On Topics in Quantum Games

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

Design and evaluation of control strategies in urban drainage systems in Kunming city

Real time control （RTC） of urban drainage systems （UDSs） is an important measure to reduce combined sewer overflow （CSO） and urban flooding, helping achieve the aims of ＂Sponge City＇. Application of RTC requires three main steps： strategy design, simulation-based evaluation and field test. But many of published RTC studies are system-specific, lacking discussions on how to design a strategy step by step. In addition, the existing studies are prone to use hydrologic model to evaluated strategics, but a more precise and dynamic insight into strategy performance is needed. To fill these knowledge gaps, based on a case UDS in Kunming city, a studio on RTC strategy design and Management Model （SWMM） - uncier four typical rainfall events characterized by different return periods （1-year or 0.5 year） and different spatial distributions （uniform or uneven）. The equal filling strategy outperformss other two strategies and it can achieve 10% more CSO reduction and 5% more flooding reduction relative to the no-tank case.