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Games with Symmetric Incomplete Information and Asymmetric Computational Resources

Author

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  • Misha Gavrilovich

    (National Research University Higher School of Economics, 3 Kantemirovskaya st., St. Petersburg, Russia2St. Petersburg Institute for Economics and Mathematics, RAS, 38 Serpuhovskaya st., St. Petersburg, Russia)

  • Victoria Kreps

    (National Research University Higher School of Economics, 3 Kantemirovskaya st., St. Petersburg, Russia2St. Petersburg Institute for Economics and Mathematics, RAS, 38 Serpuhovskaya st., St. Petersburg, Russia)

Abstract

We consider random public signals on the state of two-person zero-sum game with incomplete information on both sides (both players do not know the state of the game). To learn the state, each player chooses a finite automaton which receives the public signal; the player only sees the output of the automaton chosen. Supposing that the size of automata available to Player 1 is essentially bigger than that available to Player 2, we give an example of public signal with random length of output strings where the posterior belief of Player 1 is the state and the posterior belief of Player 2 is close to his original belief. Thus, we demonstrate that asymmetric information about the state of a game may appear not only due to a private signal but as a result of a public signal and asymmetric computational resources of players.Besides, for a class of random signals with fixed length of output strings, we estimate the fraction of signals such that some automaton of given size may help Player 2 to significantly reestimate prior probability of the state. We show that this fraction is negligible if the size of automata of Player 2 is sufficiently smaller than length of output strings.

Suggested Citation

  • Misha Gavrilovich & Victoria Kreps, 2018. "Games with Symmetric Incomplete Information and Asymmetric Computational Resources," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-16, June.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:02:n:s0219198917500347
    DOI: 10.1142/S0219198917500347
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    References listed on IDEAS

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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. Hernández, Penélope & Solan, Eilon, 2016. "Bounded computational capacity equilibrium," Journal of Economic Theory, Elsevier, vol. 163(C), pages 342-364.
    3. Abraham Neyman, 1998. "Finitely Repeated Games with Finite Automata," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 513-552, August.
    4. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    5. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    6. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
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    Cited by:

    1. Anna Bogomolnaia & Misha Gavrilovich & Egor Ianovski & Galina Lyapunova & Hervé Moulin & Alexander Nesterov & Marina Sandomirskaia & Fedor Sandomirskiy & Elena Yanovskaya, 2021. "In memory of Victoria Kreps (3 September 1945–3 March 2021)," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 597-601, September.

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