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Equilibrium uniqueness in aggregative games: very practical conditions
- Source :
- Optimization Letters, 16(7), 2033-2058, Optimization Letters 16 (2022) 7
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has $$\mathbb {R}_+$$ R + as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten–Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games.
- Subjects :
- Computer Science::Computer Science and Game Theory
Class (set theory)
Control and Optimization
0211 other engineering and technologies
WASS
02 engineering and technology
Oligopoly
symbols.namesake
Contest game
Selten–Szidarovszky technique
0502 economics and business
Uniqueness
Mathematics
Smoothness
021103 operations research
05 social sciences
Stochastic game
TheoryofComputation_GENERAL
Pseudo-concavity
Urban Economics
Discontinuity (linguistics)
Equilibrium (semi-)uniqueness
Nash equilibrium
Aggregative game
symbols
Business, Management and Accounting (miscellaneous)
050206 economic theory
Nikaido–Isoda theorem
Mathematical economics
Subjects
Details
- ISSN :
- 18624480 and 18624472
- Volume :
- 16
- Database :
- OpenAIRE
- Journal :
- Optimization Letters
- Accession number :
- edsair.doi.dedup.....34df7b06ed7ccefcde05def86a7546ac