Abstract
We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game induced by the scheme generalizes finite strategic form game. In particular, it covers normal representations of extensive games, i.e., strategic games generated by extensive ones. We illustrate our idea with an example of extensive game and prove that rational choices in the classical game and its quantum counterpart may lead to significantly different outcomes.
Highlights
A 15-year-period research on quantum games results in many ideas of how a quantum game might look like and how it might be played
The idea behind the scheme is that the players can choose whether they play a classical game or its quantum counterpart defined by the MW scheme
In our earlier paper [16], we introduced a quantum scheme for playing an extensive game by using its normal representation
Summary
A 15-year-period research on quantum games results in many ideas of how a quantum game might look like and how it might be played. The quantum scheme for 2 × 2 games introduced in [1] (the EWL scheme) has become one of the most common models and it has already found application in more complex games (see, for example, [2]). The more complex the classical game is, the more sophisticated techniques are required to find optimal players’ strategies in the EWL-type scheme. While in the scheme for 2 × 2 games the result of the game depends on six real.
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