Equity–Efficiency Optimizing Resource Allocation: The Role of Time Preferences in a Repeated Irrigation Game

AuthorEls Lecoutere,Bjorn Van Campenhout,Ben D'Exelle
Date01 April 2015
Published date01 April 2015
DOIhttp://doi.org/10.1111/obes.12058
234
©2014 TheAuthors. OxfordBulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
Thisis an open access article under the ter ms of the CreativeCommons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properlycited.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 0305–9049
doi: 10.1111/obes.12058
Equity–Efficiency Optimizing ResourceAllocation:
The Role of Time Preferences in a Repeated Irrigation
Game*
Bjorn Van Campenhout, Ben D’Exelle‡ and Els Lecoutere§
International Food Policy Research Institute (IFPRI – Kampala), Plot 15, East Naguru
Road, PO Box 28565, Kampala, Uganda (e-mail: b.vancampenhout@cgiar.org)
School of International Development, University of East Anglia, UK (e-mail: b.dexelle@
uea.ac.uk)
§Conflict Research Group, Ghent University, Belgium (e-mail: els.lecoutere@ugent.be)
Abstract
Westudy repeated water allocation decisions among small scale irrigation users in Tanzania.
In a treatment replicating water scarcity conditions, convexities in production make that
substantial efficiency gains can be obtained by deviating from equal sharing, leading to an
equity–efficiency trade-off. In a repeated game setting, it becomes possible to reconcile
efficiency with equity by rotating the person who receives the largest share, but such a
strategy requires a longer run perspective. Correlating experimental data from an irrigation
game with individual time preference data, we find that less patient irrigators are less likely
to use a rotation strategy.
I. Introduction
Livelihood systems that rely on a common pool resource are often confronted with an
equity–efficiency trade-off. For instance, in a setting characterized by a scarce common
resource that serves as an input into a convex production function, the optimal outcome
in terms of aggregate production may be to allocate all resources to a single individual.
Withoutany form of ex-post redistribution, such an allocation may conflict with local equity
norms, which tend to be particularly strong in small-scale societies. The convexities in the
production function means that distributing the common resource more equally between
all users leads to significant aggregate welfare losses.
However, in a dynamic context, where the common pool resource has to be allocated
repeatedly, it may become possible to reconcile efficiency with equity. If agents consider
*Wekindly acknowledge the financial support received from the Institute of Development Policyand Management
(University of Antwerp), Ghent University,MICROCON and the Fonds voor Wetenschappelijk Onderzoek.We are
also grateful for the support of Incomet 2001, MuCoBa and Dr Beatrice K. Mkenda; and the excellent field support
provided by Charles Kyando.This research received research clearance from the Tanzania Commission for Science
and Technology (COSTECH) and the Mufindi District Council.
JEL Classification numbers: D900, Q210.
Equity–efficiency optimizing resource allocation 235
utility overmore than one period, a rotation strategy where one individual takes all resources
in one round and another person takes all in the following period may become a preferred
strategy.In fact, for strictly convex production functions, any deviation from equal sharing,
followedby an equal deviation in the other direction will improve aggregate utility, without
jeopardizing equality.
Repeated interactions introduce an element of timing, such that individuals do not
only consider instantaneous utility, but a stream of future utility, appropriately discounted.
Individual time preferences will therefore influence what equilibrium prevails. Rotation
will only be an optimal strategy if players sufficiently value the utility derived from future
payoffs.In other words, the optimal solution in terms of both equity and aggregate efficiency
will only come about when agents are patient enough.
In this article, we test if patience is indeed a prerequisite for equity–efficiencyoptimizing
distribution behaviour whenagents have social preferences and rely on a convex production
technology.We start by presenting a simple two period model where one player decides on
the distribution of a single production input between himself and another producer. With
convex production technology, our model predicts that taking everything in one round and
taking nothing in the following round is optimal if the player that makes the decisions
becomes more patient. To test our model, we run a field lab experiment amongst traditional
small-scale irrigation users in the Southern Highlands of Tanzania.The data on distribution
behaviour is then correlated with a measure of time preference, which we obtained from
a standard time preference elicitation experiment. We find a remarkable tendency to share
equally (D’Exelle, Lecoutere and Van Campenhout, 2012a). From a dynamic perspective,
we find that manyplayers rotate, and that more impatient irrigation users rotate significantly
less.
This article is related to several other articles. First of all, it builds on the growing evi-
dence that people not only care about their ownincome, but also about how it compares with
the income of others (see Camerer, 2003 for an overview in a behavioural economics con-
text). New utility models have been elaborated that account for social preferences through
inequality aversion (e.g. Fehr and Schmidt, 1999; Bolton and Ockenfels, 2000). While
most evidence on inequality aversion comes from experiments with university students
(Camerer and Thaler, 1995), this aversion seems to be particularly large in small-scale,
close-knit societies (see e.g. Henrich et al., 2001).
The importance of impatience has been noted in the theoretical bargaining literature.
In bilateral bargaining, if agents are identical and make alternating offers, equilibrium
distributions approach equality as impatience diminishes (Rubinstein, 1982). Experiments
that test these models find some support, but also note a countervailing tendency that favours
fair outcomes (Binmore, Swierzbinski and Tomlinson, 2007). In our model, only one player
can decide on the distribution, but the fact that this player has social preferences makes
our model reminiscent of such bargaining games. As such, this article also contributes to
the large literature that empirically investigates multi-period non-cooperative interactions,
while avoiding the main criticism on this literature that agents do not behave in the rational
and selfish way these models assume (Binmore, Shaked and Sutton, 1985;Weg and Zwick,
1999; Camerer, 2003).
This article is also an extension to D’Exelle et al. (2012a). In that article, we provide a
detailed account of the irrigation experiment and describe how small scale irrigation users
©2014 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and JohnWiley & Sons Ltd.

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT