[For the entire collection see Zbl 0553.00014.]
The author reports on recent work on the existence of Cournot-Nash equilibria in games with (i) a measure space of players, (ii) pay-offs generated by non-ordered binary relations, and (iii) strategy sets in Banach spaces. This work stems from the pioneering contributions of J. Nash [Proc. Natl. Acad. Sci. USA 36, 48-49 (1950)] and G. Debreu [Proc. Natl. Acad. Sci. USA 38, 886-893 (1952; Zbl 0047.388)]. For the record, however, it is worth stating that Debreu did not use the Kakutani fixed point theorem in his 1952 paper but rather its generalization due to Eilenberg and Montgomery. It is also worth mentioning that the problem left open in paragraphs 3 and 5 of the introduction to this paper has been independently solved by the author and Papageorgiou [Bureau of Economic and Business Research Faculty, Paper No.1126, Univ. of Illinois at Champaign], and Kim, Prikry and Yannelis [Center for Economic Research, Discussion Paper No.218, University of Minnesota at Minneapolis].