What to do about governors that defect in the stimulus-bill maneuvering, their version of the Prisoner's Dilemma?

From Wikipedia's description of the game-theory challenge:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

The governors threatening to defect from participating in the stimulus package are likely to still benefit from a recovering economy, without assuming any responsibility for it. The game, and the governors, both exploit the commons.

In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.

But when one plays repeatedly, other options exist:

In this case, the incentive to defect can be overcome by the threat of punishment. When the game is infinitely repeated, cooperation may be a subgame perfect Nash equilibrium although both players defecting always remains an equilibrium and there are many other equilibrium outcomes.

What is a suitable sanction to discourage the defecting governors? Can we start with ridicule?

Obama is apparently pursuing a cooperation strategy, which was discovered by Robert Axelrod, (no apparent relation), and explained in his book "The Evolution of Cooperation".

Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selction.

[Axelrod had a contest for programmers to run game models.]

The best deterministic strategy was found to be "Tit for Tat," which Anatol Rapaport developed and entered into [Axelrod's] tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his opponent did on the previous move. Depending on the situation, a slightly better strategy can be "Tit for Tat with forgiveness." When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1%-5%). This allows for occasional recovery from getting trapped in a cycle of defections.

Obama has started off by inviting GOP cooperation, and when he doesn't actually get it, he reciprocates. Let's hope this is a winning strategy for the long run. The opposing party can reap a lot of credit if things improve, by arguing it had helped limit actions. And of course it can dodge responsibility if things get worse.