The core and the Weber set for bicooperative games
This paper studies two classical solution concepts for the structure of bicooperative games. First, we define the core and the Weber set of a bicooperative game and prove that the core is always contained in the Weber set. Next, we introduce a special class of bicooperative games, the so-called bisupermodular games, and show that these games are the only ones in which the core and the Weber set coincide.
AMS Subject Classification91A12
KeywordsBicooperative games Core Weber set Bisupermodular games
Unable to display preview. Download preview PDF.
- Bilbao JM (2000) Cooperative games on combinatorial structures. Kluwer, BostonGoogle Scholar
- Felsenthal D, Machover M (1997) Ternary voting games. Int J Game Theory 26:335–351Google Scholar
- Gillies DB (1953) Some theorems on n-person games. PhD Thesis, Princeton University Press, PrincetonGoogle Scholar
- Myerson RB (1991) Game Theory: analysis of conflict. Harvard University Press, CambridgeGoogle Scholar
- Rockafellar RT (1970) Convex analysis. Princeton University Press, PrincetonGoogle Scholar
- Schrijver A (1986) Theory of linear and integer programming. Wiley, New YorkGoogle Scholar
- Weber RJ (1988) Probabilistic values for games. In: Roth AE (eds) The Shapley value: essays in honor of Lloyd S. Shapley. Cambridge University Press, Cambridge, pp 101–119Google Scholar