Dear all,
Next week's talk will be by Ghislain Fourny at 5pm on Tuesday in HIT
K51. The title and abstract are below.
See you there,
Roger
---
Perfect Prediction: an intriguing paradox, a prediction model and its
application to game theory
In the first part of the talk, we will introduce and discuss Newcomb's
paradox. Newcomb's paradox is a thought experiment in which a player is
faced with a choice between two outcomes. Her choice was predicted
before the game even takes place. According to his prediction, the
predictor acted on the outcomes, also before the game takes place,
bringing along a cyclic dependency between the past and the future. The
paradox relies in the apparent conflict between prediction and free
will. This paradox (and whether it actually is a paradox) is much
debated among philosophers and decision theoreticians. It leads to two
"schools of thought", the reasonings of which seem equally correct, but
lead to opposite results. We will see that it can be accounted for by
different models of prediction. Surprisingly, even the stronger model,
which we call perfect prediction, is compatible with free will. This
comes at the cost of giving up the fixity of the past: the past is
"unbestimmt" until the player has made her decision. What looked like a
grandfather paradox then all comes down to a fix-point problem.
In the second part of the talk, we will apply this concept of perfect
prediction to game theory, as a refinement of a concept which is
widespread in economics, that of rational expectations. The concept of
rational expectations "asserts that outcomes do not differ
systematically from what people expected them to be" (Sargent). For
games in extensive form, modeled as trees, with strict preferences, a
new equilibrium concept can be defined, called Perfect Prediction
Equilibrium. Although general algorithms exist to compute it, we will
rather familiarize ourselves with this equilibrium concept and the
intuition behind it by the means of simple examples. The main feature
behind Perfect Prediction Equilibrium is that a perfect predictor has
the power to "preempt" an outcome by breaking the causal bridge leading
to it. This equilibrium has many interesting properties, such as its
existence, its uniqueness, as well as its transparency: although the
players, who are perfect predictors, know the outcome of the game in
advance, it is still their interest to play towards this outcome.
Finally, the Perfect Prediction Equilibrium is also Pareto-optimal,
meaning that no other outcome would make both players better off.