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Risk Sharing in Public-Private Partnerships

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Public-private partnerships (PPPs) have been widely used to finance many projects. Despite the growing importance of PPPs, a serious attempt has not been made to come up with a unified theory which can understand the different incentive mechanisms, risks, and heterogeneity embedded in a PPP structure which can often lead to their failure. Using a global games framework, this paper achieves to do exactly that by elaborating upon the role of coordination and uncertainty in these projects. With heterogeneous information, the incidence of failure can be uniquely identified by characterizing and defining the equilibrium. Comparative static results point to how policymakers can improve the probability of success in these partnerships. The incentive mechanisms also highlight how a PPP structure can do better than other forms of investment organization.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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  1. The investment by the World Bank in support of PPPs across the globe has also increased significantly in both absolute terms and in relative terms, from $ 0.9 to $ 2.9 billion and from 4% in 2002 to 7% in 2012 [38].

  2. Levin and Tadelis [31], Iossa and Martimort [11] and Renneboog and Sarmento [32]

  3. [38].

  4. This database has data on 6400 infrastructure projects in 139 low- and middle-income countries.

  5. This is an aspect that I model explicitly later.

  6. Yuan et al. [33] study a novel Z-number-based real option model to study PPPs.

  7. We can assume there is a monetary equivalent to this utility gain, which is the total investment required to complete the project.

  8. A standard assumption in papers trying to study public good provision [34, 35].

  9. Simply think of all citizens privately, equating marginal utility and marginal cost, where the cost can be either through votes or through taxes.

  10. Think of this as a hydro-project which generates electricity. The fact that it generates electricity for the citizens is a utility gain; however, the electricity is sold at a certain price which depends on several factors besides demand and is therefore uncertain.

  11. We assume away the existence of debt repudiation mechanisms—openly or through inflation, as highlighted by Calvo [36]

  12. This can be thought of as the funds it is ready to collect and still leave enough to win votes and the election.

  13. The source of the fund for \(\alpha\) is not considered in the model. The only assumption is that this source does not affect the economy in any other way. We can think of the utilization of taxes to generate funds for the project. It can also be sourced from printing money.

  14. Alternatively, one can think about each i as a shareholder or investor in a firm when a group of firms are acting as the private creditors.

  15. The assumption of no time discounting can be made without loss of generality as I have assumed that the private investors are risk-neutral and have a negligible share as compared to the total investment in the project.

  16. \(\alpha + \beta\) being equal to at least one guarantees the completion of the project. If it is greater than one, it just means that the project still has enough funds to allow it to be completed.

  17. We assume that the project generates high revenue stream even when gains equal disruption. All results go through if equality leads to low revenue.

  18. First highlighted by Carlsson and Van Damme [15]

  19. This is proved when we identify the conditions for the uniqueness of the equilibrium.

  20. This lemma was first used by Vives [37] for supermodular games. The use of this proof here is possible because the structure of our model is similar to the one used by Morris and Shin [17], which is a simplification of the supermodular games where iterated deletion of dominated strategies yields unique equilibrium.

  21. Here, I have that the single private investor undertaking the entire project has a private noisy signal about \(\theta\).

  22. Although the total investment is higher when the project is being completed by a single individual, using assumptions on risk-neutrality, we can make comparisons on the marginal investment.

  23. The next aim would be to calibrate the model and run a counterfactual analysis. That is out of the scope of the paper. It would also allow for more formal sensitivity tests which were addressed in the comparative static exercises.


  1. Geddes R, Wagner B (2013) Why do U.S. states adopt public-private partnership enabling legislation? J Urban Econ 78:30–41

    Article  Google Scholar 

  2. Helby Petersen O (2019) Evaluating the costs, quality, and value for money of infrastructure public–private partnerships: a systematic literature review. Ann Public Coop Econ 90(2):227–244

    Article  Google Scholar 

  3. Park J, Chung E (2021) Learning from past pandemic governance: early response and public-private partnerships in testing of COVID-19 in South Korea. World Dev 137

  4. Anwar A, Sharif A, Fatima S, Ahmad P, Sinha A, Khan SAR, Jermsittiparsert K (2021) The asymmetric effect of public private partnership investment on transport CO2 emission in China: evidence from quantile ARDL approach. J Clean Prod 288

  5. Marx A (2019) Public-private partnerships for sustainable development: exploring their design and its impact on effectiveness. Sustainability 11(4):1087

    Article  Google Scholar 

  6. Hart O (2003) Incomplete contracts and public ownership: remarks, and an application to public-private partnerships. Econ J 113(486):C69–C76

    Article  Google Scholar 

  7. Valero V (2015) Government opportunism and public-private partnerships. J Public Econ Theory 17(1):111–1

    Article  Google Scholar 

  8. Guasch JL (2004) Granting and renegotiating infrastructure concessions: doing it right, Washington. DC, The World Bank

    Book  Google Scholar 

  9. Iossa E, Martimort D (2016) Corruption in PPPs, incentives and contract incompleteness. Int J Ind Organ 44:85–100

    Article  Google Scholar 

  10. Hoppe E, Schmitz P (2013) Public-private partnerships versus traditional procurement: innovation incentives and information gathering. The RAND J Econ 44(1) (Spring 2013)56-74

  11. Iossa E, Martimort D (2015) The simple microeconomics of public-private partnerships. J Public Econ Theory 17(1):4–48

    Article  Google Scholar 

  12. Schmitz P (2015) Government versus private ownership of public goods: the role of bargaining frictions. J Public Econ 132(2015):23–31

    Article  Google Scholar 

  13. Hammami M, Ruhashyankiko J, Yehoue E (2006) Determinants of public-private partnerships in infrastructure, IMF Working Paper, WP/06/99

  14. Besley T, Ghatak M (2001) Government versus private ownership of public goods. Quart J Econ 116:1343–1372

    Article  Google Scholar 

  15. Carlsson H, van Damme E (1993) Global games and equilibrium selection. Econometrica 61:989–1018

    Article  MathSciNet  Google Scholar 

  16. Morris S, Shin HS (1998) Unique equilibrium in a model of self-fulling currency attacks. Am Econ Rev 88:587–597

    Google Scholar 

  17. Morris S, Shin HS (2004) Coordination risk and the price of debt. Eur Econ Rev 48(2004):133–153

    Article  Google Scholar 

  18. Compos R (2013) Risk-sharing and crises: global games of regime change with endogenous wealth. J Econ Theory 148(4):1624–1658

    Article  MathSciNet  Google Scholar 

  19. Morris S, Shin HS (1999) Risk management with interdependent choice. Oxf Rev Econ Policy 15(3):52–62

    Article  Google Scholar 

  20. Corsetti G, Dasgupta A, Morris S, Shin HS (2004) Does one Soros make a difference? A theory of currency crises with large and small traders. Rev Econ Stud 71(2004):87–114

    Article  MathSciNet  Google Scholar 

  21. Angeletos GM, Pavan A (2004) Transparency of information and coordination in economies with investment complementarities. Am Econ Rev 94(2):91–98

    Article  Google Scholar 

  22. Angeletos GM, Pavan A (2007) Efficient use of information and social value of information. Econometrica 75(4):1103–1142

    Article  MathSciNet  Google Scholar 

  23. Heinemann F, Nagel R, Ockenfels P (2004) The theory of global games on test: experimental analysis of coordination games with public and private information. Econometrica 72(5)(September, 2004):1583–1599

  24. Bardhan P, Mitra S, Mookherjee D, Nath A (2014) Changing voting patterns in rural West Bengal role of clientelism and local public goods. Econ Polit Wkly vol. XLIX no. 11

  25. Dow J, da Costa Werlang SR (1992) Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica 60(1):197–204

    Article  Google Scholar 

  26. Diamond D, Dybvig P (1983) Bank runs, deposit insurance and liquidity. J Polit Econ 91:401–419

    Article  Google Scholar 

  27. Morris S, Shin HS (2002) Social value of public information. Am Econ Rev 92(5):521–534

    Article  Google Scholar 

  28. Hellwig C (2002) Public information, private information, and the multiplicity of equilibria in coordination games. J Econ Theory 107(2):191–222

    Article  MathSciNet  Google Scholar 

  29. Kamenica E, Gentzkow M (2011) Bayesian persuasion. Am Econ Rev 101(6):2590–2615

    Article  Google Scholar 

  30. White L (2010) Markets: the credit rating agencies. J Econ Perspect 24(2):211–226

    Article  MathSciNet  Google Scholar 

  31. Levin J, Tadelis S (2005) Profit sharing and the role of professional partnerships. Q J Econ 120(1):131–171

    Google Scholar 

  32. Renneboog L, Sarmento JM (2016) Anatomy of public-private partnerships: their creation, financing and renegotiations. Int J Manag Proj Ed 9:94–122

    Google Scholar 

  33. Yuan J, Lu W, Ding H, Liu J, Mahmoudi A (2023) A novel Z-number based real option (ZRO) model under uncertainty: application in public-private-partnership refinancing value evaluation. Expert Syst Appl 213

  34. Wildasin DE (1984) On public good provision with distortionary taxation. Economic Inquiry Vol. XXII, April 1984

  35. Cowell FA, Gordon J (1988) Unwillingness to pay: tax evasion and public good provision. J Public Econ 36(1988):305–321

    Article  Google Scholar 

  36. Calvo G (1988) Servicing the public debt: the role of expectations. Am Econ Rev 78:647–661

    Google Scholar 

  37. Vives X (1990) Nash equilibrium with strategic complementarities. J Math Econ 19(3):305–321

    Article  MathSciNet  Google Scholar 

  38. World Bank Report (2012).

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RM wrote and analyzed the model for the study. RM has read and approved the final manuscript.

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Correspondence to Ronit Mukherji.

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1.1 Model Variables









Private Investor



Government’s share of the total finance in the project



Private Creditor’s share of the total finance in the project



Mass of private investors



Investment by a single investor



Revenue generated from the project



Maximum revenue possible from the project



Lowest revenue possible from the project



Underlying state of the economy



Share of investors who withdraw from the project



Total wealth of private investors



Mean of \(\theta\)



Precision of \(\theta\)



Signal of \(\theta\)



Precision of preivate noisy signal


\(\epsilon _{i}\)

Mean of posterior Beliefs

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Mukherji, R. Risk Sharing in Public-Private Partnerships. Oper. Res. Forum 4, 72 (2023).

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