US government shutdown: another bargaining game with incomplete information

At the end of last year the main preoccupation in United States politics was anticipating the consequences of the infamous fiscal cliff. A quick reminder for the readers; back then the two main political parties had to reach a consensus over necessary budget cuts and tax increases in order to avoid automatic large spending cuts and tax hikes that would immediately lower the budget deficit but would also push the country into another recession (hence the term "push off the fiscal cliff"). The very threat of a fiscal cliff necessitated a consensus from the two parties. Its December 31st deadline was the status quo restriction on the policymakers to avoid another recession and "do the right thing" by agreeing on which taxes should rise and where in the budget should they cut. By the end of December things were getting really unstable while signals sent by the media were implying that no solution will be reached. However in the very last minute President Obama and John Boehner (House speaker - the House has a Republican majority) did reach a decision temporarily saving America from a double dip and postponing the debt ceiling decision for another month or so.

Back then I analyzed this situation using a game theory framework, implying that a Nash equilibrium outcome would be No deal, i.e. both sides are likely to stick to their agenda and push the country off the fiscal cliff.

Why the shutdown?

Ten months later, a similar situation is arising, but this time with different consequences. After having failed to agree on the budget for this fiscal year which would inevitably raise the debt ceiling, President Obama declared a government shutdown. This is nothing strange as it happened before, and is actually allowed by the US Constitution which requires Congress to regularly pass laws funding the government. If it doesn't the government shuts down some of its operations. The idea is something I essentially agree with - the Constitution implies that elections alone are insufficient to protect the citizens against potential government usurpation of their rights. If you think this through the concept of interest group state capture, or the current crony political system, you tend to understand the power in Madison's words.

The consequences of the shutdown aren't nearly as severe as they would be in case of a fiscal cliff (I mean if the government can operate fine with a third of their employees not coming to work, then the conclusion is self-evident, isn't it?), but they are inconvenient, and they do put the US in a difficult position regarding its credit rating. The markets are sending signals of concern over how the dispute will be settled, while international politicians (IMF) are urging the US to find a consensus and not put the entire world recovery at risk. 

However, despite the warnings, both sides remain stubbornly confident in their position, not showing any signs of backing down. President Obama declared he won't consider any bipartisan efforts to curb the long term deficit and the unsustainable costs of Medicare and Medicaid, until the current budget is approved and the debt ceiling is raised. On the other hand the Republicans are given an opportunity to show to the public that the US doesn't need such a large government after all. Even though this might be true, the actual shutdown is likely to be more costly than the regular operations of government*. The last time this happened (1996) it cost the government around $1.4bn, which was effectively even higher as when people got back to work there were backlogs which made everyone less efficient. It may also cause temporary economic activity to slow down as public sector employees aren't getting their paychecks on time. Moody's have estimated that a three week shutdown will cost 1.4 percentage points in terms of growth in the fourth quarter. This is indeed a significant cost. 

The bargaining game

And now the game starts (table below). Once again, the situation is very similar to that of 10 months ago. Whoever caves in and allows the other party to claim victory loses significantly (payoff of -6). If the debt ceiling isn't increased, both parties lose as the electorate will blame them both for causing a mess. However, both parties could resort to ideology and persuade their partisan voters that the blame is on the other party. Even as the country as a whole loses out the loss to one party is arguably less than if they back out and admit defeat. This is why in the game table (the same one we had before but with lower payoffs) a No deal is a better solution for a party than admitting defeat and letting the other party retain its position. The standard noncooperative game ends up in a No deal, No deal equilibrium with a payoff of (-3,-3).  

If they do reach a consensus and cooperate, they benefit by "saving the country" and can go to their electorates (and radical party members) announcing they've made a good deal, but had to cave in to some of the suggestions the other party made. With political discourse as it currently is, that outcome is getting increasingly unlikely. 

Dems/ Reps	Strike deal	No deal
Strike deal	-1,-1	-6,0
No deal	0,-6	-3, -3 *

Last time I introduced a dynamic component to the game solving if for a subgame perfect Nash equilibrium and getting the same outcome of No deal. This applies today as well if we assume that the shutdown (a status quo) is a more preferred option than succumbing to the other party's optimal position. The problem then, as it was now, was in the perception of the strength of the commitment device (the punishment). If the politicians of either parties don't perceive the threat of shutdown or the debt ceiling severe enough, they aren't likely to cooperate. But if the commitment device (the threat of default) is strong enough, eventually it will yield a cooperative solution, just as Axelrod (1984) has predicted for many real-life scenarios. And just as it eventually did happen during the fiscal cliff negotiations. 

The outcome for the economy? More uncertainty. High costs.  

* If one wants to lower to size of government, shutting down some of its services this way isn't the way to do it. For example if we want private provision for certain government services (like parks, monuments, etc.), one needs to allow time for market actors to react upon this signal and provide such a service.