Reduced game and converse consistency

http://dx.doi.org/10.1016/j.geb.2006.08.002

Reduced game and converse consistency

Chih Chang^a and Cheng-Cheng Hu^{b, ,
a}Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
^bCenter for General Education, Southern Taiwan University of Technology, No. 1, Nantai Street, Yung-Kang City, 71005 Tainan County, Taiwan
Received 17 August 2004. Available online 12 September 2006.

Abstract

The initiating points of the current paper are the axiomatic characterizations, in terms of consistency, of the equal allocation of nonseparable cost value (by Moulin), the Shapley value (by Hart and Mas-Colell), and the prenucleolus (by Orshan). The basic axioms are the same, but three different reduced games can be used to distinguish these three solutions. The main purpose of the paper is to illustrate that besides the definitions of reduced games are different, the axiom converse consistency also plays an important role to distinguish these three solutions.

Keywords: Shapley value; Prenucleolus; EANSC value; Reduced game; Consistency; Bilateral consistency; Converse consistency

JEL classification codes: C71