Approximate Equilibrium Situations with Possible Concessions in Finite Noncooperative Game by Sampling Irregularly Fundamental Simplexes as Sets of Players' Mixed Strategies

摘要

An approximation technique for solving finite noncooperative game is represented. By this technique, the approximate solution is found in two stages. Firstly, fundamental simplexes as sets of players' mixed strategies are converted into finite lattices. Probabilities on simplex are allowed to be sampled irregularly for the conversion generalization. Requirements imposed on the simplexes' conversion are stated purposely to maintain the approximation quality. Secondly, approximate Nash equilibrium strategies are searched on the finite set of situations in mixed strategies. In order not to obtain empty solution, the corresponding payoff inequalities are relaxed. Algorithms for searching both the approximate Nash equilibria and approximate strong Nash equilibria are general-schemed. By adjusting magnitudes of relaxations, a unique (strong) Nash equilibrium can be got. The represented approximation technique is a constructive practice-oriented development of the finite noncooperative game and models based on it. Universality of the approximation technique is determined with the generalized sampling and controlled equilibration, and the general-schemed search algorithms.