Single threshold selection strategy in the group interview problem

In many decision situations such as selling an asset on the open market, a decision maker receives a random sequence of offers. Following an evaluation of each offer, the decision maker must decide whether to take the current offer or reject it and consider the next one. One of the simple selection strategies in the sequential decision problem is via an aspiration-level or a threshold value, which allows the decision maker to select the first offer that is higher than the pre-determined threshold value. For the so-called group interview problem in which a number of offers or choices are presented sequentially in groups, we derive the optimal threshold value (1) to maximize the probability of selecting the best choice and (2) to maximize the expected value of the selected choice. For the cases where the order of groups can be rearranged for evaluation, an exact solution is derived for the optimal sequencing of groups. There are many potential applications of the selection strategy, including product pricing strategy and consumer search and purchase process.