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An allocation is in the core if there's no coalition that blocks it.

A strong equilibrium (Aumann, 1959) is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all members of the coalition.

How are these distinct? I usually don't think of the core as a solution concept, but I'm struggling to disentangle it from strong equilibrium.

Metta World Peace
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Shane
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  • By singleton action spaces, do you mean there's one good and the action choice is a quantity? That is, the action choice is a continuum, whereas in Aumann, the action space is a finite set? – Shane May 06 '15 at 16:29
  • Sorry, I got it wrong. They're not singletons, which should be two actions, which can be interpreted as, participate and, refuse to parcipate. I think, in this case, two solution concepts should be the same. – Metta World Peace May 06 '15 at 16:35
  • In Aumann's setting, the players forming the coalition can deviate by more than one way, and at least one of the corresponding strategy profile should be profitable in terms of the sum of payoffs of these deviant players for them. – Metta World Peace May 06 '15 at 16:39
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    That would make sense, but I thought the core was defined in richer environments also. Consider a housing allocation problem. I'm not sure how you would define an action space in this setting. So maybe that's the difference -- the core is more related to the social planner's (i.e. centralized) problem whereas the strong equilibrium relates to the decentralized problem. – Shane May 06 '15 at 16:44
  • Could you please specify what housing allocation problem is? – Metta World Peace May 06 '15 at 16:46
  • It's the question of how to allocate finitely many students to finitely many housing places, such that there's a fixed quota of students for each housing place and each student may only be assigned to one housing place. See http://web.stanford.edu/~niederle/HouseAllocation.pdf for an introduction. Hylland & Zeckhauser, JPE 1979, set it up well also. – Shane May 06 '15 at 16:49
  • You're right. In this question, a player's action space is a function of other players' chosen actions. It's similar to the problem of general equilibrium. – Metta World Peace May 06 '15 at 16:56
  • But in your second paragraph, strong equilbirum is a Nash equibrium with more stringent conditions, which means action spaces should be predetermined. So I think strong equilibrium is not applicable to housing allocation problem. – Metta World Peace May 06 '15 at 17:03
  • But you should aware, the notion of Nash equilibrium is not applicable to a problem in which a player's action space is determined by other players' actions. – Metta World Peace May 06 '15 at 17:07
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    OK - thank you. If you want to synthesize your comments into an answer, I'll accept it. – Shane May 06 '15 at 17:28
  • I have a similar question. First, I think I know why Core is a solution concept. As stated in Chwe (1994), if structure a is directly dominated by b via group S and S is capable of moving to b, structure a cannot be stable. But I also can not clearly distinguish the definitions of core and strong nash equilibrium. Maybe, the core just prevents the deviations via "effective groups"? – dre wang Apr 15 '22 at 03:52

1 Answers1

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Strong Nash equilibrium is different from core mainly because of communication. In a Strong Nash, unlimited private communication is allowed. The core is a concept that is linked to Coalition-proof Nash equilibrium rather than Strong Nash. People can freely communicate but cannot make binding commitment before deciding.

In some games, both happen to be the same, but in generality, the core is a concept derived from Coalition-proof Nash equilibrium rather than from Strong Nash Equilibrium.

VicAche
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