On Topics in Quantum Games

This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but included for the sake self consistence, as devoted to introduction mathematical and physical grounds pertinent topics, way in which a simple classical game modified become (a procedure referred quantization game). The connection between theory information science briefly stressed, role entanglement (that plays central games), exposed. Armed with these tools, we investigate some basic concepts like existence (or absence) pure strategy mixed Nash equilibrium its relation degree entanglement. main results this are follows: 1) Construction numerical algorithm based method best response functions, designed search formalism discretization continuous variable into mesh points, can be applied games that built upon two-players two-strategies games, functions. 2) Application study question how related (specified by parameter γ ). It shown when GC has Pareto efficient, then GQ maximal (γ = π/2) no equilibrium. By studying non-symmetric prisoner dilemma game, found there critical value 0γc such γγc γ≥γc behavior two payoffs function starts at ones (D, D) approaches cooperative (C, C) (C confess, D don’t confess). 3) We Bayesian show under certain conditions, even maximal. 4) define ingredients two-player three strategies game. requires trits (instead bits) bits). proved commensurability sense obtained special case strategies.