Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Contingent Contracts and Value Creation

  • 237 Accesses

  • 1 Citations


In negotiations in which the potential value creation depends upon external uncertainties, and the players have different beliefs about these uncertainties, it is well known that contingent contracts can enable agreement. But by allowing contingent payments, each player’s expected value capture can, in some situations, be made arbitrarily large. This fact prompts two natural questions. Does the increase in the players’ expected value capture imply an increase in expected value creation? And is there a point at which the contract can become more about making a wager and less about exploiting differences to enable agreement? We address these questions by showing that a player’s expected value capture can be separated into two components: an expected share of ex post value creation and an expected transfer of value from one player to another. The latter can be represented by a zero-sum wager. We show that if contracts are restricted to be ex post individually rational—a natural condition implicit in Arrow (1953) and Raiffa (The art & science of negotiation, Harvard University Press, Cambridge, 1982)—a joint increase in the players’ expected value captures can always be attributed to a division of ex post value creation that better exploits the players’ beliefs rather than to an increase in an embedded zero-sum wager.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    Note that by assuming risk neutrality, there will be no value created through risk sharing.

  2. 2.

    Bazerman and Gillespie (1999) specifically mention the need for ‘enforceability’ and provide the advice, ‘Don’t bet if you can’t collect.’

  3. 3.

    We are assuming that the players take no pleasure in betting for the sake of betting.


  1. Arrow KJ (1953) Le Role des Valeurs Boursieres pour la Repartition la Meilleure des Risques. International Colloquium on Econometrics, 1952, Centre National de la Recherche Scientifique, Paris (1953) Translated as The role of securities in the optimal allocation of risk-bearing. Review of Economic Studies 31, 1964

  2. Aumann R (1976) Agreeing to disagree. Ann Stat 4:1236–1239

  3. Bazerman MH, Gillespie JJ (1999) Betting on the future: the virtues of contingent contracts. Harv Bus Rev 77(5):155–160

  4. Brunnermeier MK, Simsek A, Xiong W (2014) A welfare criterion for models with distorted beliefs. Q J Econ 129(4):1753–1797

  5. Forges F, Minelli E, Vohra R (2002) Incentives and the core of an exchange economy: a survey. J Math Econ 38:1–41

  6. Gayer G, Gilboa I, Samuelson L, Schmeilder D (2014) Pareto efficiency with different beliefs. J Leg Stud 43:S151–S171

  7. Gilboa I, Samuelson L, Schmeilder D (2014) No-Betting-Pareto Dominance. Econometrica 82(4):1405–1442

  8. Holmström B, Myerson RB (1983) Efficient and durable rules with incomplete information. Econometrica 51(6):1799–1819

  9. Kay J (2015) Other people’s money: the real business of finance. PublicAffairs, New York

  10. Lax DA, Sebenius JK (1986) The manager as negotiator: bargaining for cooperation and competitive gain. Free Press, New York

  11. Radner R (1968) Competitive equlibrium under uncertainty. Econometrica 36(1):31–58

  12. Raiffa H (1982) The art & science of negotiation. Harvard University Press, Cambridge

Download references

Author information

Correspondence to H. W. Stuart Jr..

Additional information

The author thanks Patrick Bolton, Fangruo Chen, Patrick Sileo, and George Wu for many helpful discussions about this paper. The author also thanks two anonymous referees for paper-improving suggestions. Financial support from Columbia Business School is gratefully acknowledged. This paper is dedicated to the memory of Howard Raiffa.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Stuart, H.W. Contingent Contracts and Value Creation. Group Decis Negot 26, 815–827 (2017). https://doi.org/10.1007/s10726-016-9522-6

Download citation


  • Contingent contract
  • Value creation
  • Ex post rationality
  • Negotiation