The Shapley Value in One-to-One Markets with Homogeneous Goods: An Application to the CO2 Emissions Trading System

Abstract

This thesis aims to derive an alternative formula for the Shapley Value in one-to-one markets with homogeneous goods, also known as Böhm-Bawerk markets. The formula is expressed in terms of the valuations of both buyers and sellers, considering all possible coalitions formation orders. As a corollary, we also compute a closed-form formula when goods are homogeneous for the Banzhaf Value. We provide the corresponding functions in R, enabling easy calculation of both índices and representing a significant computational improvement. To illustrate the applicability of these cooperative solution concepts, we analyze the CO2 emissions trading market, where buyers (airlines) purchase credits from sellers (sustainable projects such as reforestation or renewable energy initiatives). Our focus is on the European Union context, ending in a game involving 54 players in total. We compute the optimal matching, the distribution of bargaining powers and payoffs, and the exchange price at which the transactions take place for each pair.