Abstract
Abstract This work presents novel results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very useful approach for modeling interactions between competing agents and Nash equilibrium represents a powerful solution concept, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.
Highlights
Game theory aimed to study and model socio-economic phenomena and the interaction between agents, whose actions drive the overall process - typically the decision of a specific player may modify the course of the whole game
Being an important analytical tool when studying interactions between players, in which the final results depend on the collective strategies chosen by agents, the idea of equilibrium in game theory is considered a good model for a stable outcome of a given game, working well as a solution concept [8]
The choice of the most effective approach for computing Nash equilibria of a given finite game depends on various conditions, including whether the immediate need is to find pure or mixed strategy equilibria, or finding only one or all equilibria
Summary
Game theory aimed to study and model socio-economic phenomena and the interaction between agents (or players), whose actions drive the overall process - typically the decision of a specific player may modify the course of the whole game. The classical problem of finding Nash equilibria of finite normal form games may be solved by finding fixed points of some specific functions [11], a very significant theoretical result relatively to the same topic states that the problem may be faced as a global optimization one [10, 11, 21] The latter approach opens up the way for the synthesis of a large number of possible methods of solution for the problem at hand, considering the substantial number of effective optimization methods available in the literature, especially those using computational intelligence techniques [19]. In the sequence the paper will briefly describe the Fuzzy ASA paradigm, its application to the underlying problem and the obtained results
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