Resumen de Aggregation and Disaggregation of European Players in the IMF Compound Games

Carlos Bowles

• We address the question of the desirability of the merger of the representatives of European States at the International Monetary Fund using the classical concept of value from cooperative game theory. We decompose the whole game into a main quotient game (the Executive Directors� Game) and different subgames (the European and Constituencies ones). The classical composition of games being here inadequate, we axiomatically define a new product operator on the space of simple games. Under this new product, it is shown that the value of the product of the games is equal to the product of the values of the subgames and the quotient game. Using the probabilistic representation of values, we provide a formal interpretation of this product as an independence assumption with respect to the probability of coalition formations between the different games that identifies our restriction as an orthogonality condition.

  This property leads to the nice feature that it becomes possible to aggregate and disaggregate easily the value of the whole game, depending on the kind of player, European Union or European States, we want to consider.