On the Consistency of Weak Equilibria in Multicriteria Extensive Games

Denis Kuzyutin

Authors

Denis Kuzyutin Saint Petersburg State University

Abstract

This paper considers weak equilibria properties for multicriteria n-person extensive games. It is shown that the set of subgame perfect weak equilibriums in multicriteria games with perfect information is non-empty, however one can not use the backwards induction procedure (in the direct way) to construct equilibria in multicriteria extensive game. Furthermore, we prove that weak equilibria satisﬁes time consistency in multicriteria extensive games (with perfect or incomplete information).

Keywords:

multicriteria games, extensive games, equilibria, time consistency

Downloads

Download data is not yet available.

References

Borm, P. , Megen F. and Tijs, S. (1999). A perfectness concept for multicriteria games. Mathematical Methods of Operation Research, 49, 401–412.

Fahretdinova, V. (2002). Positional games with vector payoﬀs (in Russian). MKO-10, 151–153.

Kuhn, H. (1953). Extensive games and the problem of information. Annals of Mathematics Studies, 28, 193–213.

Kuzyutin, D. and Nikitina, M. (2011). On the consistency of equilibria in multicriteria extensive games. The Fifth International Conference ”Game Theory and Management”, SPbGU, 144–145.

Nash, J. (1950). Equilibrium points in n-person games. Proc. Nat. Acad. Sci., USA, 36, 48–49.

Petrosjan, L. and Kuzyutin, D. (2008). Consistent solutions of positional games (in Russian). Saint Petersburg University Press.

Petrosjan, L. and Puerto, J. (2002). Folk theorems in multicriteria repeated n-person games. Sociedad de Estadistica e Investigation Operativa Top, Vol. 10, No. 2, 275–287.

Shapley, L. (1959). Equilibrium points in games with vector payoﬀs. Naval Research Logis tics Quarterly, P. 57–76.

Zhukovskiy, V. and Salukvadze, M. (1994). The vector-valued maximin. N.Y., Academic Press.