To play matching pennies, players need to decide whether their
opponent is more likely to play heads or tails next.
What is ideally needed for forecasting applications is a probability
density function over the possible outcomes. So, in this case, the probability
of the next symbol being heads.
If you have a probability density function over the possible outcomes,
that means that a forecast of the future possibilities can be made.
That would look somethinng like the following diagram:
Iterative predictions produce a forecast
There is a fairly simple way of motivating participants to
provide probability density functions over the possible outcomes: have them
set odds on those outcomes, and then force them to accept bets on them.
If they give a high certainty - and are correct - then they get a greater
reward. However, if they give a high certainty - and are wrong - then they get
However, this is considered to be too much of a complication for the early
versions of the matching pennies tournament.
Tim Tyler |