On the Masami Yasuda stopping game

TL;DR

This paper reviews the development of the Masami Yasuda stopping game, highlighting its theoretical significance, extensions, and applications in system detection, emphasizing its role in advancing stochastic game theory.

Contribution

It discusses the formulation, extension, and application of Yasuda's stopping game model, emphasizing its importance in solving equilibrium existence problems in stochastic games.

Findings

Yasuda's model solved equilibrium existence issues.

Application to detector systems demonstrates practical power.

Extensions broaden the model's applicability.

Abstract

The sero-sum stopping game for the stochastic sequences has been formulated in late sixties of the twenty century by Dynkin (1969). The formulation had the assumption about separability of decision moment of the players which simplified the construction of the solution. Further research by Neveu (1975) extended the model by admitting more general behaviour of the players and their pay--offs. In new formulation there is the problem with existence of the equilibrium. The proper approach to solution of the problem without restriction of former models was developed by Yasuda (1975). The results was crucial in these research. The author made often reference to the Yasuda's (1985) result in his works (see the author's papers (1993,1995)) as well as see results of others stimulated by this paper. Withal, in this note another stopping game model, developed by Yasuda with coauthors (see e.g. Kurano at al. (1980) and the author and Yasuda (1995)) is recalled. The application of the model to an analysis of system of detectors shows the power of the game theory methods. In the last part of the paper I would like to express my personal relation to the Masami Yasuda game.