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Equilibrium points for three games based on the Poisson process

Published online by Cambridge University Press:  14 July 2016

M. T. Dixon
M. T. Dixon*
Affiliation:
University of Cambridge
*
∗ Present address: 18 Orwell Close, St. Ives, Huntingdon, Cambs PE 17 6FP, UK.
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Abstract

An arbitrary number of competitors are presented with independent Poisson streams of offers consisting of independent and identically distributed random variables having the uniform distribution on [0, 1]. The players each wish to accept a single offer before a known time limit is reached and each aim to maximize the expected value of their offer. Rejected offers may not be recalled, but they are passed on to the other players according to a known transition matrix. This paper finds equilibrium points for two such games, and demonstrates a two-player game with an equilibrium point under which the player with the faster stream of offers has a lower expected reward than his opponent.

Keywords

OPTIMAL STOPPINGSEQUENTIAL GAMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 627 - 638
Copyright
Copyright © Applied Probability Trust 1993 

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References

[1] Enns, E. G. and Ferenstein, E. Z. (1989) A competitive best choice problem with Poisson arrivals. J. Appl. Prob. 27, 333–342.Google Scholar
[2] Enns, E. G. and Ravindran, K. (1989) A two Poisson stream competitive decision problem. Preprint.Google Scholar
[3] Majumdar, A. A. K. (1987) Optimal stopping for a full-information bilateral sequential game related to the secretary problem. Math. Japonica 32, 63–74.Google Scholar
[4] Neveu, J. (1975) Discrete Parameter Martingales. North-Holland, Amsterdam.Google Scholar
[5] Sakaguchi, M. (1989) Multiperson multilateral secretary problems. Math. Japonica 34, 459–473.Google Scholar
[6] Sakaguchi, M. (1991) Sequential games with priority under expected value maximization. Math. Japonica 36, 545–562.Google Scholar