Complexity and effective prediction
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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- Abraham Neyman, 2008.
"Learning Effectiveness and Memory Size,"
Discussion Paper Series
dp476, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000002427, David K. Levine.
- Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000001945, David K. Levine.
- Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 309-325.
- Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.