The nucleolus and the tau-value of interval games

P. 421–430.

Yanovskaya E. B.

Interval cooperative games are models of cooperative situation where only bounds for payoffs of coalitions are known with certainty. The extension of solutions of classical cooperative games to interval setting highly depends on their monotonicity properties. However. both the prenucleolus and the tau-value are not aggregate monotonic on the class of convex TU games Hokari (2000, 2001). Therefore, interval analogues of these solutions either should be defined by another manner, or perhaps they exist in some other class of interval games. Both approaches are used in the paper: the prenucleolus of a convex interval game is defined by lexicographical minimization of the lexmin relation on the set of joint excess vectors of lower and upper games. On the other hand, the tau-value is shown to satisfy extendability condition on a subclass of convex games -- on the class of totally positive convex games. The interval prenucleolus is determined , and the proof of non-emptiness of the interval \tau-value on the class of interval totally positive games is given.

 

Keywords: кооперативная игра, пред n-ядро, convex game, выпуклая игра, interval game, интервальная игра, cooperative game, tau-value, tau-значение

In book

Contributions to game theory and management

Issue 3. , St. Petersburg: Graduate School of Management, St. Petersburg University, 2010.