Game Theory, Divorce and Market Research

By Michael Lieberman

I am reading Robert Greene’s The 33 Strategies of War, a book all marketing professionals should get their hands on. The title could easily have been The 33 Strategies of Marketing or The 33 Strategies of Life.

The 33 Strategies of War teaches us that transactions almost always boil down to four points:

• Agenda
• Goals
• Strategy
• Tactics

This rule holds true nearly across the board. Where to dine with your in-laws, setting a price for an auction bid, which company to buy, or how to approach a legal issue. Strategies of war are commonly employed in complex litigation, solving divorce issues, corporate mergers and international diplomacy. Goals and agendas are typically highly related, while strategy and tactics are subsets of these.

Greene’s premise applies absolutely to marketing research.

Decision modeling—commonly known as Game theory—makes use of all four of the aforementioned concepts to mathematically predict outcomes for various situations. Game theory has been employed widely in such fields as international diplomacy, economics and criminology. Large corporations retain expensive management consulting firms to ‘game’ scenarios of mergers and acquisitions or performance of product lines. Decision/game theory is often referred to as revenue management.

Game theory seeks to understand what constitutes a rational course of action in situations where other people’s responses determine outcomes. For decades, academic game theorists have explored how promises, commitments, threats, the elimination of options, and other tactics can affect outcomes and the resulting “equilibrium.” Game theory is a powerful tool for predicting outcomes of a group of interacting firms where an action of a single firm directly affects the payoff of other participating players. In the well-known movie, A Beautiful Mind, the protagonist founded Nash Equilibrium, a groundbreaking company in strategic decision modeling. The Nash equilibrium is a solution concept of a non-cooperative game in which each player is assumed to know the strategies of the other players, and no player has anything to gain by changing their own strategy.

The good news for clients: Game theory models are now accessible to the marketing researcher. Moreover, core skills utilized in qualitative research are perfectly suited to enter this lucrative consulting market.

Below, we run through the basics of Game theory. One crucial caveat: as with most strategic games, input determines prediction accuracy. In other words, ‘Garbage in, garbage out.’

This is where the interviewing skills of a qualitative researcher or the survey writing skills of a product manager make a real difference. We will conclude by showcasing one particular application of Game theory, its implications, induction and conclusion.

Game theory in a nutshell

The most common uses of Game theory modeling are:

• Calculate Maximum Negotiation that the other side is likely to accept
  • Divorces
  • Mergers & Acquisitions
  • Negotiations
• Power Calculation
  • For example, shareholders and CEOs vote in a given company. We can calculate precisely the influence of a particular individual or group, producing ‘What if’ scenarios for alliances and Power Calculations. This leads to a bigger slice of the pie for our client.
• Calculate Fairest Distribution of Outcome
  • Given a merger or complex allocation of funds, we can calculate the most balanced payout given each player’s contribution. This is commonly known as the Shapley Value.
• Auctions
  • We can model negotiations over repeated rounds to predict the actual outcome of a negation or the best strategy to “win” an auction.
• Litigation Outcome and Criminal Trial Outcomes

Prediction ABCs

Mathematical predictions are surprisingly simple to make. The critical part is carefully interviewing experts or interested parties:

• Identify every individual or group with a meaningful interest in trying to influence the outcome.
• Estimate as accurately as possible what each of the above wants.
• Approximate how important each issue is for each player.
• Relative to the other players, how influential can each player be in the prediction (Power Calculation).

Marketing Researcher Advantage

Strategic-model input is generally not survey-driven. Rather, input is derived from interviews of interested parties or the quantified findings of an industry expert.

Most number crunchers can push the right buttons, run models and reach Nash Equilibrium. A few Excel macros and voilà: model performance. The crunchers and the consultants are separated by one main thing: interviewer skills. Teasing out all the players within certain games; normalizing realistic opening outcomes and normalizing interactions; discovering alliances that are relieved during the opening phase of most projects: these are skills native to a qualitative interviewer, who can be easily trained by a consultant who knows how to create the model.

Working with a numbers person who runs the model, marketing researchers then create a viable predictive model for smaller firms that cannot afford to hire, say, a Kinsley.

We have a market niche.

Adjusted Winner – The Divorce of Ian and Traci

Game theory rests on a single, vital assumption: Everyone is self-interested.

Adjusted Winner is an algorithm developed by Professor Steven J. Brams of New York University. It is used to divide divisible goods between two parties as fairly as possible. Adjusted Winner is a non-cooperative, fair-division game. In problems of fair division, the adjusted winner procedure is used to partition a bundle of goods between two players in such a way as to minimize envy and maximize efficiency and equitability. The procedure, used in divorce settlements, illustrates well the concept of Nash equilibria.

Adjusted Winner assumes two interested parties with:

• adversarial positions;
• desire to maximize outcome in a dispute; and
• a need to quantify “fairness” and “envy,” which must fall within a specific boundary.

Adjusted Winner is used in negotiations to plan a strategy most likely to be accepted by all parties. The consultant may be employed by a mediating service to calculate the most equitable solution, or by either party’s attorney for a strategic look at a realistic outcome.

Let’s assume that we are retained by Ian’s attorney. Ian is a successful businessman who wishes to divorce, Traci, his wife of 10 years. Aside from the mathematical elements of Adjusted Winner, there are human components that need to be factored into the model. This is the qualitative niche.

Importantly, most divorces, even high profile ones, are fairly limited with regard to basic issues. Interviews with Ian and his attorney provide us with the data to construct the initial matrix, shown below. The backstory column to this matrix is crucial to the calculation of the initial positions of Ian and Traci. It is the derived quantification of envy and practicality.

In the initial calculation of Adjusted Winner, the party with the greatest interest in a given issue is awarded that issue. Below is Ian and Traci’s first solution.

In Adjusted Winner, initial allocation are points awarded to the party who gives an issue higher priority. Ian’s initial point total: 70. Traci’s initial point total: 60. (Ian wins on alimony because Traci has won the house, which is worth a lot more) To sum up, Traci gets the kids and the house. Ian keeps his money and his initial offer of child support and alimony.

Traci will certainly not accept this settlement.

After running the Adjusted Winner algorithm, including a Shapely value regression for calculation of fair division for the alimony amount, investments and the house, we arrive at the following settlement:

The interpretation of the derived Adjusted Winner matrix is as follows. The children will remain with Traci in the Connecticut house. However, Ian will retain 25% ownership of the residence and cannot force Traci to sell the house until the youngest child has reached the age of 18. Traci has the option of buying Ian out at fair market value or selling the house at any time she wishes. Ian would then collect 25% of its value.

We suggested to Ian’s attorney that he raise the alimony offering by approximately 33%. This is because, according to the algorithm, even though both parties have come down from their initial point totals of 20, Ian’s points are roughly twice that of Traci when we calculate equilibrium. The figure of 33% was discussed with and agreed to by Ian and his attorneys. Ian also yields some of the joint investments—we recommend around 20%—but Traci has no right to his consulting practice.

Now the ball is in Ian’s attorney’s court. Game theory has provided him with a great deal of useful information that he can use to negotiate a better deal for his client.

Conclusion

Game theory has guided the decision-making of marketing managers for more than half a century. A potent tool no longer available to academics and the largest firms alone, game theory permits marketing researchers and their clients to make data-driven, high-end decisions.

Michael Lieberman is founder and president of Multivariate Solutions. He can be reached at 1.646.257.3794, or at [email protected].