where m denotes the number of world regions; s , k, and g are the number of players in every coalition of world regions S , every coalition of countries K, every coalition of firms G , respectively; r. represents the number of countries in the world region R ; and ch is the number of firms in the country Ch.

Consider the example of the five world regions using the population criterion. If we take into account the fact that players a and b act together, the payoff vector using the allocation rule VF] will be [ —,—,—,—,— B 12 12 6 6 2

2.2 Strong threat and the quotient game lobbying principle

The payoff function in this section uses more information than in the first, given that here we need to know the amount a country can obtain by forming a coalition with other world regions, an amount that is different for each country. Hence, the degree of bargaining power varies among the countries, which produces the demand for lobbying activities. This bargaining procedure within world regions consists in accounting for the amount U(K) that every coalition K (such as KqRj, KeB2) can obtain itself and the amounts u(KuRqu...uRm) that K could obtain if it would replace world region Rj and form a coalition with one or more of the remaining world regions of Bl. A country can threaten to leave a coalition on the basis of being able to gain more elsewhere. Even thought this threat is never carried out, it can be used to compute the relative power of each country in a given world region, and to capture much of the "lobbying game" of countries at the international level.7

Formally, for any KdRj, and K' its complement relative to Rj, we define a restricted game M

Rj / K,VR ] as representing the quotient game (M,V) when K replaces the world region Rj in Bl. This restricted game is the formal representation of a bargaining situation which involves K and the other world regions. Its characteristic function is given by vRj/K{s) = u

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