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The Big Match with a Clock and a Bit of Memory

Author

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  • Kristoffer Arnsfelt Hansen
  • Rasmus Ibsen-Jensen
  • Abraham Neyman

Abstract

The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage. Blackwell and Ferguson (1968) give an $\varepsilon$-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. The present paper proves that there is such a strategy that is $\varepsilon$-optimal. In fact, we show that just two states of memory are sufficient.

Suggested Citation

  • Kristoffer Arnsfelt Hansen & Rasmus Ibsen-Jensen & Abraham Neyman, 2018. "The Big Match with a Clock and a Bit of Memory," Discussion Paper Series dp716, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp716
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    Cited by:

    1. Maya Bar-Hillel & Cass R. Sunstein, 2019. "Baffling bathrooms: On navigability and choice architecture," Discussion Paper Series dp726, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Hansen, Kristoffer Arnsfelt & Ibsen-Jensen, Rasmus & Neyman, Abraham, 2021. "Absorbing games with a clock and two bits of memory," Games and Economic Behavior, Elsevier, vol. 128(C), pages 213-230.

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