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What is the difference between nonhedonic and hedonic coalitional games?

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Hedonic coalition games are a variant of coalition building games in which each "player" has a defined preference list that ranks all possible coalitions that the player could be a member of in order of preference. In example, in a 4-person game with players (A,B,C,D), the preference list for player A could be represented as (AB> AC> ABCD> ABC> AD> ACD). This means that A would most prefer to be in collaboration singly with B and least prefer to be in coalition with C and D together.

The solution of a hedonic game is a partition of the set of players into groups that achieve game-theoretic stability, which can be defined in many ways.

Non-hedonic coalititonal games do not have a prefernce list of coalitions for each player. In these cases coalitions form between the players to accomplish tasks or win payoffs based in the attributes that each player may add to a coalition.

A solution in the sense of a non-hedonic game is a division of the payoff(s) among the players in the winning coalition, that is subject to a large body of constraints that among other things reward productive coalition members more than less productive members.

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