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Public-Private Partnership Contractual Design: A Computational Model of the Moral Hazard with Lotteries


Public-Private Partnership (PPP) is a new model of public management which consists of the contractual relationship between public and private entities. In particular, PPPs enable risk share between public and private sectors making the asymmetric information problem in a contractual arrangement more evident. The aim of this paper was to study a moral hazard problem applied to PPP contracts. To achieve this objective, a PPP computational contractual model including the moral hazard with lotteries was developed to assess how contractual changes could affect the optimum behavior of arrangement members. Simulations indicate that projects with higher economic value should attract more qualified firms, which may be why the companies expend more effort. To deal with possible contractual contingencies and try to minimize the moral hazard problem, the government could draw up more flexible contracts in order to include possible necessary changes and punish unwanted or improper consortium behavior.

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  1. In this sense, a high effort level implies in a better product, see Hart and Holmstrom (1987) and Jewit (1988) for more details.

  2. See Holmstrom and Milgrom (1991) to understand the agency problem.

  3. In the probability theory, the Bayes theorem shows the relationship between a conditional probability and its inverse. Formally, P(A|B)P(B) = P(AB) = P(BA) = P(B|A)P(A).

  4. This algorithm implementation was done in Octave 3.6-4. This software is available at

  5. Following (Iossa and Martimort 2009) the assumption indicates an interesting note: Without moral hazard,the optimal risk allocation demands that the public entity bears all risk. It could be questioned in the case of a small local government whose PPP project is still under evaluation and it represents a big part of the public budget constraint. , i.e., it has a welfare function which is given by

    $$ sw(q,c)=q-c. $$
  6. A constant relative risk aversion (CRRA) utility function is used. The aversion grade is measured by the Arrow-Pratt coefficient of relative risk aversion: \(\rho =-x\frac {u^{\prime \prime }(x)}{u^{\prime }(x)}\). For more details, see Varian (1992).

  7. This function solves a linear problem of the minf x s.a. A xb kind. For maximization, we invert the signal of f.


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The authors wish to thank the Associate Editor and two anonymous referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. Helton Saulo gratefully acknowledges financial support from CAPES which facilitated his research visit to McMaster University. Rodrigo Nobre Fernandez gratefully acknowledges to comments and suggestions from: Claudio Shikida, Cristiano M. Costa, Klenio Barbosa and Hudson Torrent. We point out that any mistake committed here is the entire responsibility of the authors.

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Correspondence to Rodrigo Nobre Fernandez.

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Fernandez, R.N., Saulo, H., Carraro, A. et al. Public-Private Partnership Contractual Design: A Computational Model of the Moral Hazard with Lotteries. Public Organiz Rev 18, 39–51 (2018).

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  • Public-private partnership
  • Asymmetric information
  • Moral hazard
  • Linear program algorithm