Bolton and Ockenfels ERC paper replaces the standard utility function with a motivation function: m = m(y, sig), where y is player i’s wealth and sig is y / (total wealth = c).

When a player has average wealth, sig = 1/n, where n = # of players.

Assumption 3 states that, for any y, dm/dsig = 0 for sig = 1/n. And the second partial of m w.r.t. sig < 0 for all sig. Hence m(y,sig) is maximized for any y, by sig=1/n.

This appears to be contradictory:

- Consider m() for a specific player i
- m(1, 1/2) has a zero derivative w.r.t. sig in a 2-player game with c = 2.
- so m(1, 1/3) does not have zero derivative.
- But consider the same player in a 3-person game, with c =3, and we find:
- m(1, 1/3) has a zero derivative w.r.t. sig.

There seem to be two ways out.

- Assume that a player is described by a family of motivation functions, one for each number of players. I.e., define: m = m(y, sig, n).
- Define m = m(y, R), where R = n y / c = wealth / (average wealth).

c.d. mclean says

re “family of motivation functions” …

you may find some of the work of B. Mandelbrot

on multi-fractal systems ( … and the connections

to general dynamical systems and chaotic attractors)

both interesting and useful.

best,

cdm

sstoft says

I wrote the fastest program for calculating the Mandelbrot set, and handed it to him on a floppy many years ago when he gave a talk at UC Berkeley. Never heard back. The fractals are very cool, but chaos theory seems to have produced mostly chaos, as far as I can tell.

I agree that human behavior is chaotic, scientific testing will require a far more modest approach for a long time to come. Mandelbrot was anything but modest.

Thanks much for your interest. –Steve

Vlasova says

That’s a posting full of insgthi!