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.

Open PDF

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

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • California
  • Computer Science
  • Construction
  • Contrast
  • Graph Theory
  • Information Operations
  • Markov Chains
  • Probability
  • Probability Distributions
  • Sequences
  • Specifications
  • Terminals
  • Theorems
  • Transitions
  • Zero-Sum Games

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Military History of the United States in the 20th Century.