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Time-unit shifting in 2-person games played in finite and uncountably infinite staircase-function spaces

Romanuke Vadim

Journal of Mathematics and Applications

2022

Vol. 45

133--179

A computationally efficient and tractable method is presented to find the best equilibrium in a finite 2-person game played with staircase-function strategies. The method is based on stacking equilibria of smaller-sized bimatrix games, each defined on a time unit where the pure strategy value is constant. Every pure strategy is a staircase function defined on a time interval consisting of an integer number of time units (subintervals). If a time-unit shifting happens, where the initial time interval is narrowed by an integer number of time units, the respective equilibrium solution of any “narrower” subgame can be taken from the “wider” game equilibrium. If the game is uncountably infinite, i. e. a set of pure strategy possible values is uncountably infinite, and all time-unit equilibria exist, stacking equilibria of smaller-sized 2-person games defined on a rectangle works as well.