# MULTIPLE BUYING OR SELLING WITH VECTOR OFFERS

### F. THOMAS BRUSS and THOMAS S. FERGUSON

#### Abstract:

This paper contains a generalization of the multiple
house-selling problem to vector offers. The offers, X(1), X(2), . . .,
are independent, identically distributed k-dimensional random
vectors with finite second moments, having a distribution known to
the decision maker. The decision maker is to choose simultaneously
k stopping rules, N(1), . . .,N(k), one for each component. The payoff
is the sum over j of the jth component of X(N(j)) minus 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 a discount and to problems with recall of past offers.