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High probability guarantees in repeated games: Theory and applications in information theory

Delgosha, P

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  1. Type of Document: Article
  2. DOI: 10.1109/ISIT.2016.7541573
  3. Publisher: Institute of Electrical and Electronics Engineers Inc
  4. Abstract:
  5. We introduce a 'high probability' framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high probability counterpart of the classical result of Mertens and Zamir for the zero-sum repeated games. Any payoff that can be guaranteed with high probability can be guaranteed in expectation, but the reverse is not true. Hence, unlike the average payoff case where the payoff guaranteed by each player is the negative of the payoff by the other player, the two guaranteed payoffs would differ in the high probability framework. One motivation for this framework comes from information transmission systems, where it is customary to formulate problems in terms of asymptotically vanishing probability of error. An application of our results to compound arbitrarily varying channels is given
  6. Keywords:
  7. Information theory ; Expected values ; High probability ; Information transmission systems ; Non equilibrium ; Probability of errors ; Repeated games ; Zero sums ; Probability
  8. Source: 2016 IEEE International Symposium on Information Theory, ISIT 2016, 10 July 2016 through 15 July 2016 ; Volume 2016-August , 2016 , Pages 1621-1625 ; 21578095 (ISSN) ; 9781509018062 (ISBN)
  9. URL: http://ieeexplore.ieee.org/document/7541573