that we consider are imposed not on the whole domain, but rather on a self…

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…

Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner's dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD…

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

In this paper, we consider a Nash equilibrium seeking problem for a class of high-order multi-agent systems with unknown dynamics. Different from existing results for single integrators, we aim to steer the outputs of this class of…

We present a consistent formulation of quantum game theory that accommodates all possible strategies in Hilbert space. The physical content of the quantum strategy is revealed as a family of classical games representing altruistic game play…

The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a…

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 --…

Entanglement is perhaps the most non-classical manifestation of quantum mechanics. Among its many interesting applications to information processing, it can be harnessed to reduce the amount of communication required to process a variety of…

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…

Distributed Nash equilibrium (NE) seeking problem for multi-coalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This paper considers a…

We describe a quantum model of simple choice game (constructed upon entangled state of two qubits), which involves the fundamental problem of transitive - intransitive preferences. We compare attainability of optimal intransitive strategies…

We demonstrate that quantum entanglement can help separated individuals in making decisions if their goal is to find each other in the absence of any communication between them. We derive a Bell-like inequality that the efficiency of every…