On effectivity functions of game forms

Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


To each game form g an effectivity function (EFF) Eg is assigned. An EFF E is called formal (formal-minor) if E = Eg (respectively, E ≤ Eg) for a game form g. (i)An EFF is formal iff it is superadditive and monotone.(ii)An EFF is formal-minor iff it is weakly superadditive. Theorem (ii) looks more sophisticated, yet, it is simpler than Theorem (i) and instrumental in its proof. In addition, (ii) has important applications in social choice, game, and even graph theories. Constructive proofs of (i) were given by Moulin, in 1983, and by Peleg, in 1998. Both constructions are elegant, yet, sets of strategies Xi of players i ∈ I might be doubly exponential in size of the input EFF E. In this paper, we suggest another construction such that | Xi | is only linear in the size of E. Also, we extend Theorems (i), (ii) to tight and totally tight game forms.

Original languageBritish English
Pages (from-to)512-531
Number of pages20
JournalGames and Economic Behavior
Issue number2
StatePublished - Mar 2010


  • Dual-minor
  • Effectivity function
  • Game form
  • Monotone
  • Self-dual
  • Superadditive
  • Tight
  • Totally tight
  • Weakly superadditive


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