By Jon Riley
How we got where we are.
Outline of the Game.
As Congress lurches from budget crisis to budget crisis, constantly inventing new looming disasters to fight over and imposing palpable uncertainty onto a still fragile economy, Americans have become increasingly cynical about our country's ability to govern itself. Since the 2010 mid-term elections, the House Republicans have repeatedly taken the American people hostage, threatening to inflict severe economic pain if they don't get their way. Why can't both sides just agree to compromise?
We will create a simple model of the budget chicken game Washington has been playing for the past two years. Everyone knows the country would be better off if Democrats and Republicans could avoid the last minute brinksmanship and agree to a Grand Bargain with both revenue and entitlement reform. But we will show that it is structurally impossible for both sides to simply come together. Each political party has an incentive to backstab the other, so mutual compromise is not a stable equilibrium.
We will create a simple model of the budget chicken game Washington has been playing for the past two years. Everyone knows the country would be better off if Democrats and Republicans could avoid the last minute brinksmanship and agree to a Grand Bargain with both revenue and entitlement reform. But we will show that it is structurally impossible for both sides to simply come together. Each political party has an incentive to backstab the other, so mutual compromise is not a stable equilibrium.
Lest we forget, here's the list of hostage situations the GOP has created over the past two years:
- Bush Tax Cuts -- Part 1 December 2010
- Unemployment Benefits -- Part 1 December 2010
- Government Shutdown Part 1 Spring 2011
- Debt Ceiling -- Part 1 Summer 2011
- Supercommittee Showdown Winter 2011
- Payroll Tax Cut Winter 2011
- Unemployment Benefits -- Part 2 Winter 2011
- Bust Tax Cuts -- Part 2 Winter 2012
Now they're threatening to take even more hostages:
- Sequester Present - ?
- Debt Ceiling -- Part 2 Spring 2013
- Government Shutdown -- Part 2 Spring 2013
And that's just the list of hostage situations on budget-related issues alone.
Outline of the Game.
Imagine a typical scenario: Congress finds itself approaching another self-imposed crisis that will be automatically triggered if the House Republicans and the President fail to compromise on the budget by a certain date. At the last minute before the deadline, each side decides whether or not to compromise, but they can't know if the other party can be trusted to compromise until it's too late. If Obama compromises by offering entitlement cuts and the House Republicans compromise by agreeing to new revenue, then we get a bipartisan "Grand Bargain." If the Republicans cave on revenues but Obama won't budge on spending, then Obama wins. If Obama caves but Republicans stand strong, then the Republicans win. But if neither side is willing to compromise, then no deal is reached, and a budget crisis will set in, causing a recession that both sides will be harshly blamed for.
In the illustration below, Obama's payoffs for each scenario are in blue, and the GOP's are in red. I will argue that the following payoffs are correctly ranked for each player. But the precise magnitudes of these payoffs are just for the sake of concreteness, by which I mean totally made up.
Nash Equilibria.
The Grand Bargain would be best for the country overall. Both sides would get +1, so the total for everyone would be +2, which is the best outcome. So then why can't both sides "just come together?" Because unfortunately, this is not a stable equilibrium. Say Obama compromised by taking revenues off of the table. The GOP could compromise and take the Grand Bargain (payoff = +1), but they could do even better by demanding even more spending cuts (payoff = +2.) Since the game is symmetrical, the same is true for Obama. If the GOP compromised on taxes, he'd be better off pocketing that concession and continuing to reject entitlement cuts (payoff = +2), than he would be if he agreed to the Grand Bargain (payoff = +1.) This explains why in 2011 during the first debt ceiling showdown, when Obama and Boehner were closer than ever to a bipartisan $4 trillion debt reduction package, they both pulled out at the last minute and reneged on their commitments.
There are two pure strategy Nash Equilibria in this game: "Obama Wins" and "GOP Wins." The definition of a Nash Equilibrium is that neither side has an incentive to change their strategy unless the other side does first. Let's say we're starting the game in the top right corner of the illustration. The GOP refuses to compromise while Obama is willing to compromise. If Obama knew the GOP wasn't going to change its strategy, then Obama would be better off letting them win (payoff = -2), than letting the sequester cuts occur (payoff = -10.) Similarly, if the GOP knew Obama would cave in the end, they would have no reason to compromise. So unlike with the Grand Bargain, if we started out at "House GOP Wins," then neither party would have an incentive to change it's strategy unilaterally. Since the game is symmetrical, the same is true for the other Nash equilibrium where Obama wins (bottom left corner.)
But how do we know which of these two Nash Equilibrium we'll end up with? For example, how can the Republicans ensure they end up at the equilibrium where they win, instead of the one where Obama wins?
Commitment Devices and Credible Threats.
In a game of chicken, if you throw your steering wheel out the window, your opponent has no choice but to swerve or face the inevitable collision. This is called a "commitment device." As discussed in previous posts, the House GOP has attempted to use their no-tax pledge as a type of commitment device. Republican representatives pledged to never raise taxes, so they would have no choice but to refuse all revenue, or else risk losing in the primaries for violating their pledge. The GOP leaders hoped this would force Obama to "swerve" by taking revenue off the table.
The problem is that the Republicans' commitment to never compromise is no longer credible. Although they have taken the country hostage several times now with these budget showdowns, in the end they always vote to avoid a crisis. In the debt ceiling battle, the material consequences of allowing the US government to default turned out to be way too real for the GOP to actually allow. If the US had defaulted on its debt, global financial markets would have imploded far worse than they did in 2008. And oh, by the way, Congressmen who purposely destroy the world don't get re-elected. It was a clever strategy. But not a credible threat.
So if this strategy isn't credible since it's not a Nash Equilibrium, then how does the potential for disaster become leverage for either side? In part two of this series on the budget crisis, we'll show how Obama and the Republicans can use mixed strategies to control the probability that a miscalculation will cause a catastrophe. Read Part 2 >>
