Preferences in Quantum Games

TL;DR

This paper explores how preferences influence the outcomes of quantum games, proposing a reverse engineering approach to construct games that produce desired equilibrium states based on measurement-induced preferences.

Contribution

It introduces a framework linking preferences in quantum games to measurement outcomes and payoffs, offering new insights into state preparation via game-theoretic methods.

Findings

Preferences can be modeled as measurement payoffs.

Distance-based preferences are equivalent to strictly-competitive measurement payoffs.

The approach provides a method to engineer quantum states through game design.

Abstract

A quantum game can be viewed as a state preparation in which the final output state results from the competing preferences of the players over the set of possible output states that can be produced. It is therefore possible to view state preparation in general as being the output of some appropriately chosen (notional) quantum game. This reverse engineering approach in which we seek to construct a suitable notional game that produces some desired output state as its equilibrium state may lead to different methodologies and insights. With this goal in mind we examine the notion of preference in quantum games since if we are interested in the production of a particular equilibrium output state, it is the competing preferences of the players that determine this equilibrium state. We show that preferences on output states can be viewed in certain cases as being induced by measurement with an appropriate set of numerical weightings, or payoffs, attached to the results of that measurement. In particular we show that a distance-based preference measure on the output states is equivalent to a having a strictly-competitive set of payoffs on the results of some measurement.