On Existence of alpha-Core Solutions for Games with Finite or Infinite Players

TL;DR

This paper establishes new existence results for alpha-core solutions in both finite and infinite player games, introducing P-open conditions and linking to fixed point theorems, thereby broadening the theoretical understanding of core solutions.

Contribution

It introduces P-open and strong P-open conditions for games without ordered preferences, proving existence of alpha-core solutions in infinite-player games and connecting to fixed point theorems.

Findings

Existence of alpha-core solutions under P-open conditions.

Extension of alpha-core existence to infinite-player games.

Equivalence of Kajii's theorem to Browder's fixed point theorem.

Abstract

This gives two existence results of alpha-core solutions by introducing P-open conditions and strong P-open conditions into games without ordered preferences. The existence of alpha-core solutions is obtained for games with infinite-players. Secondly, it provides a short proof of Kajii's (Journal of Economic Theory 56, 194-205, 1992) existence theorem for alpha-core solutions, further, the Kajii's theorem is equivalent to the Browder fixed point theorem. In addition, the obtained existence results can include many typical results for alpha-core solutions and some recent existence results as special cases.