The Big Match with a Clock and a Bit of Memory (joint work with Kristoffer Arnsfelt Hansen and Rasmus Ibsen-Jensen

Location: 
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
Dates: 
Sunday, May 13, 2018 - 14:00 to 15:45
Lecturers: 
Abraham Neyman
HUJI
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.