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A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game

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  • Grigory Belyavsky

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, ul. Milchakova 8A, Rostov-on-Don 344090, Russia)

  • Natalya Danilova

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, ul. Milchakova 8A, Rostov-on-Don 344090, Russia)

  • Guennady Ougolnitsky

    (Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University, ul. Milchakova 8A, Rostov-on-Don 344090, Russia)

Abstract

This paper considers resource allocation among producers (agents) in the case where the Principal knows nothing about their cost functions while the agents have Markovian awareness about his/her strategies. We use a dynamic setup of the stochastic inverse Stackelberg game as the model. We suggest an algorithm for solving this game based on Q -learning. The associated Bellman equations contain functions of one variable for the Principal and also for the agents. The new results are illustrated by numerical examples.

Suggested Citation

  • Grigory Belyavsky & Natalya Danilova & Guennady Ougolnitsky, 2018. "A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game," Mathematics, MDPI, vol. 6(8), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:8:p:131-:d:160726
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    References listed on IDEAS

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    1. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 2: Dynamic Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 601-618, December.
    2. Tharakunnel, Kurian & Bhattacharyya, Siddhartha, 2009. "Single-leader-multiple-follower games with boundedly rational agents," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1593-1603, August.
    3. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    4. G. J. Olsder, 2009. "Phenomena in Inverse Stackelberg Games, Part 1: Static Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 589-600, December.
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