Climate negotiations are a sort of prisoner’s dilemma, so we need to find a way to change the game or change the outcome of a prisoner’s dilemma. Hofstadter proposes that if we can induce players to be “super-rational” we may get a more cooperative outcome. Does this make sense? [Read more…]

# A Real Prisoners’ Dilemma

Kane and Nestor exploited a bug in video poker machines to win hundreds of thousands. So the casinos had them arrested. But the Fed’s case began to fall apart. No, they had not hacked any computers. [Read more…]

# Motivation Function Upgrade for ERC

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).