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Contracts versus Trust in Water Allocation: growing & sharing the pie in Northeast Brazil

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Contracts versus Trust in Water Allocation: growing & sharing the pie in Northeast Brazil Alexander Pfaff ( Duke University -- Public Policy, Economics, and Environment & Maria Alejandra Vélez (

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Contracts versus Trust in Water Allocation:

growing & sharing the pie in Northeast Brazil

Alexander Pfaff (

Duke University -- Public Policy, Economics, and Environment


Maria Alejandra Vélez (

Universidad de los Andes -- Facultad de Administración

Funded by CRED, Columbia University (NSF-funded DMUU center)

We explore the efficiency and equity resulting from allocation of a fixed resource within a bargaining institution.
  • We wish to compare enforceable contracts with settings where responders must ‘trust’.
We use generically framed field experiments (artefactual) based on water allocation in NE Brazil.
  • 570 participants in Ceará, in Fortaleza or the Jaguaribe (largest agricultural) Valley.

State of Ceará in Northeast (Nordeste)

(popul > 7m)

(rural > 2m)

75% below poverty line







City: Tourism and Industry

These areas are soon to be further connected by a large canal to bring water towards Fortaleza.

Its completion signals the arrival of new allocation decisions for which no decision process or body has been announced.

Rural area: Mainly rice production

the experimental design
The Experimental Design
  • Games are neutrally framed. Thus, we do not mention water but just ’tokens’ and describe actors not as locations, valley and city, but as players A (proposers) and B (responders).
  • Each set of paired participants had to allocate 10 tokens in a one shot experiment.
  • Proposers are more productive than responders
  • 2:1 productivity ratio case: each chip was worth $R2 for proposers but $1R for responders (low productivity case).
  • 4:1 productivity ratio case: $R4 for proposers but $R1 for responders (high productivity case)
the experimental design1
The Experimental Design
  • Our experiments have three steps:

[1] proposers set the agenda by requesting an amount of the resource

[2] responders accept or reject, the latter giving both a small default payment of R$ 5

[3] if responders accept, then proposers must decide whether to send back some of their earnings.

For 2:1, the maximum possible total earnings is R$20; for 4:1, it is R$40.

the experimental design2
The Experimental Design
  • ‘No Communication’ provides no signal to responders of a proposer’s intention of sharing in the 3rd step, so the responder decides based on the initially requested split of the resources
  • ‘Message’ provides with the initial proposed split a non-binding written message stating what transfer of surplus will occur in the 3rd step if, in the 2nd step, the responder accepts the request
  • ‘Contract’ provides with the initial proposal a binding written message about that transfer.
the experimental design3
The Experimental Design
  • No Communication and Message allows for Trust.
  • Proposers, essentially invite responders to trust by asking for a larger share of the resource.
  • If accept, responders give up a sure gain, the R$5, for the chance of gaining more yet also a risk of gaining less
  • Our design is different from the classical trust or investment game (Berg et al. 1995 or Guth et al. 1997), where the first mover must trust the second mover for trust’s gains to arise.
  • Trust is productive, as the largest total pie is created by initially sending everything to proposers.
  • For instance, in Ceará, output rises as water is shifted from flooded rice to tourism and industry.
  • In our one-shot game, as previously reported in the literature, we find evidence of trusting behavior, by responders and expectations of trust by the proposers.
  • Trust exists and it pays off in the sense of raising not only efficiency, i.e. total earnings, but also the earnings of the responder.
  • However, we also find that contracts do even better than trust in terms of efficiency and equity.
results no communication
RESULTS – “No Communication”
  • We see proposer asking for 66% across productivity ratios in ‘No Communication’.
  • Thus, proposers to some extent expect trust (leaving initial a allocation for responders less than the default).
  • They are right, acceptance is high for the high productivity(86%) despite higher requests for resources, though lower for the low productivity case(70%).
  • In accepted cases, the Average Ask For in “No Communication” is 59% for low productivity case and 61% for high productivity which yields less than R$5 for responders
results no communication1
RESULTS – “No Communication”
  • Trust is present on average because the responders accept on average an initial split of resources that gives them less than the default payment they would receive if they reject the initial request.
  • The reason to do so is trusting that the expected 3rd-step transfer will be sufficient for a gain greater than the default they’ll get with rejection.
results no communication2
RESULTS – “No Communication”
  • Trust pays off
  • Transfers in the 3rd, sharing step are not high (R$4.8 in high productivity , R$ 2.5 in low productivity ) but added to the initial resource split they beat the default payment (R$5) a rejection would earn
results message
RESULTS – “Message”
  • With a non-binding ‘Message’ (coordination device) raises further the initial allocation to the proposer and thus efficiency.
  • The average proposer request rises to 70% for low productivity and 69% for high productivity with accompanying messages about 3rd-step sharing averaging R$4 for low productivity and R$8.3 for high productivity.
  • Proposers expect trust and they are right.
  • Acceptance increased to 88% for low productivity and while lower for high productivity , at 73%, the efficiency is still greater on average with the ‘Message’.

Again trust pays off:

  • But is not fully justified:
  • Proposers are lying!

RESULTS – “Message”

  • 3rd-step actual transfers are lower than the non-binding messages.
results contract
RESULTS – “Contract”
  • Both efficiency and equity rise with enforceability..
  • Proposed initial resource splits rise to 83% in low productivity and 78% in high productivity and the modal proposed split in both 2:1 and 4:1 is a striking 100%.
  • Acceptance for low productivity is down to 68%, likely due to binding transfers being low, while acceptance for high productivity is 80%.
  • Transfers are higher too, with an average of R$6 for accepted offers for low productivity ,and R$10 for high productivity.
efficiency results
Efficiency Results
  • For 2:1, the maximum possible total earnings is R$20; for 4:1, it is R$40.
  • “Contract” earnings ranked first in efficiency (Earnings Sum), closer to the possible maximum
equity results

Contract’ does better for equity as measured in three key ways:

1. The ratio of proposers to responders’ earnings.

2. Aiding the lowest earner

3. The frequency of earnings being allocated as if by a 50-50 distribution rule.

Equity Results

‘“Contract” had also the greater percentage of accepted observations where the total earnings were distributed evenly:

- In “Contact” 37% in low productivity and 27% for high productivity .

- In “No Communication” the percentage of accepted observations where earnings were distributed evenly was 26% for low productivity and 13% for high productivity

- In “Message” the percentage of even sharing was 11% for both productivities

to conclude
To Conclude…
  • Trust exists and is socially productive
  • However, both efficiency and equity rise with enforceability.
  • This could provide insights into the design of any new institution to allocate water in Ceara but also other relevant settings.
  • Our reports of trust obtained in a one shot game could be considered as the minimal trust.
  • We expect trust to increase with a repeated game since punishment, reputation and learning could help to develop more trust.
  • Next experiments, will do repeated to allow for learning and reputation.