Finding applications of Quantum Game Theory

[rajkk1]

Finding applications of Quantum Game Theory would help direct the research in a meaningful way. One place to start might be section 12 of this paper by Khan et al. (2018).

[rajkk1]

Spectrum sharing in wireless communication environments in which transmitters compete for access.

[from Khan et al. (2018)] A base station distributes an n-partite entangled quantum state among n individual transmitters, i.e., players, who then apply local strategies to each part of the quantum state before measuring. Based on the observed, correlated outcomes, the players select whether to transmit (1) or wait (0). Zabaleta et al. showed that using the quantum resource in this game reduces the probability of transmission collision by a factor of n while retaining fairness in access management.

[rajkk1]

A quantum routing game for sending transmissions through a communication network.

[from Khan et al. (2018)] The conventional routing game has been extensively studied as a representation of flow strategies in real-world network, for example, Braess’ paradox that adding more routes does not always improve flow. Solmeyer et al. developed a quantized version of the routing game modified to include a distributed quantum state between players representing the nodes within the network. Each player is permitted to apply a local quantum strategy to their part of the state in the form of a unitary rotation before measuring. Solmeyer et al. simulated the total cost of network flow in terms of overall latency and found that the minimal cost is realized when using a partially entangled state between nodes. Notably, their results has demonstrated Braess’ paradox but only for the case of maximal and vanishing entanglement. If, and when, quantum networks become a reality, with multiple independent quantum agents operating distributed applications, quantum game theory may not only provide possible applications, but may also be necessary for their analysis.

[rajkk1]

The selection of open access publishing decisions in scientific literature.

[from Khan et al. (2018)] Motivated by the different publication patterns observed across scientific disciplines, they perform a comparative analysis of open-access choices using three different games: zero-sum, Prisoner’s Dilemma and stag hunt. The formal solutions from each of these classical games provide Nash equilibria that either discourage open access publication or include this choice as a minority in a mixed strategy. By contrast, Hanauske et al. found that quantized versions of these games which include distributed quantum resources yield Nash equilibria that favor open access publication. In this case, quantum game theory may provide a more general probability theory to form a descriptive analysis of a such socially constructed environments. In addition to decision making applications, game theory may also serve as a model for understanding competitive processes such as those found in ecological or social systems.

[rajkk1]

Quantum game theory also shows promise for the study of strictly quantum mechanical processes as well.

[from Khan et al. 2018] In particular, several non-cooperative processes underlying existing approaches to the development of quantum technology including quantum control, quantum error correction, and fault-tolerant quantum operations. Each of these application areas require a solution to the competition between the user and the environment, which may be considered to be a ‘player’ in the game theoretic setting. The solutions to these specific applications require a model of the quantum mechanical processes for dynamics and interactions which are better suited for quantum game theory.

[rajkk1]

Criticism of quantum games - a discussion

Reading and understanding section 4 in the paper by Khan et al. (2018) will help us understand some context behind what "quantumness" to game theory really does.