Ramsey, David M. and Szajowski, Krzysztof (2000): Bilateral Approach to the Secretary Problem. Published in: Annals of the International Society of Dynamic Games , Vol. 7, (2005): pp. 271284.
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Abstract
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 
Language:  English 
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 > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games 
Item ID:  19996 
Depositing User:  Krzysztof Szajowski 
Date Deposited:  16. Jan 2010 20:42 
Last Modified:  19. Feb 2013 11:29 
References:  Bellman, R. (1957) Dynamic Programming. Princeton Press. Dynkin, E.B. (1969) Game variant of a problem on optimal stopping. Soviet Math. Dokl., 10:270274. Enns, E.G., Ferenstein, E. (1985) The horse game. J. Oper. Res. Soc. Jap., 28:5162. Ferenstein, E.Z. (1992) Twoperson nonzerosum games with priorities. In: Ferguson, T.S., Samuels, S.M. editors, Strategies for Sequential Search and Selection in Real Time, Proceedings of the AMSIMSSIAM Join Summer Research Conferences held June 2127, 1990, Contemporary Mathematics, vol. 125, 119133, University of Massachusetts at Amherst. Fushimi, M. (1981) The secretary problem in a competitive situation. J. Oper. Res. Soc. Jap., 24:350358. Radzik, T., Szajowski, K. (1988) On some sequential game. Pure and Appl. Math. Sci, 28:5163. Radzik, T., Szajowski, K. (1990) Sequential games with random priority. Sequential Analysis, 9(4):361377. Ramsey, D., Szajowski, K. (2002) Random assignment and uncertain employment in optimal stopping of Markov processes. Game Theory and Appl., 7:147157. Ravindran, G., Szajowski, K. (1992) Nonzero sum game with priority as Dynkin's game. Math. Japonica, 37(3):401413. Sakaguchi, M. (1984) Bilateral sequential games related to the noinformation secretary problem. Math. Japonica, 29:961974. Sakaguchi, M. (1985) Nonzerosum games for some generalized secretary problems. Math. Japonica, 30:585603. Smith, M.H. (1975) A secretary problem with uncertain employment. J. Appl. Probab., 12:620624. Szajowski, K. (1994) Uncertain employment in competitive best choice problems. In: K.Ano, editor, International Conference on Stochastic Models and Optimal Stopping, Nagoya 1921.12.1994}, 112, 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):13921410. Yasuda, M. (1983) On a stopping problem involving refusal and forced stopping. J. Appl. Probab., 20:7181. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/19996 
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