Abstract
The aim of the paper is to study the problem of absentminded driver in the quantum domain. In the classical case, it is a well-known example of a decision problem with imperfect recall that exhibits lack of equivalence between mixed and behavioral strategies. The optimal payoff outcome is significantly lower than the maximum payoff appearing in the game. This raises the question whether a quantum approach to the problem can increase the strategic position of the decision maker. The results that we present in the paper clearly reveal the benefits from playing the absentminded problem with the aid of quantum objects. Through appropriately chosen initial quantum state, the unitary strategies enable the decision maker to obtain the maximum possible payoff. At the same time, our scheme comes down to the classical problem with a suitable restriction of unitary strategies.
Highlights
Quantum game theory is a field developed at the interface between game theory and quantum computing
Application of quantum computing to game theory can go beyond standard games and explore single-player decision problems, in particular, as we show in this paper, decision problems with imperfect recall
The model enables the decision maker to obtain the maximum payoff provided for the game equal to 4, by using separable initial states
Summary
The first formal approach to playing a general 2 × 2 game was introduced by Eisert et al [2] They used their scheme for the Prisoner’s Dilemma game and showed that the players’ strategies extended to the two-parameter unitary operators can lead to the Pareto-optimal Nash equilibrium. Another quantum approach to 2 × 2 games was presented in [3] and further generalized to m × n bimatrix games in [4]. The Eisert–Wilkens–Lewenstein scheme [2] was applied Both models of quantum playing the absentminded driver problem implied the optimal payoff of 2.
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