arXiv:1110.4678

Quantum Strategies

Gordon B. Dahl, Steven E. Landsburg

Published Oct 21, 2011• 0 citations

Abstract

We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated equilibria appear as quantum equilibria. The classical and quantum theories diverge further in games of private information. In the quantum context, we show that Kuhn's equivalence between behavioral and mixed strategies breaks down. As a result, quantum technology allows players to achieve outcomes that would not be achievable with any classical technology short of direct communication; in particular they do not occur as correlated equilibria. In general, in games of private information, quantum technology allows players to achieve outcomes that are Pareto superior to any classical correlated equilibrium, but not necessarily Pareto optimal. A simple economic example illustrates these points.

DOI: 10.48550/arxiv.1110.4678

Related papers

Quantum Correlated Equilibria in Classical Complete Information Games

Alan Deckelbaum

We study the scenario where the players of a classical complete information game initially share an entangled pure quantum state. Each player may perform arbitrary local operations on his own qubits, but no direct communication is allowed. In this framework, we define the concept of quantum correlated equilibrium (QCE) for both normal and extensive form games of complete information. We show that in a normal form game, any outcome distribution implementable by a QCE can also be implemented by a classical correlated equilibrium (CE). We prove that the converse is surprisingly false: we give an example of an outcome distribution of a normal form game which is implementably by a CE, yet we prove that in any attempted quantum protocol beginning with a partition of a pure quantum state, at least one of the players will have incentive to deviate. We extend our analysis to extensive form games, and find that the relation between classical and quantum correlated equilibria becomes less clear. We compare the outcome distributions implementable in our quantum model to those implementable by a classical extensive form correlated equilibrium (EFCE). For example, we show that there exists an extensive form complete information game and a distribution of outcomes which can be implemented by a QCE but not by any EFCE, in contrast to the result for normal form games. We also consider the concept of an immediate-revelation extensive form correlated equilibrium (IR-EFCE) and compare the power of IR-EFCE to EFCE and to QCE.

arXiv:1101.3380Jan 18, 20110 citations

CORRELATED EQUILIBRIA OF CLASSICAL STRATEGIC GAMES WITH QUANTUM SIGNALS

Pierfrancesco La Mura

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even greater efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.

arXiv:quant-ph/0309033International Journal of Quantum InformationDec 16, 200453 citations

Efficiency of Classical and Quantum Games Equilibria

M. Szopa

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner's dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism and the Frąckiewicz-Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied.

EntropyApr 22, 202121 citations

On Correlated Equilibria in Marinatto–Weber Type Quantum Games

Piotr Frąckiewicz

Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games.

Applied SciencesDec 16, 20200 citations

Quantum volunteer's dilemma

Dax Enshan Koh, Kaavya Kumar, Siong Thye Goh

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 quantum variant of the classical volunteer's dilemma, generalizing it by allowing players to utilize quantum strategies. Employing the Eisert-Wilkens-Lewenstein quantization framework, we analyze a multiplayer quantum volunteer's dilemma scenario with an arbitrary number of players, where the cost of volunteering is shared equally among the volunteers. We derive analytical expressions for the players' expected payoffs and demonstrate the quantum game's advantage over the classical game. In particular, we prove that the quantum volunteer's dilemma possesses symmetric Nash equilibria with larger expected payoffs compared to the unique symmetric Nash equilibrium of the classical game, wherein players use mixed strategies. Furthermore, we show that the quantum Nash equilibria we identify are Pareto optimal. Our findings reveal distinct dynamics in volunteer's dilemma scenarios when players adhere to quantum rules, underscoring a strategic advantage of decision making in quantum settings.

arXiv:2409.05708Physical Review ResearchJan 27, 202510 citations

Can quantum entanglement implement classical correlated equilibria?

Alan Deckelbaum

We ask whether players of a classical game can partition a pure quantum state to implement classical correlated equilibrium distributions. The main contribution of this work is an impossibility result: we provide an example of a classical correlated equilibrium that cannot be securely implemented without useful information leaking outside the system. We study the model where players of a classical complete information game initially share an entangled pure quantum state. Players may perform arbitrary local operations on their subsystems, but no direct communication (either quantum or classical) is allowed. We explain why, for the purpose of implementing classical correlated equilibria, it is desirable to restrict the initial state to be pure and to restrict communication. In this framework, we define the concept of pure quantum correlated equilibrium (PQCE) and show that in a normal form game, any outcome distribution implementable by a PQCE can also be implemented by a classical correlated equilibrium (CE), but that the converse is false. We extend our analysis to extensive form games, and compare the power of PQCE to extensive form classical correlated equilibria (EFCE) and immediate-revelation extensive form correlated equilibria (IR-EFCE).

Quantum Information and ComputationMay 1, 20141 citation