Easy to Win, Hard to Master: Optimal Strategies in Parity Games with Costs

Authors Alexander Weinert, Martin Zimmermann

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Alexander Weinert
Martin Zimmermann

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Alexander Weinert and Martin Zimmermann. Easy to Win, Hard to Master: Optimal Strategies in Parity Games with Costs. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the distance between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games while retaining most of their attractive properties, i.e, determining the winner is in NP and co-NP and one player has positional winning strategies. We show that the characteristics of parity games with costs are vastly different when asking for strategies realizing the minimal such bound: the solution problem becomes PSPACE-complete and exponential memory is both necessary in general and always sufficient. Thus, playing parity games with costs optimally is harder than just winning them. Moreover, we show that the tradeoff between the memory size and the realized bound is gradual in general.
  • Parity Games with Costs
  • Optimal Strategies
  • Memory Requirements
  • Tradeoffs


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