where M\Rj / K represents the set of players when world region Rj is replaced by K. Given this function, a reasonable expectation for K is the Shapley value (p^M^Rj / K^j of player K in this restricted game. This amount also represents the relative payoff, in game (N, U), of K if it would replace the world region Rj and bargain with the m-1 other world regions.
Using the measure of the relative payoff of each country of the world region Rj, we can define the sub-game [nr.,Wr^ of world region Rj by its characteristic function given in Eqs. (4), (6) and by:
Thus, each country Ch c Rj can obtain the amount (PhyNR . ,WR. j, which is the Shapley value of player h in the sub-game [nr. ,Wr. j. To determine the division of the amount received by the country Ch among the firms of this country, we use the same argument. Each firm / eCj,c Rj can obtain the amount (Pi[Nch )> which is the Shapley value of player / in the sub-game defined on country C^. Given this sub-game, we can define a
7 The possibility for a country to threaten the coalition allows us to compute its relative power and, hence, capture the lobbying force of this country.
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