Seminars and Events - Research Colloquia

Probability Seminar

Department of Statistics
and
Department of Mathematics

Monday, March 10, 2003
3:30 PM in REC 227

Professor Krzysztof Szajowski
Visiting Purdue University

will speak on

On Stopping Games Related to the Secretary Problem

Abstract
The aim of the paper is to present some results on stopping games, in particular on Dynkin games with an emphasis on the role of randomized stopping times in their solution and the examples related to the secretary problem. The Dynkin game can be thought of as a problem faced by 2 employers, who observe a series of candidates for a post and wish to employ the best candidate. Another example of a stopping game is as follows: 2 firms observe the state of a market. At some point a change occurs in the market and the firms, which react most quickly to the change, reap the benefits. The example of the continuous-time two person nonzero sum game extension of the best choice problem is discussed in details.

The objects appear according to the Poisson process with unknown intensity assumed to be exponentially distributed. Each player can choose only one applicant. If both players would like to select the same one, then the priority is assigned randomly. The aim of the players is to choose the best candidate. A construction of Nash equilibria for such game is given. The optimal stopping problem for such stream of option has been presented and solved by Bruss(1987). The considered game is an generalization of the discrete time finite horizon two person non-zero sum game with stopping of Markov process solved by the author (1993). The extension of the game to admit the sets of the randomized stopping times is taken into account. The Nash values for the randomized Nash equilibria is obtained. Analysis of the solutions for different lotteries are given.