Abstract
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which conditions there is an equivalence. In this paper, we consider quantum games as those that allow non-factorizable probabilities. We discuss two approaches for obtaining a non-factorizable game and study the outcome of such games. We demonstrate how the standard version of a quantum game can be analysed as a non-factorizable game and determine the limitations of our approach.
Highlights
The realization has emerged [1,2,3] that the processing of information cannot be separated from the underlying fundamental physics and that the physical aspects of information processing must be taken into consideration
The finding that physical aspects can have a crucial role in information processing has natural implications for player strategies, and the considerations of underlying fundamental physics become important for game theory
We explore how a quantum game can be considered as a non-factorizable game by considering the scheme of Eisert et al for quantization of a bimatrix game that involves four quantum probabilities
Summary
The realization has emerged [1,2,3] that the processing of information cannot be separated from the underlying fundamental physics and that the physical aspects of information processing must be taken into consideration. Such questions have led to creation of the research area of quantum games [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70]. We reexpress the players’ pay-off relations in a form that allows us to obtain a non-factorizble game directly from the factorizable game by defining a function of players’ strategies that satisfies certain constraints
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