Termcard for Hilary 2013
Unless otherwise stated, events take place on a Tuesday in the Maths Institute at around 8:15pm
Tuesday Week 4, 5th February - The Reality Game
Doyne Farmer
We introduce an evolutionary game with feedback between perception and
reality, which we call the reality game. It is a game of chance in
which the probabilities for different objective outcomes (e.g. heads
or tails in a coin toss) depend on the amount wagered on those
outcomes. By varying the ‘reality map’, which relates the amount
wagered to the probability of the outcome, it is possible to move
continuously from a purely objective game in which probabilities have
no dependence on wagers to a purely subjective game in which
probabilities equal the amount wagered. We study self-reinforcing
games, in which betting more on an outcome increases its odds, and
self-defeating games, in which the opposite is true. This is
investigated in and out of equilibrium, with and without rational
players, and both numerically and analytically. We introduce a method
of measuring the inefficiency of the game, similar to measuring the
magnitude of the arbitrage opportunities in a financial market. We
prove that the inefficiency converges to equilibrium as a power law
with an extremely slow rate of convergence: the more subjective the
game, the slower the convergence.
