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Strategy complexity of limsup and liminf threshold objectives in countable MDPs, with applications to optimal expected payoffs

Author

Listed:
  • Richard Mayr

    (University of Edinburgh)

  • Eric Munday

    (University of Edinburgh)

Abstract

We study Markov decision processes with a countably infinite number of states. The $$\limsup $$ lim sup (resp. $$\liminf $$ lim inf ) threshold objective is to maximize the probability that the $$\limsup $$ lim sup (resp. $$\liminf $$ lim inf ) of the infinite sequence of directly seen rewards is non-negative. We establish the complete picture of the strategy complexity of these objectives, i.e., the upper and lower bounds on the memory required by $$\varepsilon $$ ε -optimal (resp. optimal) strategies. We then apply these results to solve two open problems from (Sudderth in Decis Econ Finan 43:43–54, 2020) about the strategy complexity of optimal strategies for the expected $$\limsup $$ lim sup (resp. $$\liminf $$ lim inf ) payoff.

Suggested Citation

  • Richard Mayr & Eric Munday, 2025. "Strategy complexity of limsup and liminf threshold objectives in countable MDPs, with applications to optimal expected payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 48(1), pages 643-692, June.
    • Handle: RePEc:spr:decfin:v:48:y:2025:i:1:d:10.1007_s10203-024-00485-7
    DOI: 10.1007/s10203-024-00485-7
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    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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