Econometrica: Mar, 1981, Volume 49, Issue 2

A Social Coalitional Equilibrium Existence Lemma

https://doi.org/0012-9682(198103)49:2<369:ASCEEL>2.0.CO;2-7
p. 369-377

Tatsuro Ichiishi

The purpose of this paper is to construct an abstract model of a society in which each member can cooperate with others by forming a coalition, but at the same time can be influenced by the members outside the coalition. A new concept of equilibrium, called here a social coalitional equilibrium, is proposed, and a sufficient condition for its existence provided. The social coalitional equilibrium may be considered a synthesis of the Nash equilibrium (a noncooperative solution concept) and the core (a cooperative solution concept). The paper provides a broadly applicable mathematical tool for proving existence of equilibrium for models of labor-managed market economies.