Tuesday, July 19, 2011

US Debt Ceiling Is An Unstable Prisoner's Dilemma

We do not like to comment on politics, as politics can be a very emotional subject for a lot of people. However, we feel compelled to point to the dilemma the US finds itself in currently, with the stalemate over the debt ceiling. For those that are not familiar with the issue, here's a refresher from Wikipedia:

"Article I Section 8 of the United States Constitution gives the Congress the sole power to borrow money on the credit of the United States. From the founding of the United States through 1917 Congress authorized each individual debt issuance separately. In order to provide more flexibility to finance the United States' involvement in World War I, Congress modified the method by which it authorizes debt in the Second Liberty Bond Act of 1917. Under this act Congress established an aggregate limit, or "ceiling," on the total amount of bonds that could be issued."

The current debt ceiling was set in February 2010 when it was raised to $14.3 Trillion dollars, and unless Congress passes another increase by August 2 (the US Treasury estimates it will run out of room by this date), the US government may be forced to default on its debt obligations and a financial crisis far larger than the so called 'Great Recession' may result. Why do we care?

We care because the outcome of the debt negotiations between the Democratic White House and the Republican Congress will directly impact the value of our portfolio. We also cannot stand to watch the grandstanding that is taking place right now.


To us, the current stalemate (notwithstanding Obama's endorsement of the Gang of Six's plans earlier today) is a classical prisoner's dilemma in game theory. Let us illustrate:

Both (D)emocrats and the (R)epublicans can either choose to (C)o-operate or (F)ight. Obviously, if both sides choose to co-operate and negotiate a credible deficit reduction plan that includes both tax increases and budget cuts, the world would be a better place. But both sides would be seen to 'compromise' by their constituents, so politically, the payoff of State I is (D,R) = (1,1) (see figure below).

                                         Democrats
                 R                   _C__ __F__
                 e              C  | (1,1) | (3,-3) |
                 p                   |_S1_ |_S2_ |
                 u               F  | (-3,3) | (X,X)|
                 b                   |_S3_ |_S4 _|
                 .
If either side choose to fight while the other side choose to co-operate, then the fighting side (who stands 'firm and wouldn't give an inch') would be able to claim 'victory' come the next presidential election in 2012, and their opponents would be seen to have 'caved-in'. State II is if Democrats fight and Republicans co-operate, with a payoff of (3,-3). State III is vice versa, with payoff of (-3,3). 

Unfortunately, in this game, we will never get to the globally optimal State I, no matter the outcome of State IV, when both sides choose to fight and we get an eventual US default. 

First, consider the case that both sides view a State IV as a political 'cop-out', allowing them to save face in front of their constituents while ramping up the 2012 presidential campaign. We can reasonably assign a payout of (-1,-1) for State IV. Since Democrats are better off choosing to fight no matter what Republicans choose (i.e., D2 > D1 and D4 > D3), they will naturally choose to fight. Same for Republicans (R3 > R1 and R4 > R2). 

Even if the payout for Stage IV is terrible, i.e. a US debt default and armageddon, we still don't get to the globally optimal State I. Consider if State IV had the payout (-5,-5). As a Democrat, if we are starting off in State I (both co-operate), then it 'pays' politically to fight, since D2 > D1. Same for Republicans, it pays to fight, since R3 > R1. However, if both choose to fight, we get State IV. But if we are in State IV, D2 > D4 and R3 > R4, hence both would choose to co-operate, leading to State I. This is an unstable game, and would oscillate between Democrats and Republicans choosing to fight or co-operate (quite like real life, actually).


Although we can recognize the game, we cannot solve it. Solving it for the global optimal will require changing the game's rules and payoffs such that D1 > D2 and R1 > R3. If we can convince both parties that it 'pays' to co-operate, then the game will naturally conclude with both parties co-operating on a settlement to reduce the deficit and lift the debt ceiling. Unfortunately, politicians are not game theorists and it is very hard to change the political payout of this game.

- The Aspiring Analyst



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