Quantum Dynamic Games

Huimin Cheng, Ming-Xing Luo

The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.

J.M.A Figueiredo

Azhar Iqbal, A. H. Toor

An evolutionarily stable strategy (ESS) was originally defined as a static concept but later given a dynamic characterization. A well known theorem in evolutionary game theory says that an ESS is an attractor of replicator dynamics but not every attractor is an ESS. We search for a dynamic characterization of ESSs in quantum games and find that in certain asymmetric bi-matrix games evolutionary stability of attractors can change as the game switches between its two forms, one classical and the other quantum.

Παναγιώτης Αποστολίδης, Εύαγγελος Κ. Κοντονικολάου

Yuhuai Zhang, Jing Yuan, Yili Zhang

On the basis of the bounded rationality and adaptive expectations, we investigate the dynamics of quantum Cournot duopoly game with heterogeneous players by using the Li et al. scheme. Further, we discuss the effect of quantum entanglement on local stability of the system. The results show that: (i) The special form of quantum Cournot duopoly game is the classical Cournot duopoly game, and the quantum Cournot duopoly game with naïve expectation is also a special form of quantum Cournot duopoly game with adaptive expectation. (ii) The increase or decrease of the stable region is dependent on the degree of quantum entanglement. It is related to the difference of relative marginal cost. (iii) The numerical simulation reveals the complexity characteristics of quantum dynamic Cournot game system through the analysis of stability region, bifurcation, strange attractor and sensitivity to initial conditions, and shows the difference from the classical dynamic Cournot model.