A weak [formula omitted]-core existence theorem of games with nonordered preferences and a continuum of agents

Abstract

Inspired by Kajii (1992) and Askoura (2011, 2017), we introduce the notion of the weak α-core for games with nonordered preferences and a continuum of agents. First, we extend the work of Kajii (1992) to games with spaces of strategies defined on Hausdorff topological vector spaces. Furthermore, we prove the nonemptiness of the weak α-core. Finally, we establish the relations between normal-form games, games with nonordered preferences and games with pseudo-utilities.