Stable coalition formation through bargaining for the preservation of public goods

Elvio Accinelli, Atefeh Afsar, Filipe Martins, José Martins, Bruno Oliveira, Alberto A. Pinto and Luis Quintas
Additional contact information
Elvio Accinelli: Facultad de Economia, Universidad Autonoma de San Luís Potosí, México
Atefeh Afsar: Mathematics Department, Allen University, Columbia, SC, United States
Filipe Martins: University of Coimbra, CeBER and Faculty of Economics
José Martins: LIAAD INESC TEC, Escola Superior de Tecnologia e Gestão, Politecnico de Leiria
Bruno Oliveira: LIAAD INESC TEC, Faculdade de Ciências da Nutrição e Alimentação, Universidade do Porto
Alberto A. Pinto: LIAAD–INESC TEC, Departmento de Matemática, Faculdade de Ciências, Universidade do Porto
Luis Quintas: Universidad de La Punta, San Luis, Argentina

No 2025-03, CeBER Working Papers from Centre for Business and Economics Research (CeBER), University of Coimbra

Abstract: Baliga and Maskin introduced a model of contributions for the provisions of public goods such as contributing for the reduction of air pollution. In this work we consider an extended version of Baliga and Maskin's model with a parameter a which is the elasticity of the benefit function, and with heterogeneous agents, each with their own preferences for the good. For this generalized version of the model, we consider the formation of stable coalitions which are absorbing states of a bargaining Markov chain, where agents join or leave coalitions according to their cooperation and free-riding incentives. We show that there is a stable high coalition consisting of the set of agents most preferring/valuing the public good. The increase of the elasticity parameter a increases the size of the stable high coalition that changes from a single member (called the competitive coalition as appearing in Baliga and Maskin's paper) to the grand coalition involving all agents. However, the utility of members of the stable coalition can be very small when compared to the utility of the free-riders, rendering the formation of stable coalitions difficult. We show that a variant of the coalition folk theorem holds, meaning that member heterogeneity will tend to decrease the size of stable coalitions. We show that the formation of stable coalitions is subject to the paradox of cooperation, since even when stable coalitions are large and free-riders have not very low preferences for the public good, the utility of the stable coalition may still be low when compared to the full cooperation scenario of the grand coalition. However, the paradox does not hold when the free-riders have a very low preference for the public good, which also facilitates the spontaneous formation of stable coalitions, or when there are no free-riders and the grand coalition is stable, which is always the case when the elasticity a is large enough.

Keywords: public and common goods; free-riding; coalitions; stability; Barrett's paradox of cooperation; Markov chains (search for similar items in EconPapers)
JEL-codes: C7 D7 H4 (search for similar items in EconPapers)
Pages: 48 pages
Date: 2025-05
New Economics Papers: this item is included in nep-cdm and nep-upt
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