A Game-Theoretic Perspective on Coalition Formation by Debraj Ray

By Debraj Ray

The formation of coalitions to accomplish either collaborative and aggressive pursuits is a phenomenon we see throughout us. The checklist is lengthy and sundry: creation cartels, political lobbies, customs unions, environmental coalitions, and ethnic alliances are only a number of daily circumstances. Drawing upon and increasing his inaugural Lipsey Lectures on the collage of Essex, Debraj Ray seems at coalition formation from the point of view of online game conception. How are agreements decided? Which coalitions will shape? And are such agreements always effective from a social viewpoint? Ray brings jointly advancements in either cooperative and noncooperative video game thought to check the analytics of coalition formation and binding agreements. This booklet concentrates on natural thought, yet discusses numerous strength purposes, similar to oligopoly and the supply of public items.

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The examples illustrate well the use of partition functions that capture externalities across players. The payoff to a single “deviant” from the grand coalition is not defined in isolation: it is fully contextual and depends on what the other players do. A theory that encompasses such externalities will automatically be able to handle a variety of real-world applications, something that the traditional characteristic function cannot do. Closely related to this point is the role played by farsightedness.

Now consider player i in the game at hand. 14 Let i be the set of all probability distributions over coalitions S with i ∈ S (the choice of each coalition to be interpreted as the making of an acceptable offer to that coalition) as well as individuals j i (the choice of each j to be interpreted as the making of an unacceptable offer to that individual). Define to be the product over the i ’s. π stands for the coalition structure π with S appended to it. 14 There is no loss of generality in assuming that no unacceptable proposals are made to larger coalitions.

Consider a payoff vector u “pieced together” from a particular partition π, so that uS ∈ U(S, π) for every S ∈ π. Then it must be the case that there exists u ∈ U(N, {N}) such that u ≥ u. In short, the grand coalition can do everything a partition can. 28 Coalitions, Cooperation and Noncooperation Is that a good assumption? Very often it is, but very often it isn’t. 4 and Chapter 10 for more. 2 Examples. In this section, I list several examples of characteristic and partition functions. The examples are often impressionistic and not presented in a rigorous format.

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