An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers

Abstract

An asset selling problem is one of well-known problems in the decision making literature. The problem assumes a stream of bidders who would like to buy one or several identical objects (assets). Offers placed by the bidders once rejected cannot be recalled. The seller is interested in an optimal selling strategy that maximizes the total expected revenue. In this paper, we consider a multi-asset selling problem when the seller wants to sell several identical assets over a finite time horizon with a variable number of offers per time period and no recall of past offers. We consider the problem within the framework of the optimal stopping theory. Using the method of backward induction, we find an optimal sequential procedure which maximizes the total expected revenue in the selling problem with independent observations.

On Asymptotics of Optimal Stopping Times

“…This problem has arisen in a number of contexts, such as deciding how many candidates for a job should be interviewed before deciding upon one particular candidate, known in literature as the secretary problem [1][2][3]. Optimal stopping has been used to determine when assets should be bought and sold in order to maximize profits; this has been described as the house-selling problem and is discussed in [4][5][6]. Optimal stopping has been incorporated into the theory of online auctions, as in [7].…”

Mixed Mechanisms for Auctioning Ranked Items

“…From the earliest work by Milgrom and Weber ([21,22]) in the early 1980s up to the present day (see, for example, Reference [23]), multi-object auctions have received wide attention due to their use in numerous money-generating markets. Some relevant examples of these markets that have received special attention are Treasury bill and bond markets, raw materials or other product markets (fish, flowers.…”