Evolutionarily Stable Sets in Quantum Penny Flip Games

11/30/2012
by   Tina Yu, et al.
0

In game theory, an Evolutionarily Stable Set (ES set) is a set of Nash Equilibrium (NE) strategies that give the same payoffs. Similar to an Evolutionarily Stable Strategy (ES strategy), an ES set is also a strict NE. This work investigates the evolutionary stability of classical and quantum strategies in the quantum penny flip games. In particular, we developed an evolutionary game theory model to conduct a series of simulations where a population of mixed classical strategies from the ES set of the game were invaded by quantum strategies. We found that when only one of the two players' mixed classical strategies were invaded, the results were different. In one case, due to the interference phenomenon of superposition, quantum strategies provided more payoff, hence successfully replaced the mixed classical strategies in the ES set. In the other case, the mixed classical strategies were able to sustain the invasion of quantum strategies and remained in the ES set. Moreover, when both players' mixed classical strategies were invaded by quantum strategies, a new quantum ES set emerged. The strategies in the quantum ES set give both players payoff 0, which is the same as the payoff of the strategies in the mixed classical ES set of this game.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/19/2018

Quantum Nash equilibrium in the thermodynamic limit

The quantum Nash equilibrium in the thermodynamic limit is studied for g...
research
06/08/2018

Quantum Penny Flip game with unawareness

Games with unawareness model strategic situations in which players' perc...
research
11/21/2019

Comment on "Quantum Games and Quantum Strategies"

We point out a flaw in the unfair case of the quantum Prisoner's Dilemma...
research
09/11/2018

Strategies for quantum races

We initiate the study of quantum races, games where two or more quantum ...
research
05/30/2023

Steering control of payoff-maximizing players in adaptive learning dynamics

Evolutionary game theory provides a mathematical foundation for cross-di...
research
08/17/2015

Reflective Oracles: A Foundation for Classical Game Theory

Classical game theory treats players as special---a description of a gam...
research
05/12/2020

Repeated Quantum Games and Strategic Efficiency

Repeated quantum game theory addresses long term relations among players...

Please sign up or login with your details

Forgot password? Click here to reset