Characterizing Compromise Stability of Games Using Larginal Vectors

CentER Discussion Paper Series No. 2011-058

21 Pages Posted: 28 May 2011

See all articles by Trine T. Platz

Trine T. Platz

University of Copenhagen - Department of Economics

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Marieke Quant

Tilburg University - Department of Econometrics & Operations Research

Date Written: May 25, 2011

Abstract

The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an order of the players and describes the efficient payoff vector giving the first players in the order their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. In this paper we describe two ways of characterizing sets of larginal vectors that satisfy the condition that if every larginal vector of the set is a core element, then the game is compromise stable. The first characterization of these sets is based on a neighbor argument on orders of the players. The second one uses combinatorial and matching arguments and leads to a complete characterization of these sets. We find characterizing sets of minimum cardinality, a closed formula for the minimum number of orders in these sets, and a partition of the set of all orders in which each element of the partition is a minimum characterizing set.

Keywords: Core, core cover, larginal vectors, matchings

JEL Classification: C71

Suggested Citation

Platz, Trine T. and Hamers, Herbert and Quant, Marieke, Characterizing Compromise Stability of Games Using Larginal Vectors (May 25, 2011). CentER Discussion Paper Series No. 2011-058. Available at SSRN: https://ssrn.com/abstract=1852349 or http://dx.doi.org/10.2139/ssrn.1852349

Trine T. Platz

University of Copenhagen - Department of Economics ( email )

Ă˜ster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Herbert Hamers (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Marieke Quant

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
11
Abstract Views
408
PlumX Metrics