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From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem. (English) Zbl 1353.91013

Summary: The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of \(N\) player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article, we emphasize the role of optimal transport theory in (i) the passage from Nash to Cournot-Nash equilibria as the number of players tends to infinity and (ii) the analysis of Cournot-Nash equilibria.

MSC:

91A44 Games involving topology, set theory, or logic
91A07 Games with infinitely many players
91A06 \(n\)-person games, \(n>2\)
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[1] Nash, PNAS 36 (1) pp 48– (1950) · Zbl 0036.01104
[2] 34 pp 1– (1966) · Zbl 0142.17201
[3] 32 pp 39– (1964) · Zbl 0137.39003
[4] C R MATH ACAD SCI PARIS 343 pp 619– (2006) · Zbl 1153.91009
[5] C R MATH ACAD SCI PARIS 343 pp 679– (2006) · Zbl 1153.91010
[6] JPN J MATH 2 pp 229– (2007) · Zbl 1156.91321
[7] 7 pp 295– (1973) · Zbl 1255.91031
[8] J MATH ECON 3 pp 201– (1984) · Zbl 0545.62068
[9] SIAM J MATH ANAL 29 pp 1– (1998) · Zbl 0915.35120
[10] DUKE MATH J 156 pp 229– (2011) · Zbl 1215.35045
[11] ARCH RATION MECH ANAL 209 pp 1055– (2013) · Zbl 1311.49053
[12] J NONLINEAR SCI 24 pp 93– (2013)
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