Math Games and Collaborative Law

By Attorney Gregg Herman
November 1, 2002

On the theory that the book is always better than the movie, I recently read Sylvia Nasar’s biography of John Nash, “A Beautiful Mind”. In the book, she describes Nash’s obsession with game theory, which resulted in a Nobel Prize in Economics. While not professing to understand much of the extraordinary complexity of the mathematics, I find that there is a correlation between game theory and divorce settlement negotiations. In fact, some game theory explains the importance of handling divorce negotiations in a collaborative manner and how it can work for the benefit of all involved.

For example, take the famous puzzle “The Prisoner’s Dilemma.” Originated by Nash’s contemporaries at Princeton, the puzzle posits that two people are arrested for the same crime. Since the police do not have sufficient evidence to charge either one, they separate them for interrogation and try to get each one to turn state’s evidence against the other [Author’s Note: Having served as an Assistant District Attorney for 7 years, this is exactly how real life works!]. Each prisoner is told that the other one is betraying and that it would be to their advantage to cut a deal.

The best scenario is if both cooperate with each other, refuse to talk and they both walk free. However, if one of them does not cooperate with his co-defendant, but talks to the police, the defector will get a reduced sentence, while the other one will get full punishment. If they both talk, they will both be punished, but less severely than if they had refused to talk. The dilemma is that each prisoner has a choice between only two options, but cannot make a good decision without knowing what the other one will do.

Isn’t this precisely what happens in standard divorce negotiations? Both parties are meeting with their attorneys privately, both suspicious of what is going on with the other side. If they could cooperate with each other, they have the best chance for optimum results for both. What typically happens instead is that the mistrust and lack of communication lead to the worst results for both. For example, recently I represented a client who was offered a promotion with a substantial pay increase.

Unfortunately, it would require relocating overseas for several years. As the children were grown, he was inclined to consider the offer only if he could be assured that he would not have to pay all of the additional income in either taxes or spousal support. In a collaborative divorce, we could have placed the offer on the table and suggested that the wife will get an increase in support if the husband takes the promotion, but not the full amount that might have otherwise been indicated had they gone to court. Since he could not be forced to take the promotion, the wife’s alternatives would be to get some additional support or none at all. However, since the divorce was not collaborative, my client turned down the offer, afraid that the additional support obligation would negate the financial advantages. The result was a loss for both parties.

Another mathematics game described in the book is the “zero sum game”. In such a game, in order for one player to win, another player has to lose. A poker game is an example. In a “non-zero sum game”, on the other hand, all of the players may benefit. Some of John Nash’s Nobel Prize winning work involved using “non-zero sum” games to described the working of a nation’s economy, where everyone can benefit from growth.

The application to divorce is obvious. Most cases are “zero-sum” games. The more the payor pays, the less he has. Wouldn’t it be nice to negotiate a settlement which expands the pie available, rather than dividing it? In the above example, by my client taking the higher paying, but less convenient job, more money is available for both parties. More typically, by using tax tables, sometimes divorce can be a “non-zero sum game”, even in an non-collaborative case. However, by bringing everyone to the table, perhaps, for example, the payor will take the overseas job. Or, work overtime. Or whatever it takes to expand the pie, knowing that the spirit of the negotiations is not simply to take from one and give it to the other, but to expand the amount available for division.

Why are divorce negotiations usually played as a zero-sum game? Again, the mistrust between the parties frequently causes one to believe that “any money going to the other party must come from me”.

Collaborative divorce, appropriately practiced, eliminates the “prisoner’s dilemma” mentality by doing the planning in the open, rather than in secret. By doing so, the game can become a larger game than “zero sum”, to the benefit of all involved.

This article originally appeared in Wisconsin Law Journal.
