# Applying Game Theory to the Debt Standoff

by: Cam Hui, CFA

The markets have been fairly sanguine about the debt ceiling debate, largely because there is an underlying assumption that some sort of deal will get done before the deadline. Then I got to thinking - the markets are highly top-down, macro-economic focused about this debate, what if the proper framework for analysis is micro, not macro, economics?

Game Theory as analytical framework
For a micro-economic point of view, I turn to Game Theory as a way of forecasting behavior. The classic problem in Game Theory is the Prisoner's Dilemma, described by Wikipedia in the following way:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full one-year sentence. If both remain silent, both prisoners are sentenced to only one month in jail for a minor charge. If each betrays the other, each receives a three-month 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?

If we cast the Republicans and the Democrats as the two prisoners in the problem and the incentive is winning the next election, then we can see the debt ceiling issue in a different light [emphasis added]:

If we assume that each player cares only about minimizing his or her own time in jail, then the prisoner's dilemma forms a non-zero-sum game in which two players may each either cooperate with or defect from (betray) the other player. In this game, as in most game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution, that is, rational choice leads the two players to both play defect, even though each player's individual reward would be greater if they both played cooperatively.

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.

In other words, when faced with a choice between the common good and personal gain, the optimal decision is to defect for personal gain, or allow the deadline to pass with no deal in order to gain political advantage in the next election.

Playing the brinksmanship game
That's what happens when you play the game of brinksmanship. Left leaning blog DailyKos described brinksmanship during the Cold War era in the following way:

That word was conjured by President Dwight Eisenhower's secretary of state, John Foster Dulles, to describe the Soviet Union's approach to international policy during the Cold War of the 1950s. Brinkmanship was most evidently realized in a pair of international crises -- the Soviet blockade of West Berlin resulting in the US-led Berlin airlift campaign to resupply the city in 1948 and 1949, and the 1962 Cuban Missile Crisis, where US and Soviet military forces nearly came to blows over the USSR's emplacement of nuclear missiles on that island nation.

Brinkmanship tactics, by the Dulles understanding, involve threats that are continuously escalated -- sometimes just by one side, sometimes by all sides. The threats need to be credible if the aggressor is to have any chance of actually obtaining capitulation. The best defense against brinkmanship is to respond with similar escalating threats. It is a flawed and risky defense in that there is always the chance one side or another will not back down, forcing a final confrontation. Often, however, one side (the USSR, in both the above mentioned incidents) did back down and disaster was averted.

Of course, DailyKos blames the Republicans for the impasse, but I am not here to lay blame but to analyze the situation. What are the chances that someone blinks because of the apocalyptic nature of the decision of both sides to "defect" in this game of Prisoner's Dilemma?

Consider the Republican position as an example. Conservative commentator David Frum describes the Republicans as backing themselves into a corner, which will likely cause them to "defect" in the game of Prisoner's Dilemma:

[The] Republicans put the gun on the table. They raised the menace of deliberate default in a way it has not been raised before.

Then, having issued the threat, they discovered that their own core supporters would not allow the gun to be holstered again.

They issued demands they knew could not be met, for budget cuts much bigger than Republicans ever enacted when they had the power to enact them. They cocked the weapon. And now here we are: the demands are unmet and Republicans find themselves facing a horrible choice between yielding on their exorbitant demands or pushing the United States into financial upheaval.

Be careful about what you wish for
On the other hand, Greg Mankiw is right in that people can and will respond to incentives. If you structure the incentive as gaining power in the next election, then a financial apocalypse looms. On the other hand, if you think about the incentives what you can do in the event that you win the next election, then the game changes. Here is Frum writing about the possibility of payback, a.k.a. Be careful about what you wish for because you might get it:

Consider this scenario: President Palin (or Romney or Perry or Pawlenty or whoever) is sworn in with great jubilation among movement conservatives in January 2013. Voter distaste with Democrats also led to the crushing defeat for Democratic Congressional incumbents, leaving Republicans with hefty majorities in the House and Senate. In a paroxysm of celebration, Republicans pass the Ryan budget, slashing taxes and putting major reforms in Medicare years down the road. However, the growth promised by advocates of this budget does not materialize, and (as the budget estimates) the federal government runs huge deficits for the first two years of the new presidentâ€™s term. Frustrated with a series of broken economic promises, voters turn Republicans out in massive numbers in the 2014 midterms. Though Republicans cling to a narrow majority in the Senate, they are wiped out in the House, and an exultant Nancy Pelosi reclaims the title of Speaker.

In passing the Ryan budget, Congress also upped the debt ceiling by a trillion or so, but perpetual deficits mean that the ceiling is coming awfully close, and federal spending is due to break it in early August 2015. So now, in May, the president must go on bended knee to Speaker Pelosi, who demands tax increases as the price for her caucus supporting an increase in the debt ceiling.

In this example, how the Republican Party thinks about incentives (winning the election, or what happens to the prize should they win) will incentivize them quite differently as to how they play this game.