Quantitative Fairness Games
Abstract
We consider twoplayer games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequencyrelated properties: (i) all colors occur with the same asymptotic frequency, (ii) there is a constant that bounds the difference between the occurrences of any two colors for all prefixes of the path, or (iii) all colors occur with a fixed asymptotic frequency. These properties can be viewed as quantitative refinements of the classical notion of fair path in a concurrent system, whose simplest form checks whether all colors occur infinitely often. In particular, the first two properties enforce equal treatment of all the jobs involved in the system, while the third one represents a way to assign a given priority to each job. For all the above goals, we show that the problem of checking whether there exists a winning strategy is CoNPcomplete.
 Publication:

arXiv eprints
 Pub Date:
 June 2010
 arXiv:
 arXiv:1006.5097
 Bibcode:
 2010arXiv1006.5097B
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing
 EPrint:
 EPTCS 28, 2010, pp. 4863