Attack on Utility

Let's attack established notions of utility function and time value of money.

Settings: economic problems in a world populated by rational consuming actors.

Every actor is characterized by its preferences between different schedules of consumption.

Definition: A schedule s : S =def= R -> Rⁿ is a function from real time to real intensity of n different modes of consumption.

Definition: A preference >= : A =def= S x S is a partial order - a binary reflexive, transitive, and antisymmetric relation between schedules.

In game theoretic term both schedule and preference form a strategy for choosing moves - consumption intensities.

Assumption (unbounded rationality): actors have no problems comparing huge or even infinite objects.

Assumption (decisiveness): actors always prefer one of two different schedules.

Thus all preferences are total orders.

In a world without other rational actors or random nature, the state of world limits the possible schedules.
E.g., if the actor has some bread, and no means to produce or acquire more, then the possible schedules are limited to those where cumulative consumption of bread over time is not more than given.

Definition: A deterministic state of world w : W =def= P(S) is a set of possible schedules.

Under certain natural conditions, every every actor prefers some schedule in every state of world.

Definition: maxWS : A x W -> S.

This induces total order between world states: lift : A -> P(W x W).

TODO: probabilistic states. how do actors know probabilities?
TODO: concurrent actors. how do actors know who caused what?
TODO: long-term decisions.