Two different approaches in cooperative games give - essentially - the same solution

What is it about?

There are a number of competing views on how to solve cooperative games: games where people share resources to reach common goals. One (the core) is based on the idea that a solution is only acceptable if all groups of players are happy. Earlier research found that (1) if such a solution exists, it can be obtained by a coalitional bargaining process (2) such solutions may not exist and (3) even if it does not exist, the coalitional bargaining process will rule out most of the outcomes. The other approach is based on standards of behaviour: a certain behaviour is only accepted if (1) there is no better accepted alternative and (2) for each behaviour there is a preferred acceptable behaviour. Finding such standards is not easy and they may not even exist. A natural generalisation considers indirect preferences and finds that for coalitional games this coincides with the core - provided this is not empty. The main result of this paper shows that the two approaches are - essentially - the same.

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Photo by WrongTog on Unsplash

Photo by WrongTog on Unsplash

Why is it important?

There is a plethora of cooperative game theoretic solution concepts and any result that puts order in this jungle is of great help. For dynamic cooperative games, that is, where there are group-based improvements, there are fewer concepts and they all look a bit similar. Finding this link between two of them, both published in some of the leading journals of the field makes them even stronger contenders.

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