Equilibrium uniqueness in aggregative games: very practical conditions
| Autor: | Pierre von Mouche, Jun-ichi Itaya |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
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 |
| Zdroj: | Optimization Letters, 16(7), 2033-2058 Optimization Letters 16 (2022) 7 |
| ISSN: | 1862-4480 1862-4472 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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