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Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$…
Petri games are a multiplayer game model for the automatic synthesis of distributed systems. We compare two fundamentally different approaches for solving Petri games. The symbolic approach decides the existence of a winning strategy via a…
In this research article, we survey existing quantum physics-related games and, based on this survey, propose a definition for the concept of quantum games. We define a quantum game as any type of rule-based game that either employs the…
By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…
The interaction of competing agents is described by classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring…
We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…
We propose an experimental implementation of a quantum game algorithm in a hybrid scheme combining the quantum circuit approach and the cluster state model. An economical cluster configuration is suggested to embody a quantum version of the…
Quantum mechanics courses focus mostly on its computational aspects. This alone does not provide the same depth of understanding as most physicists have of classical mechanics. The understanding of classical mechanics is significantly…
Hybrid games are games played on a finite graph endowed with real variables which may model behaviors of discrete controllers of continuous systems. The synthesis problem for hybrid games is decidable for classical objectives (like LTL…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of…
Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum…
This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…
Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…
We show that, for a continuous set of entangled four-partite states, the task of maximizing the payoff in the symmetric-strategy four-player quantum Minority game is equivalent to maximizing the violation of a four-particle Bell inequality…
Implementing quantum game theory on real hardware is challenging due to noise, decoherence, and limited qubit connectivity, yet such demonstrations are essential to validate theoretical predictions. We present one of the first full…
We investigate the 3-player quantum Prisoner's Dilemma with a certain strategic space, a particular Nash equilibrium that can remove the original dilemma is found. Based on this equilibrium, we show that the game is enhanced by the…
Evolutionarily Stable Strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population…