Multiple buying or selling with vector offers

Abstract

We consider a generalization of the house-selling problem to sellingkhouses. Let the offers,X1,X2, · ··,be independent, identically distributedk-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneouslykstopping rules,N1, · ··,Nk,one for each component. The payoff is the sum overjof thejth component ofminus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.