Ihor Kendiukhov

I closely follow the work of Ole Peters and collaborators and believe it is very cool.

There is, unfortunately, a lot of confusion, and it is not framed in terms of decision theory apparatus, but that is what I am going to do precisely now.

An agent who maximizes the time-average growth rate of their wealth over their entire trajectory is, I claim, doing resolute choice in the sense MacLennan described.

they evaluate the whole plan the entire sequence of bets the complete wealth process as a unified object they ask given the dynamics of this stochastic process what strategy maximizes my long-run growth rate and then they execute that strategy

The utility function that falls out of this procedure, via the agonic mapping, which finds the transformation that renders the wealth process agonic, so that time and ensemble averages coincide, depends on the dynamics of the process.

For multiplicative dynamics, you get logarithmic utility, the Kelly criterion.

For additive dynamics, you get linear utility.

For more exotic dynamics, you get whatever transformation the agonic mapping produces.

This means the effective utility function is context-dependent.

It changes when the stochastic environment changes.

And context-dependence of the utility function is precisely what the independence axiom forbids, because independence says your preference between sub-gambles should not depend on what else is in the package.

So the EE agent violates independence.

But are they exploitable?

No.

And the reason maps exactly onto the resolute choice framework.

The EE agent has committed to a trajectory-level optimization.

Maximize time-average growth.

They don't re-evaluate at intermediate nodes by asking, given that this branch of the uncertainty has been resolved, what do my local preferences say?

They continue executing the trajectory-level strategy because it was derived from a global evaluation of the entire process.

The money pump has no leverage because there is no gap between the agent's ex-antiplan and their ex-post behavior.