David M., Ramsey and Krzysztof, Szajowski (2000): Bilateral Approach to the Secretary Problem. Published in: Annals of the International Society of Dynamic Games , Vol. 7, (2005): pp. 271-284.
Download (232kB) | Preview
A mathematical model of competitive selection of the applicants for a post is considered. There are N applicants of similar qualifications on an interview list. The applicants come in a random order and their salary demands are distinct. Two managers, I and II, will interview them one at a time. The aim of the manager is to obtain the applicant which demands minimal salary. The candidate can be accepted only at the moment of its appearance. When both manager want to accept the same candidate, then some rule of assignment to one of the manager is applied. Any candidate hired by the manager will accept the offer with some given probability. An candidate can be hired only at the moment of its appearance. At each moment n one candidate is presented. The considered problem is a generalisation of <i best choice problem></i> the best choice problem with uncertain employment and the game version of it with priority or random priority. The general stopping game model is constructed. The algorithms of construction of the game value and the equilibrium strategies are given. An example is solved.
|Item Type:||MPRA Paper|
|Original Title:||Bilateral Approach to the Secretary Problem|
|English Title:||Bilateral Approach to the Secretary Problem|
|Keywords:||optimal stopping problem, game variant, Markov process, random priority, secretary problem|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory
|Depositing User:||Krzysztof Szajowski|
|Date Deposited:||13. Jan 2010 02:01|
|Last Modified:||19. Feb 2013 06:59|
Bellman, R. (1957) Dynamic Programming. Princeton Press.
Dynkin, E.B. (1969) Game variant of a problem on optimal stopping. Soviet Math. Dokl., 10:270-274.
Enns, E.G., Ferenstein, E. (1985) The horse game. J. Oper. Res. Soc. Jap., 28:51-62.
Ferenstein, E.Z. (1992) Two-person non-zero-sum games with priorities. In: Ferguson, T.S., Samuels, S.M. editors, Strategies for Sequential Search and Selection in Real Time, Proceedings of the AMS-IMS-SIAM Join Summer Research Conferences held June 21-27, 1990, Contemporary Mathematics, vol. 125, 119-133, University of Massachusetts at Amherst.
Fushimi, M. (1981) The secretary problem in a competitive situation. J. Oper. Res. Soc. Jap., 24:350-358.
Radzik, T., Szajowski, K. (1988) On some sequential game. Pure and Appl. Math. Sci, 28:51-63.
Radzik, T., Szajowski, K. (1990) Sequential games with random priority. Sequential Analysis, 9(4):361-377.
Ramsey, D., Szajowski, K. (2002) Random assignment and uncertain employment in optimal stopping of Markov processes. Game Theory and Appl., 7:147-157.
Ravindran, G., Szajowski, K. (1992) Non-zero sum game with priority as Dynkin's game. Math. Japonica, 37(3):401-413.
Sakaguchi, M. (1984) Bilateral sequential games related to the no-information secretary problem. Math. Japonica, 29:961-974.
Sakaguchi, M. (1985) Non-zero-sum games for some generalized secretary problems. Math. Japonica, 30:585-603.
Smith, M.H. (1975) A secretary problem with uncertain employment. J. Appl. Probab., 12:620-624.
Szajowski, K. (1994) Uncertain employment in competitive best choice problems. In: K.Ano, editor, International Conference on Stochastic Models and Optimal Stopping, Nagoya 19-21.12.1994}, 1-12, Nagoya, Japan, 1994. Faculty of Business Administration, Nanzan University, Nanzan University.
Szajowski, K. (1995) Optimal stopping of a discrete Markov processes by two decision makers. SIAM J.~Control and Optimization, 33(5):1392-1410.
Yasuda, M. (1983) On a stopping problem involving refusal and forced stopping. J. Appl. Probab., 20:71-81.
Available Versions of this Item
- Bilateral Approach to the Secretary Problem. (deposited 13. Jan 2010 02:01) [Currently Displayed]