The Big Match with a Clock and a Bit of Memory

Hansen, Kristoffer Arnsfelt, Ibsen-Jensen, Rasmus ORCID: 0000-0003-4783-0389 and Neyman, Abraham (2018) The Big Match with a Clock and a Bit of Memory. In: EC '18: ACM Conference on Economics and Computation.

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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 £-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. We prove that there is such a strategy that is £-optimal. In fact, we show that just two states of memory are sufficient.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	Stochastic Games, Markov Strategies, Bounded memory
Depositing User:	Symplectic Admin
Date Deposited:	06 Dec 2018 09:42
Last Modified:	07 Dec 2024 03:45
DOI:	10.1145/3219166.3219198
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029558