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Social Choice and Welfare

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02-09-2015 | Original Paper

Cooperative decision-making for the provision of a locally undesirable facility

Authors: Stefan Ambec, Yann Kervinio

Published in: Social Choice and Welfare | Issue 1/2016

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Abstract

We consider the decentralized provision of a global public good with local externalities in a spatially explicit model. Communities decide on the location of a facility that benefits everyone but exhibits costs to the host and its neighbors. They share the costs through transfers. We examine cooperative games associated with this so-called Not In My Back-Yard problem. We derive and discuss conditions for core solutions to exist. These conditions are driven by the temptation to exclude groups of neighbors at any potential location. We illustrate the results in different spatial settings. These results clarify how property rights can affect cooperation and shed further light on a limitation of the Coase theorem.

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The total disutility that such a two-player coalition can guarantee to itself is at least $-$1: both members drop their garbage on the third player but may still get his or her garbage. Additionally, the disutility of the third agent is $-$2; hence the total disutility is $-$3: social efficiency is not achieved. Hence, players may not be able to reach an efficient outcome.

The argument is reproduced by Stearns (1993) with voting instead of bargaining as a collective decision process. In his example, a Condorcet cycle arises in a situation where three communities have to collectively decide where to site a nuclear waste repository.

Some of these projects feature non-excludability of the benefits at the origin of free-riding behaviors; others not. We will emphasize here the garbage game dimension of such problems, which is common to all.

Richman and Boerner (2006) define a NIMBY as follows “a socially desirable land use that broadly distributes benefits, yet is difficult or impossible to implement because of local opposition”.

Lejano and Davos (2001) also consider coalition formation in the NIMBY problem. In a numerical example, they argue that a compensation scheme that leaves the host indifferent may fail to be a core allocation.

Barbera et al. (2012) and Manjunath (2014) have examined single-dipped preferences for the location of an indivisible bad. They deal with non-transferable utility (no money involved) whereas we assume transferable utility: players can transfer part of their welfare through side-payments. Their focus is on the localization of the public bad with strategy-proof rules. In contrast, we abstract for information problems so that the public bad can easily be efficiently located. In our setting, localization impacts the value that a deviating coalition can achieve. It thus determines the distribution of the welfare through side-payments.

We insist on the interpretation of $\delta $ as the proportion of a neighbor’s pollution cost as compared to the host’s total cost. Formally, the latter may be the sum of a technical cost $c_{t}$ (construction, management, etc.) and a pollution cost $c_{p}$. If $\alpha $ denotes the multiplicative change in the pollution cost for the immediate neighbors, the additional cost for each of them is $\alpha c_{p}$. We then get $\delta =\alpha \frac{c_{p}}{c_{t}+c_{p}}$. So $\delta $ captures the change of pollution costs with distance, as well as the share of pollution costs in the host’s total costs.

For instance, the NIMBY problem with three players defined by $b_1=b_2=b_3=2$, $c_{11}=c_{22}=c_{33}=1$, $c_{12}=c_{23}=c_{31}=1$, and $c_{21}=c_{32}=c_{13}=3$ does not lead to a superadditive TU-game. Indeed, we have $v(\{1,2,3\})=1<v(\{1,2\})+v(\{3\})=2+1=3$.

For instance, in the case of TU-games with three players, the cooperative game induced by a NIMBY problem with three communities, benefit ${\varvec{b}}$, and cost matrix ${\varvec{C}}$ has the following characteristic function:

$$\begin{aligned} v(\{i\})= & {} max(0,b_{i}-c_{ii}),i\in \{1,2,3\}\\ v(\{i,j\})= & {} max(0,b_{i}+b_{j}-\min (c_{ii}+c_{ij},c_{jj}+c_{ji})), i \ne j\\ v(\{1,2,3\})= & {} b_1+b_2+b_3-\min (c_{11}+c_{12}+c_{13},c_{21}+c_{22}+c_{23},c_{31}+c_{32}+c_{33}) \end{aligned}$$

Consider the TU-game represented by $v(\{i\})=1$, $v(\{i,j\})=0$ ($i \ne j$), $v(\{1,2,3\})=2$. It is easy to check that no vector of benefits ${\varvec{b}}$ and cost structure ${\varvec{C}}$ can make the two characteristic functions coincide.

In the first case, excluding a community at the extremity of the line allows a cost $\delta c$ to be saved so that the total cost incurred by the coalition which excludes 1 or n is $(1+\delta )c$. Yet the coalition loses the benefit b from the excluded community so that the total benefit is $(n-1)b$. In the second case, by excluding two communities that are neighbors of a middle-community i, the coalition can save the two external costs $2\delta c$ by locating the facility at i, although they loose the benefit of the two neighbors from using the facility so that the total benefit is $(n-2)b$.

A collection $\mathcal {B}$ of coalitions is said to be balanced if and only if there exist strictly positive weights ${\varvec{\chi ^{\mathcal {B}}}}=(\chi _{S}^{\mathcal {B}})_{S\in \mathcal {B}}$ such that, for any $i\in N,$ $\sum _{S\in \mathcal {N}:i\in S}\chi _{S}^{\mathcal {B}}=1$.

As not all TU-games can be represented as NIMBY cooperative games without outside cooperation, this condition cannot be expressed for any TU-game.

Other meaningful quantities could be defined in this context. For instance, Le Breton et al. (2013) focus on the least core-value in problems of local public-project provision and financing. This value quantifies the minimal tax required on deviating coalitions for stabilizing the grand coalition. In this line, the cost of stability (Bachrach et al. 2009), quantifies the minimal subsidy to the grand coalition required to stabilize it. However, neither of them has a clear explicit form in the NIMBY cooperative game.

Note that Assumption 2 is always satisfied in the uniform linear case.

Two comments are called for here. First, our restricting the attention to the set of rational decisions is in contrast with the standard approach of the $\alpha $-core and $\beta $-core which respectively consider what a coalition can achieve regardless of the behavior of outside members or when having the possibility to adjust to others actions. Consistently with a remark by Laffont (1977) in the context of the garbage game, the $\alpha $-core would never be empty in our context. Second, in our case, location decisions are independent. Yet, in the case of non-excludable benefits, strategic interactions would arise among coalitions for the provision of facilities.

On the cooperative aspects, these rules respectively correspond to the $\underline{N}$-exogenous and the $\bar{N}$-exogenous rules in Bloch and van den Nouweland (2014).

Along with Assumption 1, it emphasizes a crucial feature for our results to hold: neighborhoods should be sufficiently smaller than their complementary to induce different building decisions. For this reason, our results apply to local pollution at the scale of N.

If two communities neighboring a community i with $1<i<n$ share a facility, they incur the hosting cost but no external cost for a benefit of 2b.

We thank a referee for suggesting this point.

This exercise emphasizes a limitation in the model: in order to compute the cost matrix ${\varvec{C}}$, a hypothesis has to be made on where the facility would be located within a given municipality regardless of the coalition it belongs to. In this example, we chose the centroids of the municipalities. In a more general framework, we could expect coalitions to have some flexibility in the location choice. By increasing the value of all coalitions, such flexibility would strengthen requirements for non-emptiness. It would yield complications but, in our view, few more insights.

We assume here that $|\overset{\circ }{\mathcal {N}}(h)|>0$. If it is not, the core is always non-empty ($\bar{\delta }({\varvec{G}})=+\infty $).

Aivazian VA, Callen JL (1981) The Coase theorem and the empty core. J Law Econ 24(1):175–181CrossRef

Aumann RJ (1967) A survey of cooperative games without side payments. In: Shubik M (ed) Essays in mathematical economics. Princeton University Press, pp 3–27

Bachrach Y, Elkind E, Meir R, Pasechnik D, Zuckerman M, Rothe J, Rosenschein JS (2009) The cost of stability in coalitional games. In: SAGT’ 09:2nd international symposium on algorithmic game theory, pp 122–134

Balinski M (1970) On the maximum matching set, minimal covering. In: Proceedings of the Princeton symposium on mathematical programming

Barbera S, Berga D, Moreno B (2012) Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc Choice Welfare 39(2–3):335–352CrossRef

Bergstrom T, Blume L, Varian H (1986) On the private provision of public goods. J Public Econ 29:25–49CrossRef

Bloch F, van den Nouweland A (2014) Expectation formation rules and the core of partition function games. Games Econ Behav 88:339–353CrossRef

Chander P, Tulkens H (1997) The core of an economy with multilateral environmental externalities. Int J Game Theor 26:379–401CrossRef

Coase RH (1960) The problem of social cost. J Law Econ 3:1–44CrossRef

De Clippel G, Serrano R (2008) Marginal contributions and externalities in the value. Econometrica 76(6):1413–1436CrossRef

Dehez P (2013) Cooperative provision of indivisible public goods. Theor Decis 74:13–29CrossRef

Goemans MX, Skutella M (2004) Cooperative facility location games. J Algorithm 50:194–214CrossRef

Laffont JJ (1977) Effets externes et théorie économique. Collection Monographies du Séminaire d’Econométrie. éditions du CNRS, Paris

Laurent-Lucchetti J, Leroux J (2010) Lindhal prices solve the NIMBY problem. Econ Bull 30(3):2457–2463

Laurent-Lucchetti J, Leroux J (2011) Choosing and sharing. Games Econ Behav 73(1):296–300CrossRef

Le Breton M, Weber S (1995) Stability of coalition structures and the principle of optimal partitioning. In: Barnett W, Moulin H, Salles M, Schofield N (eds) Social choice,welfare and ethics, Cambridge University Press, Cambridge, pp 301–319

Le Breton M, Weber S (2003) The art of making everybody happy: how to prevent a secession. IMF Staff Pap 50:403–435

Le Breton M, Moreno-Ternero JD, Savvateev A, Weber S (2013) Stability and fairness in models with a multiple membership. Int J Game Theor 42:673–694CrossRef

Lejano RP, Davos CA (2001) Siting noxious facilities with victim compensation: n-person games under transferable utility. Socio Econ Plan Sci 35:109–124CrossRef

Manjunath V (2014) Efficient and strategy-proof social choice when preferences are single-dipped. Int J Game Theor 43(3):579–597

Minehart D, Neeman Z (2002) Effective siting of waste treatment facilities. J Environ Econ Manag 43:303–324CrossRef

O’Sullivan A (1993) Voluntary auctions for noxious facilities: incentives to participate and the efficiency of siting decisions. J Environ Econ Manag 25(1):S12–S26CrossRef

Perez-Castrillo D, Wettstein D (2002) Choosing wisely: a multibidding approach. Am Econ Rev 92(5):1577–1587CrossRef

Pigou AC (1920) The economics of welfare. MacMillan, London

Richman BD, Boerner C (2006) A transaction cost economizing approach to regulation: understanding the nimby problem and improving regulatory responses. Yale J Regul 23:29–76

Sakai T (2012) Fair waste pricing: an axiomatic analysis to the NIMBY problem. Econ Theor 50(2):499–521CrossRef

Shapley LS, Shubik M (1969) On the core of an economic system with externalities. Am Econ Rev 4(1):678–684

Shenoy PP (1979) On coalition formation: a game-theoretical approach. Int J Game Theor 8(3):133–164CrossRef

Starett D (1973) A note on externalities and the core. Econometrica 41(1):179–183CrossRef

Stearns ML (1993) The misguided renaissance of social choice. Yale Law J 103:1219–1292CrossRef

Thrall RM, Lucas WF (1963) N-person games in partition function form. Naval Res Log Q 10(1):281–298CrossRef

Title: Cooperative decision-making for the provision of a locally undesirable facility
Authors: Stefan Ambec
Yann Kervinio
Publication date: 02-09-2015
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 1/2016
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-015-0907-2

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