The core of the game, the core of the game
The core of the game, the core of the game
Find an allocation that, cannot be improved upon by any coalition of players. [1]
The core of the game, the core of the game
The core of the game, the core of the game
Find an allocation that/ cannot be improved upon by any coalition of players
In a large economy/ with a continuum of players the core and the general equilibrium prices coincide
None will complain,[2] what a beautiful
None will complain, what a beautiful
None will complain, what a beautiful thing!
The core of the game, the core of the game
The core of the game, the core of the game
The core of the game, the core of the game
In a large replica economy, core and the general equilibrium prices coincide[3]
The core of the game, the core of the game
The core of the game, the core of the game
The core of the game, the core of the game
The core of the game, the core of the game
None will complain, what a beautiful
None will complain, what a beautiful
None will complain, what a beautiful
None will complain, what a beautiful, thing!
The core of the game, the core of the game
The core of the game, the core of the game
The core of the game, the core of the game
Find an allocation that, find an allocation that,
cannot be improved upon, by any coalition of players.
*Text by Marco Marini. Music by Marco Marini, Elisa Pezzuto and Valter Sacripanti. All rights reserved.
Voices: Marco Marini, Elisa Pezzuto. Guitars: David Pieralisi, Marco Marini, Bass: David Pieralisi. Drum: Valter Sacripanti,
Production: Valter Sacripanti. Mastering: Fabrizio De Carolis.
[1] The core is a game theory solution concept that identifies a stable allocation of payoffs among players. In simple terms is a set of outcomes such that no group (coalition) of players can deviate and achieve a better payoff for all its members and, hence, where no coalition has an incentive to break away from the grand coalition. The idea is seminally attributed to the Anglo-Irish economist Francis Y. Edgeworth (1845-1926) when illustrating feasible allocations not improvable by individuals or groups of traders (1921). Later on, such a concept was generalized as “core of a cooperative game” (1959) by the Canadian computer scientist and mathematician Donald B. Gillies (1928-1975).
[2] Since the core is a solution concept that identifies stable payoff allocations among players, namely set of outcomes that no group of players can deviate from achieving a better payoff for all its members, in this situation no player can reasonably complain.
[3] Robert J. Aumann's (1964) core equivalence theorem states that the set of core allocations in an atomless economy (e.g. an economy with a continuum of players) coincides with the set of Walrasian equilibrium allocations, characterized by a general equilibrium price vector.
REFERENCES
Robert J. Aumann (1964), “Markets with a Continuum of Traders”, Econometrica, 1/2, No.1, 2 pp. 39-50.
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