As I’m sure all astute Duck readers are aware, today marks a critical day in the US House and Senate – if no deal is struck today on a spending bill, the US government will shut down at one minute after midnight on Tuesday morning. The issue at the heart of the controversy: a series of amendments to the spending bill that concern the Affordable Care Act (so-called “Obamacare”). In general, House Republicans are in favor of the amendments; Senate Democrats are against the amendments. So, both sides are holding firm to their stance on the amendments in hopes that the other side caves in before tomorrow. What are the likely outcomes of this situation?
Now, I’m not a specialist in American Politics. I can follow-along on tv and in the political science journals but, quite bluntly, that’s it. However, I do know my classic game theory games and this scenario seems eerily similar to the canonical Game of Chicken. Remember this one? Two hormonal teenagers are racing directly towards each other in souped-up cars on a deserted highway while their friends watch (I actually prefer the scenario in Footloose where tractors were the vehicle of choice). Although the teenagers would be relatively happy if both of them were to swerve, both teenagers want the other youth to swerve first and become the “chicken,” effectively giving the winning teen the prom date/letterman’s jacket/bragging rights. The problem: if neither teen swerves, the result would be disastrous. As James Morrow states in his 1994 Game Theory for Political Scientists, if neither teen swerves, “many hormones would be spilt on the pavement” (93). Like the classic game of chicken, as many in the popular media have remarked, the Republicans and Democrats are driving towards each other, each hoping that the other will “swerve first” on the issue of the spending bill amendments, avoiding the car-crash that would be a government shutdown.
What can the game theory version of the game of chicken teach us about this situation? I think the classic equilibrium solutions to the game of chicken imply three things with respect to the current government crisis. First, someone may decide to “swerve” today. There are three Nash equilibria (definition: if all players adopt these strategies, no one has a unilateral incentive to defect) to the game of chicken. Two are pure –strategy equilibria: in each of these, one of the players decides to swerve while the other remains steadfast. The other Nash equilibrium is a mixed strategy game where each party “mixes” or “randomize[s]” (Morrow 1994, 87) between swerving or not swerving. This implies my second point: unfortunately for all of us, the mixing strategy means that the mess-on-the-pavement actually could happen.
My third point is actually the most difficult to swallow. If we move from just focusing on Nash equilibria in a scenario with only 2 players playing the game to a scenario where there is a random pairing of individuals in an evolving environment where there can be “mutants” (this is the basic scenario needed to examine evolutionary stable strategies), the mixed strategy Nash equlibrium is the only equilibria solution that holds as an evolutionary stable strategy (ESS). What this means: the likelihood of blood on the highway tomorrow morning might actually be pretty great. I recommend holding off purchasing those tickets to the Grand Canyon.
The evolutionary chicken game analogy here emphasizes the behavioral learning aspects of Congressional strategies–how are they reinforced to behave?–and implies that we may be stuck with confrontations and even disasters for the time being. But there are some reasons to hope that this analogy is not the best one.
The inference depends on the single-shot, simultaneous-move nature of the chicken game. These guys will be continuing to interact in the future, and the budget negotiation is sequential (and indeed part of the strategy is trying to force one or the other person to be the “last mover”). I think that both of these aspects of the game make non-destructive resolution of the game more likely in equilibrium.
I thought of the situation as akin to an incomplete information conflict bargaining model, a la Fearon 1995. Both sides have misjudged each others’ resolve and the costs that each will pay to enter the conflict, eliminating any agreement possibilities in the bargaining space. A conflict will therefore emerge. Private information will then be revealed, and eventually a viable set of mutually acceptable bargains will be restored.
Nice, Justin!
I agree it’s more like Fearon 1995. One complication though, is that the two “sides” consist of multiple individual actors who all have to stand for reelection on their own. In that sense, there’s an element of the Tragedy of the Commons too. Even if the Republican Party as a whole preferred x to shutdown, if enough individual MCs figure that their one vote won’t determine whether the agreement passes or not (their own cow grazing on the pasture won’t determine whether the field goes fallow), and further believe that they’ll be primaried if they don’t take a symbolic stance, then the information problem is the least of our worries.
The third answer to Fearon that no one likes to talk about is issue indivisibility. It may be that no real bargaining space exists (maybe because of the multilevel game being played as Phil suggests, maybe because of the nature of one or more of the actors).
The thing is, issue indivisibility has to be combined with a lack of opportunities for side-payments, and that doesn’t seem plausible since Congress has all sorts of non-healthcare issues to bargain over. The real issue might be commitment problems– the GOP can’t commit to not threatening a shutdown in the future, a). because party leadership and membership changes, b). because their base might reward them for breaking any such promise, and c). because budgets can’t be passed for arbitrary, irregular intervals.
Not sure I understand this one. if the issue in truly indivisble (i.e. Obama will never take down any part of the healthcare law and the Republicans (or at least the right wing) will only ask for all of it) then side payments seem beside the point. Who cares how many side payments there could be?
The side payments issue helps to solve what might seem like an issue of indivisibility, but it doesn’t solve indivisibility. I guess it only helps us to figure out whether something truly is indivisible or if it merely looks that way because we have mistakenly forgotten some possible sidepayments.
Think in terms of utility functions. The “bargaining space” has a width based on a the deadweight loss from conflict (which in this case means a government shutdown, not war.) For any proposed compromise within that region, both sides are better off with an agreement than they would be “fighting.”
Issue indivisibility means you might have an issue which you can’t divide, that is “wider” (in utility) than the bargaining space. However, that doesn’t mean you can’t have a bargain there if there are other relevant issues people can compromise on. So, say the bargaining space on the interval [0,1] is [.4,.6], the status quo is .7 (meaning Actor 1 has .7 units of a good, and Actor 2 .3 units) and Actor 2 is demanding that Actor 1 cede an indivisible .45 units. That would seem to give them a choice between Actor 1 not backing down (causing conflict) or Actor 1 retreating to .35, which Actor 1 won’t do because it’s even worse than fighting.
However, this individual issue isn’t the only good that the actors care about. If Actor 2 cedes, say, .1 units of its original .3, then Actor 1 could concede the individual issue, and both actors are back in the bargaining range.
In other words: For it to be the case that “Obama will never take down any part of the healthcare law and the Republicans (or at least the right wing) will only ask for all of it,” the importance of the healthcare law for Obama would have to outweigh the importance of every single issue he disagrees with the GOP on, and vice versa, which is clearly implausible. Even if the value of the healthcare debate > the costs of the government shutdown, one side could give in on Obamacare and the other side could make a whole bunch of other concessions, and both sides would be better off.
Thanks for an interesting post. Do you think it is possible that, for some players in this “game,” the payoff for “crash/shutdown” is actually higher than it is for “swerve/concede to pass a clean CR” – because it provides them with an opportunity to demonstrate resolve to their base and/or because they think they won’t be blamed?
Yes, that would definitely change the dynamics! And, it could make the crash/shutdown very likely.
Yo, I would also point out that the single, unified actor assumption in the chicken game may not hold here. That is, Boehner may be holding the wheel, but Ted Cruz is sitting in the passenger seat doing everything he can to detach the steering wheel from the column. The Congressional Democrats may be acting together, but it’s not clear that the Republicans can be viewed as a decisive, cohesive unit. One could even argue that Boehner’s engaged in a bizarre two-level game right now. Sources indicate that he’s privately willing to accept a clean continuing resolution, but he’s forced to negotiate with the Senate Dems (not budging) and his own caucus (maybe budging?). Ultimately, his preference is to remain Speaker, but this entire crisis has forced him into a corner with both bargaining partners. Seems like there’s a variety of ways to model this scenario!
The problem is that Tea Party Republicans gain greater benefits by crashing than by swerving. They are not concerned about tarnishing the Republican brand by orchestrating a shutdown, and they assuage constituents who want to see Obamacare scrapped above all else.
The other problem is that Democrats have no incentive to swerve, either. If they give in to Republican demands, they undo Obama’s signature piece of legislation, and they make themselves vulnerable to further hardball Republican tactics on the debt ceiling in three weeks’ time. So they need to stay the course, no matter what.
The only ones who really lose politically from a shutdown are Republicans who worry about the party’s broad reputation. Boehner, moderates in the party, and presidential hopefuls don’t want the GOP to be branded as irresponsible and incapable of governing.
But they don’t have incentive to pass a clean CR until things really hit the proverbial fan. If Boehner acts against a large faction of his own caucus, he may lose his speakership at some point. So he needs to wait to see how the public responds to the shutdown; if the party’s numbers decline sufficiently, then and only then can he cut a deal with Democrats and not suffer a revolt within his party.
What a mess!
What if we game theory isn’t an appropriate metaphor for this conflict?
In pragmatic terms, the Government shutdown has little real impact on the negotiating parties – they still get paychecks, and their “safe” gerrymandered districts mean they stand to keep their seats. Another party altogether – 800,000 federal workers – lose their paychecks.
Perhaps Skinner’s conditioning theories (assuming inconsistent rewards) is all that is needed to explain the behavior of enough Republicans.
Inconsistently rewarded behavior is the hardest of all to extinguish, and there have been sufficient cave-ins by the President on earlier debt ceiling / sequester threats that the Tea Party faction believes there is a high enough chance that they will extract a reward in this instance?