Comparison among Some Optimal Policies in Rank-Based Selection Problems

The paper deals with the sequential selection problem of the best object. Interviewers observe applicants or items and may decide to stop and hire the current applicant. He has some knowledge about the total number of applicant available. No recall of previously observed candidates is allowed. Knowledge about current applicant is restricted to his relative rank among interviewed so far. The graders have to select, each of them, exactly one item, when it appears, and receives a payoff which is a function of the unobserved realization of random variable assigned to the item or its rank. When there is only one grader the optimal strategy for wide class of payoff functions has a threshold form. It means that in optimal behavior the decision maker should observe the fixed number of items $k^*$, a learning sample, and to choose the first one after which is better than all those previously observed. The optimality of the strategy is shown by optimal stopping methods for the Markov sequences. The experimental results have shown that the decision makers in problems like choice of partner, the best real investment, try to accept the reasonable option earlier than the optimal strategy of mathematical models suggest. The main aim of the research is to investigate the assumptions of the mathematical model to show their influence on the optimal threshold.