MULTI-VARIATE STOPPING PROBLEM WITH A MAJORITY RULE

Abstract

This paper studies the stopping problem for random vectors of p components which correspond to the payoffs to a group of p players. The observation process is stopped at the first time when no less than r(1⩽r⩽p) players declare to stop. We call it a majority rule. The object of this paper is to find out a reasonable stopping strategy under a class of these rules, in both cases of finite and infinite decision horizons. We solve our stopping problem by introducing the concept of an equilibrium point in the non-cooperative game theory. Several examples including a variant of the secretary problem are given.