Testing Randomness by Matching Pennies

TL;DR

This paper explores the concept of randomness in the game of Matching Pennies, highlighting the difficulty of detecting non-random strategies and linking randomness to strategic outsmarting.

Contribution

It introduces a perspective connecting randomness and strategic outsmarting, emphasizing the complexity of recognizing non-random behavior in game theory.

Findings

Recognizing non-random strategies can be arbitrarily hard.

Randomization is easy to implement, but detecting opponent's non-randomness is complex.

The paper links the notions of randomness and outsmarting in game theory.

Abstract

In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they display different sides, then Bob wins Alice's penny. To avoid giving the opponent a chance to win, both players seem to have nothing else to do but to randomly play heads and tails with equal frequencies. However, while not losing in this game is easy, not missing an opportunity to win is not. Randomizing your own moves can be made easy. Recognizing when the opponent's moves are not random can be arbitrarily hard. The notion of randomness is central in game theory, but it is usually taken for granted. The notion of outsmarting is not central in game theory, but it is central in the practice of gaming. We pursue the idea that these two notions can be usefully viewed as two sides of the same coin.