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Approachability in Stackelberg Stochastic Games with Vector Costs

Author

Listed:
  • Dileep Kalathil

    (EECS at UC Berkeley)

  • Vivek S. Borkar

    (IIT Bombay)

  • Rahul Jain

    (University of Southern California)

Abstract

The notion of approachability was introduced by Blackwell (Pac J Math 6(1):1–8, 1956) in the context of vector-valued repeated games. The famous ‘Blackwell’s approachability theorem’ prescribes a strategy for approachability, i.e., for ‘steering’ the average vector cost of a given agent toward a given target set, irrespective of the strategies of the other agents. In this paper, motivated by the multi-objective optimization/decision-making problems in dynamically changing environments, we address the approachability problem in Stackelberg stochastic games with vector-valued cost functions. We make two main contributions. Firstly, we give a simple and computationally tractable strategy for approachability for Stackelberg stochastic games along the lines of Blackwell’s. Secondly, we give a reinforcement learning algorithm for learning the approachable strategy when the transition kernel is unknown. We also recover as a by-product Blackwell’s necessary and sufficient conditions for approachability for convex sets in this setup and thus a complete characterization. We give sufficient conditions for non-convex sets.

Suggested Citation

  • Dileep Kalathil & Vivek S. Borkar & Rahul Jain, 2017. "Approachability in Stackelberg Stochastic Games with Vector Costs," Dynamic Games and Applications, Springer, vol. 7(3), pages 422-442, September.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0198-y
    DOI: 10.1007/s13235-016-0198-y
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    Cited by:

    1. Soham R. Phade & Venkat Anantharam, 2023. "Learning in Games with Cumulative Prospect Theoretic Preferences," Dynamic Games and Applications, Springer, vol. 13(1), pages 265-306, March.

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