Skip to main content
Log in

Incentive compatible strategies for general stackelberg games with incomplete information

  • Published:
International Journal of Game Theory Aims and scope Submit manuscript

Abstract

We study Stackelberg games with incomplete information in a general setting. In particular, we deduce the follower's reaction function, a set-valued function of the leader's action choice and a parameter specifying the follower's payoff type (a parameter about which the leader has only incomplete information), and using a generalized version of Komlos' Theorem due to Balder (1987), we show the existence of an expected payoff maximizing, incentive compatible strategy for the leader given the follower's reaction function.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ash RB (1972) Real Analysis and Probability. Academic Press, New York

    Google Scholar 

  • Balder EJ (1984) A General Approach to Lower Semicontinuity and Lower Closure in Optimal Control Theory. SIAM J Control and Optimization 22: 570–598

    Google Scholar 

  • Balder EJ (1987) New Sequential Compactness Results for Spaces of Scalarly Measurable Funtions. Preprint No. 488, Department of Mathematics, University Utrecht, (forthcoming in J Math Anal Appl.)

  • Bartle RG (1976) Elements of Real Analyis. John Wiley & Sons, New York

    Google Scholar 

  • Berge C (1963) Topological Spaces. MacMillan, New York

    Google Scholar 

  • Banks JS, Sobel J (1987) Equilibrium Selection in Signaling Games. Econometrica 55: 647–661

    Google Scholar 

  • Castaing C, Valadier M (1977) Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics No. 580, Springer-Verlag, Berlin

    Google Scholar 

  • Chan Y, Thakor AV (1987) Collateral and Competitive Equilibria with Moral Hazard and Private Information. J Finance 42: 345–363

    Google Scholar 

  • Dsosu L, Shaozhong C (1983) On Fixed Point Theorems for Random Set-Valued Maps. Nonlinear Anal 7: 309–323

    Google Scholar 

  • Green JR (1973) Temporary General Equilibrium in a Sequential Trading Model with Spot and Future Transactions. Econometrica 41:1103–1124

    Google Scholar 

  • Grossman SJ, Hart OD (1983) An Analysis of the Principal-Agent Problem. Econometrica 51:7–45

    Google Scholar 

  • Harsanyi JC (1967/8) Games with Incomplete Information Played by ‘Bayesian’ Players. Management Sci 14:159–189, 320–334, 486–502

    Google Scholar 

  • Himmelberg CJ (1975) Measurable Relations. Fund Math 87:53–72

    Google Scholar 

  • Himmelberg CJ, Van Vleck FS (1975) Multifunctions with Values in a Space of Probability Measures. J Math Anal Appl 50: 108–112

    Google Scholar 

  • Holmstrom B (1979) Moral Hazard and Observability. Bell J Econ 10: 74–91

    Google Scholar 

  • Komlos J (1967) A Generalization of a Problem of Steinhaus. Acta Math Acad Sci Hungary 18: 217–229

    Google Scholar 

  • Maskin E, Riley J (1984) Monopoly with Incomplete Information. Rand J Econ 15: 171–196

    Google Scholar 

  • Matthews S, Moore J (1987) Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening. Econometrica 55: 441–467

    Google Scholar 

  • Myerson RB (1979) Incentive Compatibility and the Bargaining Problem. Econometrica 47:61–74

    Google Scholar 

  • Myerson RB (1982) Optimal Coordination Mechanisms in Generalized Principal-Agent Problems. J Math Econ 10: 67–81

    Google Scholar 

  • Nowak AS (1984) On Zero-Sum Stochastic Games with General State Space I. Probab Math Statist 4: 13–32

    Google Scholar 

  • Page Jr FH (1987) The Existence of Optimal Contacts in the Principal-Agent Model. J Math Econ 16:157–167

    Google Scholar 

  • Parthasarathy KR (1967) Probability Measures on Metric Spaces. Academic Press, New York, 1967

    Google Scholar 

  • Robinson SM, Day R (1974) A Sufficient Condition for Continuity of Optimal Sets in Mathematical Programming. J Math Anal Appl 45:506–511

    Google Scholar 

  • Rogerson WP (1985) The First-Order Approach to the Principal-Agent Problem. Econometrica 53: 1357–1367

    Google Scholar 

  • Schal M (1974) A Selection Theorem for Optimization Problems. Arch Math 25: 219–224

    Google Scholar 

  • Shavell S (1979) Risk Sharing and Incentives in the Principal and Agent Relationship. Bell J Econ 10: 55–73

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

I would like to thank an anonymous referee and Erik Balder for helpful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Page, F.H. Incentive compatible strategies for general stackelberg games with incomplete information. Int J Game Theory 18, 409–421 (1989). https://doi.org/10.1007/BF01358801

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01358801

Keywords

Navigation