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Continuous Positional Payoffs

Author Alexander Kozachinskiy

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Author Details

Alexander Kozachinskiy
  • Department of Computer Science, University of Warwick, Coventry, UK

Funding

Supported by the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice).

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Alexander Kozachinskiy. Continuous Positional Payoffs. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CONCUR.2021.10

Abstract

What payoffs are positionally determined for deterministic two-player antagonistic games on finite directed graphs? In this paper we study this question for payoffs that are continuous. The main reason why continuous positionally determined payoffs are interesting is that they include the multi-discounted payoffs.
We show that for continuous payoffs positional determinacy is equivalent to a simple property called prefix-monotonicity. We provide three proofs of it, using three major techniques of establishing positional determinacy - inductive technique, fixed point technique and strategy improvement technique. A combination of these approaches provides us with better understanding of the structure of continuous positionally determined payoffs as well as with some algorithmic results.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
Keywords
  • Games on graphs
  • positional strategies
  • continuous payoffs

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