## The Model

Table 10-3 in Chapter 10 provides the indicator ("OECD Value of Agricultural Production ascribed to Primary Centers of Diversity") that could be used to distribute PGRFA conservation funds between regions. However, this indicator, or any other, can only be a rough guide. For example, players may attempt to utilize bargaining power and form blocks in order to receive a larger allocation than suggested by this indicator. We present an analytical framework for modeling this process.

To determine the allocation of initial allowances that explicitly accounts for heterogeneity across the players, we propose a payoff function, denoted as (p, that is derived from an n-person cooperative games construct. Application of this construct to the world regional level implies that the

3 In the manner of Rose et al. (1998), equity in our context refers to the distributional justice of the initial allocation of the conservation funds across countries, i.e., international equity.

determination of such an allocation can be achieved if all regions agree to delegate their decision power—over the definition of the agenda and the type of PGRFA benefits distribution system that can be implemented—to an international institution. In other words we suppose that all world regions accept the fact that the IT has to allocate the initial endowments to each world region. Hence, the problem of the allocation of conservation funds can be set in the form of a simple game in characteristic function form (N, U), i.e., with side payments, where N is the set of players (i.e., world region) and U is the characteristic function of the game.4 In the context of the negotiations over the distribution of PGRFA conservation funds, this side payment assumption expresses the possibility for world regions to form blocks in receiving the aggregate funds of the world regions forming the block. The characteristic function sums up all possible utility sets of every coalition S C N . For example, if population is the relevant criterion, we need to be able to calculate it for all possible coalitions. If PO(S) represents the population of coalition S, we have the following simple game with the characteristic function U(S):

with 0 < (3 < 1. For example, a value of (3 = 0.5 means that a coalition S can obtain the total conservation fund if its primary center of diversity value is equal or greater that 50% of the value of the IT membership, PO(N) . In other words, ¡3 reflects a hypothesis regarding the level of bargaining power coalitions can achieve. With the function above, while noting that bargaining power is a function of the initial allocations, bargaining power is decreasing in ¿3.

Given this framework, the Shapley allocation approach is particularly useful to solving the model (Roth, 1998; Mas-Colell, Whinston, and Green, 1995). This normative concept attempts to describe a fair way to allocate gains from cooperation, given the strategic realities captured by the characteristic form. The Shapley value in our case represents the final distribution of initial allocation of the conservation funds between all world regions.

While a lengthy discussion of Shapley values is outside the scope of this chapter, the concept is briefly described here. The Shapley value summarizes

4 The side payment assumption implies the existence of commodities that are linearly transferable. In other words, the utility functions for the individuals can be chosen so that the rate of transfer of utility among any two of them is 1:1. Hence, the total utility obtainable by a coalition S can be divided among the members of this coalition in any number of possible ways.

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