Network Games with Quantum Strategies

Scarpa, Giannicola

doi:10.1007/978-3-642-11731-2_10

Cited by 3 publications

(1 citation statement)

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“…The games have been simplified and the strategy choices restricted so that they map onto the prisoners' dilemma [6,7] where the well-known quantum solution outperforms the classical one [8]. Pigou's example was also mapped onto the prisoners' dilemma where an entangled pair was shared between two players at the same node [9]. Since the entanglement is at one node, this approach cannot not take full advantage of the non-local characteristics of quantum entanglement for larger networks.…”

Section: Pacs Numbersmentioning

confidence: 99%

Quantum routing games

Solmeyer

Dixon

Balu

2018

J. Phys. A: Math. Theor.

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We discuss the connection between a class of distributed quantum games, with remotely located players, to the counter intuitive Braess' paradox of traffic flow that is an important design consideration in generic networks where the addition of a zero cost edge decreases the efficiency of the network. A quantization scheme applicable to non-atomic routing games is applied to the canonical example of the network used in Braess' Paradox. The quantum players are modeled by simulating repeated game play. The players are allowed to sample their local payoff function and update their strategies based on a selfish routing condition in order to minimize their own cost, leading to the Wardrop equilibrium flow. The equilibrium flow in the classical network has a higher cost than the optimal flow. If the players have access to quantum resources, we find that the cost at equilibrium can be reduced to the optimal cost, resolving the paradox. PACS numbers:It is becoming increasingly important to consider congestion of information in communication networks. In ad-hoc mobile networks, that may change dynamically with nodes that act independently of one another, it can be particularly difficult to efficiently route information. In many contexts, game theory is a powerful tool for analyzing such problems [1]. Game theory is used to solve for the equilibrium flow of information when each node acts independently and routes information selfishly. The equilibrium may not be the desired flow from the point of view of a total global cost. The goal of designing a network protocol is to ensure that the equilibrium flow is close to the optimal flow.As quantum networking hardware begins to come online [2, 3], it may be possible for network games to take advantage of the benefits that quantum games have shown over classical games. By incorporating quantum information into a game setting, quantum games may have different equilibria that can outperform their classical counterpart [4]. Entanglement shared between different nodes of the network allows the players to have correlated outcomes even in the absence of communication. This leads to the quantum game sampling a larger space of probability distributions that can realize equilibria resembling classical correlated equilibria which are only possible in classical games when the players receive advice [5].There have been a few previous examples of quantization schemes of classical routing games. The games have been simplified and the strategy choices restricted so that they map onto the prisoners' dilemma [6,7] where the well-known quantum solution outperforms the classical one [8]. Pigou's example was also mapped onto the prisoners' dilemma where an entangled pair was shared between two players at the same node [9]. Since the entanglement is at one node, this approach cannot not take full advantage of the non-local characteristics of quantum entanglement for larger networks. A notable example used Bell pairs to avoid packet collisions in a software defined networking simulation of an atomic ro...

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Section: Pacs Numbersmentioning

confidence: 99%