Trading Memory for Randomness
Abstract
Strategies in repeated games can be classified as to whether or not they use memory and/or randomization. We consider Markov decision processes and 2-player graph games, both of the deterministic and probabilistic varieties. We characterize when memory and/or randomization are required for winning with respect to various classes of - regular objectives, noting particularly when the use of memory can be traded for the use of randomization. In particular, we show that Markov decision processes allow randomized memoryless optimal strategies for all Mueller objectives. Furthermore, we show that 2-player probabilistic graph games allow randomized memoryless strategies for winning with probability 1 those Mueller objectives which are upward-closed. Upward-closure means that if a set of infinitely repeating vertices is winning, then all supersets of alpha are also winning.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2004
- Accession Number
- ADA458138
Entities
People
- Krishnendu Chatterjee
- Luca De Alfaro
- Thomas Henzinger
Organizations
- University of California, Berkeley