Equilibrium uniqueness in aggregative games: very practical conditions

Jun Ichi Itaya, Pierre von Mouche*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


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 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.

Original languageEnglish
Pages (from-to)2033-2058
JournalOptimization Letters
Issue number7
Early online date20 Jul 2021
Publication statusPublished - Sept 2022


  • Aggregative game
  • Contest game
  • Equilibrium (semi-)uniqueness
  • Nikaido–Isoda theorem
  • Pseudo-concavity
  • Selten–Szidarovszky technique


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