1. ‘ Prenup Does Us Part The Game Theory
By Moon Chung, Roy Schaham, Ayako Tanaka, and K.J. Yoo
October 16, 2005
MBA 217 – Game Theory
Professor John Morgan
“Marriage is like a coffin and each kid is like
— Homer Simpson
2. Pre-marriage Agreements MBA 217 – Fall 2005
Each year, over two million couples are married in the United States but nearly half of these
marriages will end in divorce1. Given the high rate of divorce, one might assume the use of pre-
marriage contracts (also referred to herein as prenuptial agreements) would be equally high.
However, only 5-10% of married couples typically sign pre-marriage contracts, while the rest forge
ahead into what Samuel Johnson called a “triumph of hope over experience.”
This paper attempts to explain the paradox, understand individuals’ behaviors as they relate to
marriage, divorce and the use of pre-nuptial agreements. We have used the principles of game
theory to predict an equilibrium outcome relating to the use of prenuptial agreements and to
explain deviations from this outcome.
2 Background on Pre-marriage Agreements
A pre-marriage contract, also referred to as a prenuptial agreement or “ pre-nup,” is a legal contract
entered by both parties prior to marriage that defines expectations for behavior during the
marriage and sets guidelines for property division in the event of the dissolution of the marriage.
Legally speaking, a marriage is a private contract between two people who voluntarily agree to
enter a spousal relationship. 2 Couples entering into a marriage become united in many
dimensions, including social and financial. Financially, the concept of community property binds
the assets and debts of one spouse to those of the other’ Moreover, the future earnings of one
spouse become part of this community property.
Especially in the case where one partner’ assets and income are much lower than the other’ the
couple may choose to enter a pre-marriage agreement as a form of social insurance. Highly
publicized divorces without a prenuptial agreement have sometimes resulted in expensive and
acrimonious lawsuits, with the “ wealthier” spouse paying out a large proportion of his/her assets
and income. Adnan Kashoggi, a wealthy Saudi trader, reportedly paid his ex-wife Soraya $750
million to settle the divorce – nearly a third of his reported net worth at the time.
In contrast, Donald Trump, a man of comparable net worth to Kashoggi, drew up a prenuptial
agreement prior to his marriage to Marla Maples. The contract included a clause stipulating that
Ms. Maples’payout would total only $1 million if the marriage was dissolved within four years. As
a result, Trump’ divorce payout and litigation costs were considerably lower than they might
otherwise have been.3
We have chosen to model the scenario where there is a material wealth disparity between the two
parties to a marriage to better illustrate an equilibrium outcome.
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3. Pre-marriage Agreements MBA 217 – Fall 2005
3 Arguments for Signing a Prenuptial Agreement
Prenuptial agreements primarily serve three purposes, (1) to preserve personal wealth or income,
(2) to value non-monetary spousal contributions, and (3) to reduce or eliminate legal expenses in
the event of dissolution of the marriage.
Wealth or Income Preservation
Prenuptial agreements can benefit both parties entering a marriage regardless of income level. For
the wealthy, the contract provides downside protection by restricting the spouse’ claim on assets
and future income. For those less well-off, the contract provides a monetary guarantee in the event
Establish Ex Ante Values for Non-monetary Contributions
Another benefit of a pre-marriage contract is the opportunity to agree, in advance, the value of the
contributions of non-monetary contributions to the partnership. For example, a non-working
spouse may forgo a career to take on a greater role in the care of children, and as a result, may
have a claim to the future income of the working spouse after a divorce. Establishing, ex ante, the
values for these contributions also enable couples to enter a marriage with more information.
Reduce Costs Associated with Divorce
Although the proceeds from a divorce settlement may be higher than those of a prenuptial
agreement for the lower-income spouse, the potential legal and emotional costs may be substantial.
The resulting payoffs suggest that even the lower-income spouse may fare better with a prenuptial
agreement under some circumstances.
4 Arguments Against Signing a Prenuptial Agreement
Most arguments not to sign a prenuptial agreement are to an extent emotional factors and trust
issues, such as, (1) social stigma (2) negative signals, (3) moral hazard/adverse selection.
Many couples feel a strong social stigma to a prenuptial agreement. Many couples do not admit to
having one. Also, asking a partner to sign one before a marriage is an emotionally difficult task.
One partner may interpret the partner’ desire for a prenuptial agreement as a negative signal.
The request could be interpreted as likelihood to cheat, a lack of trust in the other partner, or a
lack of commitment in the relationship. Surveys4 have shown that partners sometimes interpret
these requests as negative signals.
Moral Hazard & Adverse Selection
Viewing pre-marriage contracts as “ social insurance” suggests the contract has incentive
characteristics similar to insurance. Because parties are protected from downside risk and have an
upside guarantee, the presence of a pre-marriage contract may remove a mental barrier to
engaging in bad behavior. Moreover, individuals who think they need risk protection may be the
ones with a strong preference for a prenuptial agreement.
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4. Pre-marriage Agreements MBA 217 – Fall 2005
5 Game Tree Analysis
See Appendix for “Assumptions”
Exhibit 1: Game Tree Analysis Employing Actual Probabilities of Divorce
Sub-game (90, 90)
(80, 60) [5
up (100, 100)
(55, 80) [50
The different outcomes resulting from the presence or absence of a prenuptial agreement are
mapped out in the above game tree and indexed to a maximum value of 100. Following are a
list of possible outcomes with explanations for their respective payoffs.
o No prenup & stay married [payoffs of (100,100)]: This assumes that staying married
without a prenuptial agreement is the highest possible outcome for both parties.
o Prenup & stay married [payoffs of (90,90)]: Payoffs are slightly lower than the
outcome of staying married without a prenup because we are assuming there is some
emotional cost to suggesting and signing a prenuptial agreement (see Arguments not to
sign a prenuptial agreement below).
o Prenup & divorce [payoffs of (70,30)]: This outcome is somewhat costly to the
wealthier party but a better result than either not marrying (assumes there are benefits
to marriage) or divorcing with no prenup. For the less well-to-do spouse, this is better
than never marrying but not as good an outcome as “ prenup & divorce.”
o Prenup & no marriage [payoffs of (50,0)]: This is the second worst outcome for the
wealthier partner, worst outcome for the less well-off partner. Again, this places a high
value on marriage.
o No prenup & divorce [payoffs of (10,60)]: Obviously the worst outcome for the
wealthier partner. Low combined payoff due to legal and emotional costs of negotiating a
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5. Pre-marriage Agreements MBA 217 – Fall 2005
Applying actual probabilities of divorce (50%), each party will come to a different conclusion
about their desire for a prenuptial agreement. The wealthier party will look forward and
calculate an expected payoff of 80 for the “prenup & stayed married” node. This is higher than
expected payoff of 70 from “prenup & no divorce,” or 50 from “prenup & no marriage” so those
options are eliminated.
The poorer party will do the same calculations and conclude that “ prenup” has the highest
expected payoff. However, once the request for a prenup is made by the wealthier party, the
choices are then to sign the prenup or not to sign it. This is referred to as a subgame since the
branches descend uniquely from the previous node. Analyzing this subgame on a standalone
basis, we find that the optimal outcome for the poorer party is to sign the prenuptial agreement
and get married.
The conclusion from this analysis is that requesting and signing a prenuptial
agreement is the equilibrium outcome. However, statistics show that only 5%-10% of
couples typically sign prenuptial agreements. A major reason for the low rate of prenuptial
agreement use may stem from overconfidence in the chances of succeeding in marriage. This is
typically referred to as overconfidence bias and is depicted graphically with the following game
Exhibit 2: Game Tree Analysis Employing Perceived Probabilities of Divorce
(88, 84) [90
Marr Div %]
(88, 84) e
-n (100, 100)
(91, 96) %]
Studies show that Americans perceive their probability of divorce to be approximately 10%,
rather than 50%. Applying the perceived probability of divorce to the game tree results in
different expected payoffs than in the previous example. As shown on the game tree, both
parties now calculate their highest expected payoffs of (91,96) by not using a prenuptial
agreement. Hence, the existence of overconfidence bias results in a different
equilibrium outcome for both parties.
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6. Pre-marriage Agreements MBA 217 – Fall 2005
The game shows that if partners are rational, the use of a prenuptial agreement is an equilibrium
outcome that benefits both parties. However, the game also reveals that an Equilibrium Paradox
exists, because most people greatly underestimate the likelihood of a divorce. Experience reduces
the influence that overconfidence bias has on rational decision-making. From a game theory
perspective, this is the equivalent of a repeated game. In the situation of multiple marriages,
prenuptial agreements have been found to be much more common in second, third, etc. marriages.
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7. Pre-marriage Agreements MBA 217 – Fall 2005
Appendix and Sources
For the purposes of simplification, the following assumptions have been made to the model:
There are both economic and emotional components to outcomes
Numerical rankings are based on comparatively favorable outcomes, and are indexed to a
maximum value of 100. The emotional costs and benefits of marriage are incorporated into the
payoffs (e.g. social stigma, negative signal, moral hazard, marital bliss)
Probability of divorce equals 50% (this is only applied in Game One)
The probability of divorce has been near 50% for the past 20 years. Although in the recent decade,
the divorce rate has dropped to approximately 40%, the model uses 50% as the probability of
divorce due to its historical reliability.5 (see Figure 1 below)
Figure 1. Number of Marriages and Divorces per year (1940 – 1997)
Prenups are a take-it-or-leave-it offer
Once a prenup is suggested the other partner must either take-it or leave-it. The partner asking for
the prenup cannot change his/her mind and go the path of no prenup, hence the other partner
decides to not take-it.
Prenups are enforceable and non-negotiable
There is a thin line on the interpretation of terms and agreements in legal jargon on prenuptial
agreements. Despite prenups, there are many cases where one partner sues the other claiming
misrepresentation, fulfillment of duties/loyalties, etc. Because prenups are a legal document of
agreement between the two partners, we are assuming that the prenup is enforceable and is non-
negotiable. (i.e. no re evaluation or claims will be considered later on)
Divorce is no-fault
Due to the various complications and scenarios in divorces, we are assuming that in the case of a
divorce, neither partner is at fault (i.e. the breaking vows in any way).
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8. Pre-marriage Agreements MBA 217 – Fall 2005
Large income disparity between partners
Also due to the various scenarios deemed possible in cases where both partners are poor, wealthy,
average’ this game analysis is between partners with a large income disparity.
1 National Vital Statistics Reports, Volume 54, Number 1 (12 Months Ending January 2005).
2 Legal Information Institute, Cornell University Law School. http://www.law.cornell.edu
4 Heather Maher (2003): “ Why Are There so Few Prenuptial Agreements?” John M. Olin Center for
Law, Economics, and Business, Harvard Law School. Discussion Paper No. 436.
5 Dan Hurley (2005): “ Divorce Rate: It’ Not as High as You Think,” The New York Times, April 19.
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