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payoff function Y in which the share a firm ieC^cz Rj will receive is given by the following formula (Chantreuil, 2000):

fcM KczR j GczCh m\rj\ch\

RjiSChiKHG

With the five-world region game example, if we take into account the fact that players a and b act together, the payoff vector using the allocation rule m2 .„, f 1 3 111^ will be —. 1,24 24 6 6 2

2.3 The subsidiarity principle

Finally, we can define a third payoff function that assumes that the problem of the IT is only to determine the allocation of conservation funds to each world region. This assumption can be motivated by the principle of subsidiarity, which essentially means that the IT does not make decisions for the lower levels. Instead, the world region itself has to solve the allocations problems for the lower level(s). This is the most likely scenario to become practice. For example, Central Asia and South America blocs can be given allocations, and they in turn must decide how to allocate these blocks among their member countries. In this case, as discussed in section 2, the payoff vector we are looking for corresponds to the Shapley value of the quotient game (M,v) played by the delegates of each world region. The share every world region jsM will receive is given by:

ScM m' jtS

Once this payoff vector is defined, the IT considers the problem solved at the international level. Then, with respect to the principle of subsidiarity, each world region can choose its own conservation fund allocation process regardless of what the others do. We can set this problem of the division of the gain among the countries of a given world region in the form of a simple game. Hence, the share a country will obtain corresponds to the Shapley value of the game defined on the world region of interest.

Using the same argument for the allocation of conservation funds between competing conservation proposal within each country, we can define a payoff function VF3 in which the share a firm i, such as a conservation agency, ieQc Rj will receive is given by (see Mathurin,

GcCa HG

KdRj Ch£K

where ) ^e simple game defined on the country Q and

{nr. ,Vr . j is the simple game defined on the world region R.. With the five world regions game example, if we take into account the fact that players a and b act together, the payoff vector using the allocation rule ^F3

will be

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