Core of a Game

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Definition: Core of a Game

In game theory, individuals tend to form coalitions because the return that they would get individually on forming the coalition which acts on its own behalf is more than what they would get individually on division of the total amount among all the players. Therefore they would be better off forming a coalition rather than opting for benefit of all the players.

The allocation under game theory is said to have a core when none of these coalitions are feasible. I.e. all the feasible allocations form the core of game theory.

An allocation is said to have a core when:

Here: xi is the individual return and

          v (C) is the return through the coalition

 

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