ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 90 Mignanego, Fausto, Università Cattolica Milano, Italy Rationality of players and credibility of strategies in leaderfollower games. We consider a two persons game in [0, T] descirbed by the cost functtionals J_{1}(u, v) and J_{2}(u, v) for leader (L) and follower (F) respectively, u and v are the decisions of the two players.

γ(v) = \{ \begin{matrix}u^{d} if v = v^{d} \\ uˆ if v ≠ v^{d} \end{matrix} is the threatening strategy of L where

(u^{d}, v^{d}) is the L’s desired pair. IR= [(u, v) : J)2(u, v) < q] is the set of playable pairs. The game is repeated N times to give a dynamic structure. Often in letterature optimality and credibility are too much restrictive. We want to show that under a weaker definition of rationality of F and suitable definition of credibility, there exists a sequence T_{0}, ⋯ T_{n} such that (γ(v^{d}), v^{d}) minimizes J_{1} over IR and so it is acceptable also by F. Some applications to conflict in finance are given. References: Y. Zheng and Y. Ho, Credibility in Stackelberg games, Syst. and Control Lett. 5, (1984). V. Bure and O. Malafeyev, Some gametheoretical models of conflict in finance, Nova J. of Math., 6, (1996).