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Complexity and effective prediction

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Author Info

  • Neyman, Abraham
  • Spencer, Joel

Abstract

Let G= be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k,m) in which players 1 and 2 place down finite state automata with k,m states respectively and the payoff is the average per-stage payoff when the two automata face off. We are interested in the cases in which player 1 is "smart" in the sense that k is large but player 2 is "much smarter" in the sense that m>>k. Let S(g) be the value of G where the second player is clairvoyant, i.e., would know player 1's move in advance. The threshold for clairvoyance is shown to occur for m near . For m of roughly that size, in the exponential scale, the value is close to S(g). For m significantly smaller (for some stage payoffs g) the value does not approach S(g).

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 69 (2010)
Issue (Month): 1 (May)
Pages: 165-168

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Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:165-168

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000001945, David K. Levine.
  2. Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer, vol. 29(3), pages 309-325.
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Cited by:
  1. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Discussion Paper Series dp476, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer, vol. 42(4), pages 867-890, November.
  3. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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