Game Theory & Strategic Default
Should I stay or should I go now?
If I go there will be trouble
And if I stay it will be double
So you gotta let me know
Should I stay or should I go
–The Clash, “Should I Stay or Should I Go?” lyrics
As more homeowners nationally find themselves “underwater,” i.e., they owe more than their properties are worth, they face a difficult decision: should they continue to pay the mortgage — very possibly throwing good money after bad — or should they simply walk away (“strategically default”)?
To answer the question, some homeowners invoke morality (“should we break our promise to the bank?”); others, a cost-benefit analysis (“will the savings we realize exceed the damage to our credit?”).
However, arguably the most important criterion is to ask, “what are my neighbors likely to do?”
Game theory aficionados will recognize this as a variant of the Prisoner’s Dilemma.
The classic version of the Prisoner’s Dilemma is presented as follows:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence.
If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
Like the classic version, in the real estate version of the Prisoner’s Dilemma, there are also four options.
The optimal outcome (Option #1) is for all underwater homeowners to continue to pay their mortgages.
That way, foreclosures abate, home prices (and the economy) start to recover in earnest, and borrowers gradually dig out from the holes they’re in.
At the other extreme, if underwater homeowners strategically default en masse (Option #4) . . . all hell breaks loose.
The tidal wave of foreclosures swamps still-teetering banks (notwithstanding the grotesque bonuses they’ve continued to pay out); still-fragile national housing prices resume their free-fall; and the resulting mess necessitates the “Mother of all Bailouts.”
Except that this time, the government’s cupboards are already bare, because Wall Street made off with the first bailout (and then some).
Options #2 & #3
Which leaves Options #2 and #3: you default but your neighbors don’t — and vice versa.
Clearly, the better outcome for any single underwater homeowner is the former.
That way, you move on to cheaper housing (albeit with damaged credit), but the housing market and overall economy stay afloat. (While borrowers in so-called “deficiency states” are potentially liable for any mortgage shortfall, the risk of that happening appears to be low.)
On the other hand, if your neighbors default and you don’t (Option #3) . . . you’re very much left holding the bag.
As bank foreclosures inundate your neighborhood, property values plummet, making you further underwater. Meanwhile, living on a block full of foreclosed homes poses its own safety and quality of life issues.
Best Outcome vs. Likeliest
So, how is the housing version of the Prisoner’s Dilemma likely to play out?
To forestall the horrific consequences of Option #4 — widespread strategic default — one would expect rational banks to finally get serious about proactively reducing the principal balances of underwater mortgages.
Of course, that assumes that “rational bank” isn’t an oxymoron.