Here is a series I did on my micro-blog, Tumbld Thoughts that discusses various aspects of the US Government Shutdown. This is largely a review of blog entries and opinion pieces that cover the strategic aspects behind the shutdown. At first, I was going to do my own theoretically-oriented (and more speculative) post on this topic, but subsequently found that a lot of the work has already been done for me. I conclude with my own thoughts on the strategy of gridlock.
In this section, I will be reviewing the role of game theory and game-theoretic thinking in the current US Government gridlock crisis. This introduces the game-theoretic framework and potential mitigating factors. Prior to doing this research, my initial thought was that a game-theoretic model of suicide bombing would be the best way to model the government shutdown and its resolution . However, this standoff can also (and perhaps more effectively) be modeled using the Game of Chicken .
In the Game of Chicken, the two parties drive towards each other and decide to deploy one of two strategies: remain steadfast, or swerve. The first individual to swerve loses the game. While the strategies are played simultaneously, the goal is to swerve last. However, if no one swerves, both parties lose. Unlike the case of two race car drivers displaying their bravado, there are multiple criteria that determine whether or not each side will decide to swerve first. Several of the comments in  suggests that the current showdown is an example of an incomplete information conflict bargaining model , which suggests that due to a bilateral misunderstanding of position, no one knows what the actual bargaining space looks like.
But what does this bargaining space look like? Is it only shaped by strategic interactions (e.g. maximizing individual or joint payoffs), or is it partitioned by disjoint worldviews. Jonathan Chait  discusses the standoff as a consequence of Republican intellectual insularity (a term called epistemic closure). According to him, the Democratic position that capitulating to political ransom will only lead to further hostage-taking requires a response which the Republicans are unable to conceptualize. For example, it may be that Ted Cruz and others in the Tea Party cannot conceptualize an outcome that does not involve a zero-sum outcome .
Player Strategy and Strategic Nuances
Now, we will discuss the underpinnings of why a game-theory explanation might and might not work well to model the current US Government gridlock crisis. As it turns out, there are many subtleties that must be considered to better understand the conflict. In other words, a simplistic game theory model (e.g. Chicken or Suicide Bomber) might not offer much insight.
Is this simply a problem of inadequate mental modeling of political reality, or cryptic signaling on the part of the Republican side? Thomas Edsall introduces us to the role of collective anger as a cryptic signal in political motivations . In , Jon Chait recaps the positions of Obama and Boehner and the nature of their negotiations. This article suggests that Boehner's position is weak despite the rhetoric. In fact, the entirety of Republican negotiating rhetoric (up until this point) has been a series of over-aggressive negotiating blunders . But perhaps another part of the problem involves a poor understanding of what is at stake. Matt Yglesias  explains why the debt ceiling is not at all like, say, a home mortgage, and why understanding complex phenomena through simple analogies can oftentimes misstate the actual goals and payoffs.
In , the nature of partisan conflict are explored. This was written before the current crisis, so it offers some perspective. Basically, there are two novel arguments here: that local interests that work to get people elected do not align well with solving national-level problems, and that financial debates are often polarizing by nature. On the other hand, the Republican side may have two covert goals in their negotiations . The first is that Republicans will only agree to a scenario that will give them leverage. To model this in terms of a payoff matrix, an "epistemic"  pure strategy suite is selected by the Republican players so as to create nothing but winner-take-all outcomes based on their beliefs about the consequences. The second is that Republicans cannot directly admit to their actual strategy, lest they appear to be the instigators. In the long run (since this is an unstable strategy), they risk losing leverage on this basis alone.
Perhaps things are less complex than the roots of partisan conflict suggest. In , Anatole Kaletsky considers this conflict from the standpoint of maximizing rational decision-making. This is partially a matter of timing the ultimate response. For example, it may benefit the Republicans to wait until the debt limit deadline to capitulate. On the other hand, there are pressures to capitulate before then, which may lead the Democrats to overplay their hand. This could further radicalize the Republican position, which could lead to less willingness to compromise in future standoffs.
Finally, it may be that the actual number of negotiators is hard to approximate using simple models. Dylan Matthews (Wonkblog) interviewed Daniel Diermeier from Northwestern University that provides some additional insight into modeling the crisis . The first involves the asymmetry of the negotiation: the President (representing the Democrats) is actually dealing with a caucus rather than a single individual (Boehner). The second point involves the reversion point of the negotiators: all parties are influenced not just by their position and the most rational outcome, but by public (e.g. voters, bankers) opinion as well. This may require a hierarchical model of agent interactions on each side of the game . Perhaps things aren't as dysfunctional as we like to believe.
Another game-theoretic approach that might explain features of the shutdown involves the "hold-up" problem , which enables good-faith exchanges in two-party transactions. In this scenario, a lack of faith in government can make one party inherently less invested in any bi-partisan agreement. Similarly, a significant investment by the Republicans to keep the government shut down could backfire, giving the Democrats less incentive to give their opponents anything in negotiation. But perhaps game theory is not the only game in town. One alternate perspective suggests that the shutdown is a natural by-product of a historical fluctuations and a government that is too centralized and hierarchical to respond to such (predictable) challenges .
Further Developments: the Distractor Game
To further understand the strategy of political intransigence (a minority shareholder trying to get their own way), I present something called the "distractor game", which can be applied to many problems in which a weaker position attempts to gain a reward through distraction (or a high-cost, high-risk, and seemingly nonsensical strategy). In the poster, a toy example is used, but can be generalized to a wide variety of interactions.
The distractor game resembles both the sneaker strategy found among evolutionarily stable mating strategies and the bait-and-switch tactic used in marketing. The difference lies in the payoff structure. While this might explain the broader tactic of intransigence, there may be an even broader tactic of "freezing things in stasis in the face of social change" that remains unexplored.
 Siquera, K. and Sandler, T. Games and Terrorism: recent developments. CREATE Research Archive, April 1 (2009) AND Jacobson, D. and Kaplan, E.H. Suicide Bombings and Targeted Killings in (counter-) Terror Games. Conflict Resolution, 51, 772-792 (2007).
 amurdie Game of Chicken and the US Government Shutdown: What Game Theory Can Tell Us About Likely Outcomes. Duck of Minerva blog, September 30 (2013).
 Fearon, J.D. Rationalist Explanations for War. International Organization, 49(3), 379-414 (1995).
 Chait, J. How Republicans Failed to Understand the Democrats’ Debt-Ceiling Logic. Daily Intelligencer, October 7 (2013).
 Keller, B. The Right Gets its 60's. New York Times, September 29 (2013).
 Edsall, T.B. Anger can be power. NYT Opinionator, October 8 (2013).
 Chait, J. John Boehner Too Embarrassed to Defend His Own Extortion Demands. Daily Intelligencer, October 8 (2013).
 Krugman, P. Aggressive Blunderers. Conscience of a Liberal blog, October 3 (2013).
 Yglesias, M. The Debt Ceiling Is Nothing Like Your Mortgage. Moneybox, October 8 (2013).
 El-Erian, M. How game theory explains Washington's horrible gridlock. The Atlantic, January 15 (2013).
 Sargent, G. The Morning Plum: A clarifying moment of Washington dysfunction. The Plum Line, October 9 (2013).
 Chait, J. Why the Shutdown Is Leading to Debt Default; or, What Happens When You Take Hostages Without a Plan. Daily Intelligencer, October 2 (2013).
In this case, an epistemic strategy suite is one that is restricted to strategies that allow one to argue from a certain set of premises.
 Kaletsky, A. Game theory and America’s budget battle. Reuters, October 3 (2013).
 Matthews, D. How a game theorist would solve the shutdown showdown. Wonkblog, October 4 (2013).
 Bottom picture is from: Synnaeve, G. Bayesian Programming and Learning for Multi-Player Video Games: application to RTS AI. PhD Thesis (2012).
 MacKensie, D. The maths that saw the US shutdown coming. New Scientist, October 10 (2013).