*Wissenschaftliches Programm* *Liste der Vortragenden*

**Sektion 9**

Donnerstag, 21.09.2000,
16.00–16.20 Uhr, WIL C 133

#### Krzysztof Szajowski, Institute of Mathematics, Wroclaw University of Technology

In the paper the Dynkin zero sum stopping game is considered. The players observe a discrete time
Markov process. At each moment n the players decide separately if they accept or reject the realization of
the process. One of the player is choosing at most two states, the second one is choosing at most one
state. It means that Player 1 has pairs of stopping time as strategy and Player 2 is using the
stopping time as his strategy. The payoff function depends on all choosing states. If it happens
that more than one player has selected the same moment n to accept the state, then a lottery
decides which player gets the right (priority) of acceptance. A formal model of the game and
construction of the solution for the finite horizon game is given. The example related to the
secretary problem is solved. The model is generalization of the two person games considered by
Szajowski (1994) and N person game with fixed priority scheme solved by Enns and Ferenstein
(1987).

References

- K. Szajowski, Markov stopping games with random priority, Zeitschrift für Operations
Research 37 (1993), no. 3, 69–84.
- E. G. Enns and E. Z. Ferenstein, On a multi-person time-sequential game with priorities,
Sequential Analysis 6 (1987), 239 – 256.