2016/09/27 by Faisal Shah Khan, Khan, Faisal Shah, Travis S. Humble +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #cs.GT #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1609.08360
The results pertaining to fixed point theorems for quantum games were mathematically erroneous
arxiv created 2017/12/12 · arxiv updated 2017/12/13
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.