Related papers: Nash equilibrium in quantum superpositions
Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware…
In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical…
We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem…
If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…
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 present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…
Synthesis of finite-state controllers from high-level specifications in multi-agent systems can be reduced to solving multi-player concurrent games over finite graphs. The complexity of solving such games with qualitative objectives for…
We show some chain-rules for the capacity of classical-quantum and quantum channels. We use the concept of Nash-Equilibrium in game-theory, and its existence in suitably defined games, to arrive at the chain-rules.
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…
Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…
Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a…
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…
We study solution concepts for normal-form games. We obtain a characterization of Nash equilibria and logit quantal response equilibria, as well as generalizations capturing non-expected utility. Our axioms reflect that players are…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
In this paper, we explore the historical development of playable quantum physics related games (\textit{\textbf{quantum games}}). For the purpose of this examination, we have collected over 260 quantum games ranging from commercial games,…
Experimental economics has repeatedly demonstrated that the Nash equilibrium makes inaccurate predictions for a vast set of games. Instead, several alternative theoretical concepts predict behavior that is much more in tune with observed…
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…
Our paper addresses characterizing conditions for a linear quadratic (LQ) game to be a potential game. The desired properties of potential games in finite action settings, such as convergence of learning dynamics to Nash equilibria, and the…
We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the…