Stability of mixed Nash equilibria in symmetric quantum games
نویسنده
چکیده
In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of twoqubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium. PACS: 02.50.Le, 03.67.-a, 87.23.Kg
منابع مشابه
Finite Population Dynamics and Mixed Equilibria
This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal r...
متن کاملEntanglement and Dynamic Stability of Nash Equilibria in a Symmetric Quantum Game
We study the evolutionary stability of Nash equilibria (NE) in a symmetric quantum game played by the recently proposed scheme of applying ‘identity’ and ‘Pauli spin flip’ operators on the initial state with classical probabilities. We show that in this symmetric game dynamic stability of a NE can be changed when the game changes its form, for example, from classical to quantum. It happens even...
متن کاملEquilibrium selection and the dynamic evolution of preferences
A population of fully rational agents play a symmetric 2-player game in biological fitnesses, but each agent’s play is determined by his payoffs, which are free to evolve according to “survival of the fittest” pressures. An equilibrium-selection mechanism is assumed to exist, and deliver a unique outcome for any given profile of payoffs; this allows the evolution of payoffs to be modeled as a w...
متن کاملLocal contraction-stability and uniqueness
This paper investigates the relationship between uniqueness of Nash equilibria and local stability with respect to the best-response dynamics in the cases of sum-aggregative and symmetric games. If strategies are equilibrium complements, local stability and uniqueness are the same formal properties of the game. With equilibrium substitutes, local stability is stronger than uniqueness. If player...
متن کاملCenter for the Study of Rationality
We consider stability properties of equilibria in stochastic evolutionary dynamics. In particular, we study the stability of mixed equilibria in strategic form games. In these games, when the populations are small, all strategies may be stable. We prove that when the populations are large, the unique stable outcome of best-reply dynamics in 2 × 2 games with a unique Nash equilibrium that is com...
متن کامل