# How to convince subjects that the computer is playing fairly

We are planning an experiment using the odds-and-evens game. The rules of the game are simple: player A selects either "1" or "2"; player B selects simultaneously either "1" or "2"; if both select the same number, player A wins \$1 and B wins nothing; if they select different numbers, player B wins \$1 and A wins nothing.

In our experiment, player A is a human subject and player B is a computer program (the computer is programmed to play randomly - select "1" or "2" with equal probability each time). Our concern is: how to convince the human that this is really what's going on? The problem is that, the human reveals his choice by clicking a button, before the computer reveals its choice. So in theory, we could have programmed the computer to always choose a number different than the choice of the human. Indeed, we have an incentive to do so because it will reduce the amount of money that we will have to pay to the subjects!

How can we convince the human subjects that the computer makes its choice simultaneously and does not "cheat"?

As computer scientists, the first option that came to our mind is to use a cryptographic commitment scheme. But, this might be too complicated for the subjects to understand. Are there simpler solutions?

## 1 Answer

I'm imagining a system that chooses the computer's response not in a stochastic manner, but chaotically. Suppose you have some chaotic mapping function from the [0,1] interval to the {heads, tails} set. Choosing any real number in the set will get you some deterministic mapping to heads or tails. This mapping equation should be quite complex, but made visible to the user. Have them choose a number in [0, 1], and you'll get an output that appears random, but could be computed if the user chose to take the time. You just need to make the mapping function complex enough that it's not easily computable to rig the game, and also such that it maps 50% to heads and 50% to tails.