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Optimal open loop cheating in dynamic reversedLinear ‐ Quadratic Stackelberg games

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Abstract

The distinctive characteristic of a “Reversed Stackelberg Game” is that the leader playstwice, first by announcing his future action, second by implementing a possibly differentaction given the follower's reaction to his announcement. In such a game, if the leader usesthe normal Stackelberg solution to find (and announce) his optimal strategy, there is a strongtemptation for him to cheat, that is, to implement another action than the one announced. Inthis paper, within the framework of a standard discrete time Linear‐Quadratic DynamicReversed Stackelberg game, we discuss and derive the best possible open‐loop cheatingstrategy for an unscrupulous leader.

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References

  1. T. Başar and G.J. Olsder, Dynamic Noncooperative Game Theory, Academic Press, New York, 2nd ed., 1995.

    Google Scholar 

  2. R. Barro and D. Gordon, A positive theory of monetary policy in a natural rate model, Journal of Political Economy 91(1983)589-610.

    Google Scholar 

  3. R. Barro and D. Gordon, Rules, discretion and reputation in a model of monetary policy, Journal of Monetary Economics 12(1983)3-20.

    Google Scholar 

  4. A.E. Bryson and Y.C. Ho, Applied Optimal Control, Wiley, New York, 1975.

    Google Scholar 

  5. Chinn Ping Fan, Generic non-existence of credible Stackelberg strategies, in: IFAC Symposium on Dynamic Modelling and Control of National Economies, Vol. 2, 1989, pp. 775-780.

    Google Scholar 

  6. R. Hämäläinen, On the cheating problem in Stackelberg games, International Journal of Systems Science 12(1981)753-770.

    Google Scholar 

  7. B. Herrendorf, Time consistent collection of optimal seigniorage: A unifying framework, Journal of Economic Surveys 11(March 1997)1-46.

    Google Scholar 

  8. Y. Ho, P. Luh and R. Muralidharan, Information structure, Stackelberg games, and incentive controllability, IEEE Transactions on Automatic Control 26(1981)454-460.

    Google Scholar 

  9. Y-C. Ho, P. Luh and G.J. Olsder, A control-theoretic view on incentives, Automatica 18(1982)167-179.

    Google Scholar 

  10. F. Kydland, Noncooperative and dominant player solutions in discrete dynamic games, International Economic Review 16(1975)301-335.

    Google Scholar 

  11. F. Kydland and E. Prescott, Rules rather than discretion: The inconsistency of optimal plans, Journal of Political Economy 85(1977)473-492.

    Google Scholar 

  12. P. Levine, Does time inconsistency matter?, CEPR Discussion Paper 227, 1988.

  13. F. Lewis and V. Syrmos, Optimal Control, Wiley, 2nd ed., 1995.

  14. M. Simaan and J.B. Cruz, Additional aspects of the Stackelberg strategy in nonzero-sum games, Journal of Optimization Theory and Applications 11(June 1973)613-626.

    Google Scholar 

  15. B. Tolwinski, Equilibrium solutions of a class of hierarchical games, in: Applications of Systems Theory to Economics, Management and Technology, eds. J. Gutenbaum and S. Niezgodka,, PWN, Warsaw, Poland, 1980.

    Google Scholar 

  16. B. Tolwinski, A Stackelberg solution of dynamic games, IEEE Transactions on Automatic Control 28(1983)85-93.

    Google Scholar 

  17. A.J. De Zeeuw and F. Van Der Ploeg, Difference games and policy evaluation, Oxford Economic Papers 43(1991)612-636.

    Google Scholar 

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Vallée, T., Deissenberg, C. & Basar, T. Optimal open loop cheating in dynamic reversedLinear ‐ Quadratic Stackelberg games. Annals of Operations Research 88, 217–232 (1999). https://doi.org/10.1023/A:1018982313949

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