Quantum Games with Unawareness with Duopoly Problems in View

Abstract

Playing the Cournot duopoly in the quantum domain can lead to the optimal strategy profile in the case of maximally correlated actions of the players. However, that result can be obtained if the fact that the players play the quantum game is common knowledge among the players. Our purpose is to determine reasonable game outcomes when players’ perceptions about what game is actually played are limited. To this end, we consider a collection consisting of the classical and quantum games that specifies how each player views the game and how each player views the other players’ perceptions of the game. We show that a slight change in how the players perceive the game may considerably affect the result of the game and, in the case of maximally correlated strategies, may vary from the inefficient Nash equilibrium outcome in the classical Cournot duopoly to the Pareto optimal outcome. We complete our work by investigating in the same way the Bertrand duopoly model.

Nonlinear Dynamics of a Quantum Cournot Duopoly with Bounded Rationality and Relative Profit Maximization

“…Many scholars have attempted to describe games in the quantum domain, in particular the quantum scheme proposed by Li et al [4,5]. Some new and exciting dynamical results have been discovered in this research on quantum games, which are diferent from the classical game models [6][7][8][9][10].…”

Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

“…Once the equilibrium is reached, the market participants cannot further improve their profits, and any modification of their quantity or price will result in a reduced profit [3]. Quantity (Cournot) versus price (Bertrand) competition has drawn great attention in the literature, and many researchers have compared the models, considering different assumptions [4][5][6][7].…”

The XXXVII International Conference on Multivariate Statistical Analysis 5–7 November 2018, Łódź, Poland

“…Many papers discussed also the modifications of the above-mentioned games. The Cournot duopoly model has also been considered for nonlinear price functions, quadratic cost functions [35], [36], [37] or when the knowledge of the game is not the same for both players [38]. The cases with incomplete information were considered in the Bertrand [39] and Stackelberg duopoly [40], [41].…”