Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

Abstract: A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T ) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable.

Keywords: Domination; stable set; core; TU game

JEL-codes: C71

20 pages, June 15, 2020

Full text files

dpbe6_2020.pdf  Full text

Download statistics

• University of Southern Denmark, Department of Economics
• Home page for this series

Questions (including download problems) about the papers in this series should be directed to Astrid Holm Nielsen ()
Report other problems with accessing this service to Sune Karlsson ().

RePEc:hhs:sdueko:2020_006This page generated on 2024-09-13 22:17:01.