Wednesday, April 23, 2008

Prisoner's Dilemma or Stag Hunt in the Superdelegates Commitment Game

I'm having to think back a while here, to my early grad school training, on the appropriate use of game theory to describe the superdelegate commitment problem in the Democratic Party nomination fight.

The prompt?

Jaime Sneider has argued that the propensity of some superdelegates to withhold commitment to either Hillary Clinton or Barack Obama is a "classic prisoner's dilemma" problem (via Memeorandum).

Sneider's responding to
John Podhoretz, who in turn was responding to Matthew Yglesias:

John Podhoretz on the chances of wrapping this thing up early:

Yes. Sure. Because politicians with the most valuable votes in America are just going to choose up sides and not spend three months being courted and feted and promised. They are going to forswear having their feet kissed, their backs massaged, their views requested, their wants fulfilled, their needs anticipated. They are going to throw their vote away rather than milk it for all it’s worth....

A thousand or so people are going to decide this primary. It behooves those people to have this go on as long as possible, because that is how they are going to get the most goodies. Maybe this is what Hillary truly understands.

Howard Dean has admonished superdelegates for the bazillionth time to declare which candidate they intend to support, but don’t hold your breath. The fact is the Democratic superdelegates are in a classic prisoner’s dilemma. It is in their collective interest to wrap up the nomination, but each of them gains influence as they hold out their vote. Dean recently set down a June 3rd deadline for the superdelegates. I’m looking forward to that day: the Democratic nomination won’t be settled, and Dean will inevitably look like the incompetent, impotent party leader he is.

Actually, the superdelegates' problem seems less a classic a prisoner's dilemma than a "stag hunt," from Jean Jacques Rousseau.

If memory serves me, I learned this theory in Kenneth Waltz, Man, the State, and War, but to make this quick, the Wikipedia version's going to have to do:

In game theory, the stag hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation in which two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.

The stag hunt differs from the Prisoner's Dilemma in that there are two Nash equilibria: when both players cooperate and both players defect. In the Prisoners Dilemma, however, despite the fact that both players cooperating is Pareto efficient, the only Nash equilibrium is when both players choose to defect....

Although most authors focus on the
prisoner's dilemma as the game that best represents the problem of social cooperation, some authors believe that the stag hunt represents an equally (or more) interesting context in which to study cooperation and its problems...
The superdelegate problem seems more apppriate here, as it includes a large number of actors (a situation of cooperation that might more resemble the real world, for example, as in the "carousel feeding" of a group orcas) and the situation of double Nash equilibria.

It's been a while since I studied The Evolution of Cooperation, so if any expert game theorists come along here with
a more beautiful mind, I'll be happy to defer.