The Fondazione Eni Enrico Mattei series on Economics, the Environment and Sustainable Development
Edited by Carlo Carraro
Chapter 1: Advances in the theory of large cooperative games and applications to club theory; the side payments case
Alexander Kovalenkov and Myrna Wooders 1. INTRODUCTION While the notion that individuals will act in their own self interests is fundamental to game theory and also to economics, the notion that if there are potential gains to be realized from cooperation then individuals will attempt to capture these gains is also fundamental. Indeed, the economic notion of the contract curve – the set of outcomes of trade for a two-person, two-commodity private goods exchange economy with the properties that each person’s trade is individually rational and the outcome cannot be improved upon by both traders acting together – already appears in Edgeworth (1881). In his seminal work, Edgeworth showed that the contract curve converges to the set of allocations arising from price-taking economic equilibrium. The game-theoretic notion of the core as the set of payoﬀs of a game that cannot be improved upon by any coalition, as a solution concept for cooperative games, was developed by Shapley (1952) and Gillies (1953). Since Shubik’s (1959) seminal paper highlighting the relationship between the core and the contract curve, the study of the core has generated numerous papers in both economics and in game theory. The most celebrated of these works are Debreu and Scarf (1963), showing that the core of an exchange economy, represented by allocations of commodities to individual traders, converges to the set of outcomes of price-taking economic equilibrium, a formalization and extension of Edgeworth’s result, and Aumann (1964), further extending Edgeworth’s insight in the context of a game with a...
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