The complexity of interacting automata
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This paper studies the interaction of automata of size m. We characterise statistical properties satisfied by random plays generated by a correlated pair of automata with m states each. We show that in some respect the pair of automata can be identified with a more complex automaton of size comparable to \(m\log m\). We investigate implications of these results on the correlated min–max value of repeated games played by automata.
KeywordsComplexity Automata De Bruijn sequences Bounded memory
We are grateful to three anonymous referees and an editor who contributed valuable suggestions that significantly improved the quality of this paper.
- Aumann RJ (1981) Survey of repeated games. Essays in game theory and mathematical economics in honor of Oskar Morgenstern. Bibliographisches Institut, Mannheim, pp 11–42Google Scholar
- Cover TM, Thomas JA (2006) Elements of information theory, 2nd edn. Wiley, New YorkGoogle Scholar
- De Bruijn NG (1946) A combinatorial problem. K Ned Akad Wet 49:758–764Google Scholar
- Kalai E (1990) Bounded rationality and strategic complexity in repeated games. In: Ichiishi T, Neyman A, Tauman Y (eds) Game theory and applications. Economic theory, econometrics, and mathematical economics. Academic Press, San Diego, pp 131–157Google Scholar
- Neyman A (2008) Learning effectiveness and memory size. In: Discussion paper 476, Center for the Study of Rationality, Hebrew University, JerusalemGoogle Scholar
- Shapira A (2007) Symmetric online matching pennies. PhD thesis, Hebrew University, JerusalemGoogle Scholar