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Motivational Interlude: Sums of Games
Published in Michael H. Albert, Richard J. Nowakowski, David Wolfe, Lessons in Play, 2019
Michael H. Albert, Richard J. Nowakowski, David Wolfe
Combinatorial game theory steers a middle course between these two positions. Though the ultimate goal in practice may well be to determine the outcome class of a particular game, as we do for some instances of domineering rectangles in the next section, the aim of the subject is to produce practical and theoretical tools, which enhance our ability to make such determinations. The problem with the purely pragmatic view is that it treats each game in isolation — it becomes a matter of brute-force search, possibly guided by some good heuristic techniques, to actually work out the relevant outcome class. What we would like to be able to do is to use theory to simplify this process.
Nash equilibrium sorting genetic algorithm for simultaneous competitive maximal covering location with multiple players
Published in Engineering Optimization, 2022
Abdullah Konak, Sadan Kulturel-Konak, Lawrence V. Snyder
In this article, a new GA called the NESGA was proposed to discover NE in the case of the competitive MCLP with two and three competitors, for the first time. Identifying NE is important to study competitor behaviours that would emerge as a response to market competition, conditions, rules and principles in the context of the competitive MCLP. The NESGA is a multi-population GA with a hierarchical fitness assignment method that ranks population members with respect to all candidate NE in the population. The computational experiments showed that the NESGA could discover multiple NE in a single run, and the proposed fitness evaluation method was effective in problems with three competitors. The NESGA performed robustly over a wide range of problem instances, including ones with three competitors for which the NashGA failed to converge. In addition, a novel way was proposed to demonstrate the convergence of evolutionary algorithms in the case of simultaneous game theory problems. Certainly, the NESGA can be applied to any type of combinatorial game theory problem. Studying the performance of the proposed fitness evaluation method in other combinatorial game theory problems would be an interesting avenue for further research.