Cooperation Under Ambiguity

Chapter
Part of the Energy Systems book series (ENERGY)

Abstract

Exchange of contingent claims is construed here as a cooperative game with transferable utility. Solutions are sought in the core. The novelty is that agents, being uncertainty averse, may use distorted, subjective probabilities. Choquet integrals therefore replace expected utility. When convoluted payoff is concave at the aggregate endowment, there is a price-generated, explicit core solution.

Notes

Acknowledgements

Thanks are due to Finansmarkedsfondet for financial support and a referee for good and generous comments.

References

  1. Anderson, E. W., Hansen, L. P., & Sargent, T. J. (2003). A quartet of semigrous for model specification, robustness, prices of risk, and model detection. J European Economic Association, 1(1), 68–123.CrossRefGoogle Scholar
  2. Aubin, J. -P., & Ekeland, I. (1984). Nonlinear Applied Analysis. New York: Wiley.Google Scholar
  3. Baton, B., & Lemaire, J. (1981). The core of a reinsurance market. ASTIN Bulletin, 12, 57–71.Google Scholar
  4. Billot, A., Chateauneuf, A., Gilboa, I., & Tallon, J. -M. (2000). Sharing beliefs: between agreeing and disagreeing. Econometrica, 68, 685–694.CrossRefGoogle Scholar
  5. Borch, K. H. (1960). Reciprocal reinsurance treaties. ASTIN Bulletin, 1, 171–191.Google Scholar
  6. Borch, K. H. (1960). Reciprocal reinsurance treaties seen as a two-person cooperative game. Scandinavian Actuarial Journal, 43, 29–58.CrossRefGoogle Scholar
  7. Borch, K. H. (1962). Equilibrium in a reinsurance market. Econometrica, 30, 424–444.CrossRefGoogle Scholar
  8. Cagetti, M., Hansen, L. P., Sargent, T., & Williams, N. (2002). Robustness and pricing under uncertain growth. The Review of Financial Studies, 15(2), 363–404.CrossRefGoogle Scholar
  9. Cass, D., & Shell, K. (1983). Do sunspots matter? Journal of Political Economy, 91, 193–227.CrossRefGoogle Scholar
  10. Cass, D., Chichilnisky, G., & Wu, H. -M. (1996). Individual risk and mutual insurance. Econometrica, 64, 333–341.CrossRefGoogle Scholar
  11. Chateauneuf, A. (1994). Modeling attitudes towards uncertainty and risk through the use of Choquet integral, Annals of Operations Research, 52, 3–20.CrossRefGoogle Scholar
  12. Chateauneuf, A., Dana, R.-A., & Tallon, J. -M. (2000). Optimal risk-sharing rules and equilibria with Choquet-expected-utility, Journal of Mathematical Economics, 34, 191–214.CrossRefGoogle Scholar
  13. Denneberg, D. (1994). Non-additive measure and integral. Dordrecht: Kluwer.CrossRefGoogle Scholar
  14. Dempster, A. P. (1968). A generalization of Bayesian inference. Journal of Royal Statistical Society B, 30, 205–247.Google Scholar
  15. Dow, J., Ribeiro, S., & Werlang, C. (1992). Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica, 60(1), 197–204.CrossRefGoogle Scholar
  16. Evstigneev, I. V., & Flåm, S. D. (2001). Sharing nonconvex cost. Journal of Global Optimization, 20, 3–4, 257–71.CrossRefGoogle Scholar
  17. Fishburn, P. C. (1988). Nonlinear preference and utility theory. Baltimore: The Johns Hopkins University Press.Google Scholar
  18. Flåm, S. D., & Ermoliev, Y. (2008). Investment, uncertainty and production games. Environment and Development Economics.Google Scholar
  19. Flåm, S. D., Owen, G., & Saboya, M. (2005). The not-quite non-atomic game: non-emptiness of the core in large production games. Mathematical Social Sciences, 50, 279–297.CrossRefGoogle Scholar
  20. Flåm, S. D., & Koutsougeras, L. (2010). Private information, transferable utility, and the core. Economic Theory, 42, 591–609.CrossRefGoogle Scholar
  21. Gilboa, I. (1987). Expected utility with purely subjective non-additive probabilities. Journal of Mathematical Economics, 16, 65–88.CrossRefGoogle Scholar
  22. Gilboa, I., & Schmeidler, D. (1994). Additive representations of non-additive measures and the Choquet integral. Annals of Operations Research, 52, 43–65.CrossRefGoogle Scholar
  23. Karni, E., & Schmeidler, D. (1991). Utility theory with uncertainty. In W. Hildenbrandt & H. Sonnenschein (Eds.), Handbook of Mathematical Economics (vol IV, Chap. 33). Amsterdam: North-Holland.Google Scholar
  24. Gollier, C. (2006). Does ambiguity aversion reinforce risk aversion? Applications to portfolo choice and asset prices. Typescript.Google Scholar
  25. Karni, E. (1993). Subjective expected utility theory with state-dependent preferences. Journal of Economic Theory, 69, 428–438.CrossRefGoogle Scholar
  26. Laurent, P. -J. (1972). Approximation et optimisation. Paris: Hermann.Google Scholar
  27. Machina, M. (1987). Choice under uncertainty: problems solved and unsolved. Economic Perspectives, 1, 121–154.CrossRefGoogle Scholar
  28. Maenhout, P. J. (2004). Robust portfolio rules and asset pricing. The Review of Financial Studies, 17(4), 951–983.CrossRefGoogle Scholar
  29. Obstfeld, M., & Rogoff, K. (1996). Foundations of international macroeconomics. MIT.Google Scholar
  30. Osborne, M. J., Rubinstein, A. (1994). A course in game theory. MIT.Google Scholar
  31. Rockafellar, R. T., & Wets, J. -B. (1998). Variational analysis. Berlin: Springer.CrossRefGoogle Scholar
  32. Schmeidler, D. (1986). Integral representation without additivity. Proc. Am. Math. Soc., 97, 255–261.CrossRefGoogle Scholar
  33. Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57, 571–587.CrossRefGoogle Scholar
  34. Shafer, G. (1976). A mathematical theory of evidence. Princeton University Press.Google Scholar
  35. Shapley, L. S. (1971). Cores of convex games. Int. Journal of Game Theory, 1, 12–26.Google Scholar
  36. Tallon, J. -M. (1998). Do sunspots matter when agenst are Choquet-expected-utility maximizers? Journal of Economic Dynamics and Control, 22, 357–368.CrossRefGoogle Scholar
  37. Wakker, P. (1990). Characterizing optimism and pessimism directly through comonotonicity. Journal of Economic Theory, 52, 453–463.CrossRefGoogle Scholar
  38. Wang, S. S., Young, V. R. & Panjer, H. H. (1997). Axiomatic characterization of insurance prices. Insurance: mathematics and economics, 21, 173–183.CrossRefGoogle Scholar
  39. Wilson, R. (1968). The theory of syndicates. Econometrica, 36, 119–132.CrossRefGoogle Scholar
  40. Yaari, M. E. (1985). The dual theory of choice under risk. Econometrica, 95–115.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of BergenBergenNorway

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