In A Tiny Bit of Game Theory, I explained a few basics of this study of decision theory. The Social Security claiming decision provides a good example of how to analyze a financial decision with game theory.
Our Social Security game will be a stochastic game against nature in which nature decides your life expectancy, which is, when you think about it, pretty realistic. Unrealistically, we are going to assume that you will live to age 64, to age 70, or to age 95 to simplify the game.
Your choices as the player are to claim benefits at age 62, full retirement age of 66, or at the maximum age of 70. We will assume that you are a single retiree with a typical lifetime record of FICA payments. Having a spouse makes this a very different game, of course, and a lot more complex. So would adding all the claiming age options.
For payoffs, I’ll use the total estimated lifetime benefits for each claiming option according to the Social Security website at SSA.gov for a single person born in 1955 and currently earning $75,000 annually. In this first game example, we will further assume that the retiree has adequate retirement savings to support her lifestyle between retirement at age 62 and the age at which she will claim benefits.
This simplified game in matrix form with lifetime Social Security benefits payoffs in 2014 dollars will look like this:
The retiree will need to also make a decision about her overall objectives. Many game theory analyses select strategies that will avoid the worst-case loss. Prisoner’s Dilemma, for example, encourages each perpetrator to confess first and avoid the longest prison sentence. Mutually-Assured Destruction was also an attempt to minimize the worst-case scenario, a nuclear war. These are referred to as “maximin” strategies because they seek to maximize the minimum outcomes. In other words, they seek the strategy that has the best payoff from among worst-case scenarios.
Some retirees want to minimize the chances of “leaving benefits money on the table.” They decide to claim as early as possible in case they don’t live long enough to “break even”. This strategy seems wrong to me on so many levels, but to each his own. Game theory allows us to analyze the problem with a wide range of potential objectives.
The table below shows how much Social Security benefits a retiree might “leave on the table” by waiting to claim but dying before the break-even age, which in this example ranges from ages 75 to 78 depending on the claiming ages.
As you can see from the payoffs, if you won’t live very long, you will maximize your total lifetime benefits by claiming as early as possible (Table 1) and if your objective is to wring every available dollar out of the U.S. Treasury (Table 2), claiming early would be the way to go. Of course, if you’re wrong about your checkout date, you might have done significantly better by claiming at a later age.
If you live to be very old, then you will receive the greatest lifetime benefit by claiming at age 70, when benefits top out. If you plan to live a long time but don’t, you will have missed years of benefits by not claiming early.
For retirees with the “maximin” objective of protecting against the worst-case scenario, claiming at 70 is the best choice, because minimizing your benefits by claiming them at age 62 and then living well into your 90's will be very painful for a very long time. The formal name for Social Security retirement benefits is Old Age and Survivors Insurance (OASI) and claiming as late as possible is the best use of benefits if you view them as insurance. Delaying the claim date for your benefits is the cheapest way to purchase longevity insurance.
I mentioned earlier that for this example game we would assume that the retiree has adequate resources to retire at age 62 and pay for her standard of living until she claims benefits. Another way to implement this strategy is to work longer, if you have the option.
Retirees who don’t have the option to work longer and don’t have substantial retirement savings can’t play this game. They will need to claim early because they will need the income immediately. So, you have more options with Social Security if you also have a lot of money.
I’m sure you’re shocked.
I’m sure you’re shocked.
There is one other game theory concept we can introduce with this example, that of dominant strategies.
If you were offered two bets and the first bet always paid at least as much as the second bet and sometimes more, you would always choose the first bet, right? Game theory refers to the first bet as a dominant strategy and the second as a dominated strategy. Game theory tells us never to play a dominated strategy. (And, it tells us that there usually isn’t a dominant one.)
In the Social Security benefits game I have described, there is no dominant strategy that always provides the best results under all circumstances. Sometimes claiming at age 62 pays more lifetime benefits and sometimes claiming at age 70 does, depending on how long you live.
However, claiming at age 62 is a dominant strategy if the objective is merely to leave the minimum amount of benefits on the table and claiming at age 70 is a dominant strategy if the objective is to minimize longevity risk.
Note that I’m not trying to use game theory to explain the best Social Security benefits-claiming strategy. That will depend on your individual resources and goals. I’m suggesting that it provides a good framework for laying out all the options and outcomes and for clearly identifying our objectives so we don’t focus only on the most likely outcomes.
Hopefully, that supports a better decision.