The Big Match with a Clock and a Bit of Memory

Kristoffer Arnsfelt Hansen*, Rasmus Ibsen-Jensen, Abraham Neyman

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

The Big Match is a multistage 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; otherwise, he wins a point. As soon as player 1 hides one pebble, the players cannot change their choices in any future stage. The undiscounted Big Match has been much-studied. Blackwell and Ferguson (1968) give an ε-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 on just the clock or just a finite memory is worthless (i.e., cannot guarantee strictly more than the least reward). The long-standing natural open problem has been whether every strategy that depends on just the clock and a finite memory is worthless. The present paper proves that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient.

OriginalsprogEngelsk
TidsskriftMathematics of Operations Research
Vol/bind48
Nummer1
Sider (fra-til)419-432
Antal sider14
ISSN0364-765X
DOI
StatusUdgivet - feb. 2023

Fingeraftryk

Dyk ned i forskningsemnerne om 'The Big Match with a Clock and a Bit of Memory'. Sammen danner de et unikt fingeraftryk.

Citationsformater