Applying Nash’s Equilibrium to M&A Negotiations*

January 10, 2023
Applying Nash’s Equilibrium to M&A Negotiations*

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I first learned my craft on Wall Street in the 1980s, a very different time characterized by the bravado of Gordon Gekko’s “Greed is Good” speech. During that period, I was taught that all negotiations are zero-sum games. If I win, you lose. That philosophy is illustrated by a graph line with a negative slope. If there were only eight marbles in a negotiation, the curve would look like this:

In M&A negotiations, I thought one-dimensionally. If I represented the seller, I only cared only about maximizing price. If I represented the buyer, I only cared only about minimizing price. In retrospect, I was a poor negotiator.

Two experiences dramatically caused me to change my method. First, I sold my own business to the second-highest bidder (more on that in future articles). Second, I was fortunate to study Organization Behavior under Dr. Robert Bontempo at Columbia Business School. He taught me a plethora of useful management theories, but the most impactful was Nash’s Equilibrium.

Investopedia defines Nash’s Equilibrium as: 

“The solution to a game in which two or more players have a strategy, and with each participant considering an opponent’s choice, he has no incentive, nothing to gain, by switching his strategy. In the Nash equilibrium, each player's strategy is optimal when considering the decisions of other players. Every player wins because everyone gets the outcome they desire. To quickly test if the Nash equilibrium exists, reveal each player's strategy to the other players. If no one changes his strategy, then the Nash equilibrium is proven.” 

There are many gaming exercises, such as the prisoner’s dilemma, that demonstrate the theory.

In class, Dr. Bontempo divided us into groups of two, one player was the buyer of a business, the other the seller. Each player was given a set of criteria (price, employee retention, non-compete, etc.) which was ranked by importance. 

The idea was to negotiate a deal that was in the third quadrant (shown below) in which both sides are satisfied: 

The catch was: one player could not share their priority list with the other.

I thought, with my years of Wall Street experience, this was going to be child’s play. So, I morphed into my Gordon Gekko persona, got to work and proceeded to get the lowest score in the class. Why? My attempt to win on all points resulted in the seller leaving the negotiations.

Humbled, I examined why I failed. Simply put, I applied the 1980s “take no prisoners” approach to a complex situation.

Fortunately, the real-life application of Nash’s Equilibrium can differ from game theory exercises. In these exercises, one player must guess the other’s criteria or decision-making process. In M&A negotiations, you can ask.  I know this sounds naïve. After all, one is not allowed to disclose too much in negotiations, right?? Wrong. Frankly, amateurs play by that rule. Professionals know that those games dramatically slow down, and often derail, the process.

How do you initiate a frank dialog with the other side? Through trial and error, I developed these approaches:

  • Build Trust: I try to do this by being frank. For example, I will have the “warts and all” conversation early in the relationship.  This conversation has two mutually exclusive results, the counterparty either: (i) appreciates the frank dialog and becomes more transparent with you; or (ii) bails on the transaction altogether. Don’t worry if you get the latter outcome. It means is that you ended the discussion early in the process and saved a lot of brain damage. (Watch out: amateurs will advise you to “wait until the other side is more invested in the process before disclosing bad information.”). 

For example, I once represented a German company seeking to acquire the chemical division from a large U.S. conglomerate. This division had a spill site that required environmental remediation but was not willing to pay for the clean-up since it decided to exit the chemical business. This fact was disclosed on day one along with estimates for the cost of the remediation project. Most of the buyers did not want to deal with the headache and walked. My client opened a dialog with the seller and both sides agreed to lower the price by the cost of the remediation and structure certain indemnities into the purchase and sale agreement.

  • Do your homework but don’t be afraid to be the “dumbest guy in the room”  Great interviewers have several things in common including: (i) doing their research and using it to create a game plan for the discussion; (ii) being sincerely self-deprecating; (iii) asking relevant follow up questions; and (iv) getting out of the way when the other side starts talking. At this point, use your prepared questions effectively but sparingly to acquire the information you need. Feather the questions into the discussion so it is more of an open exchange of information than an interrogation.

Too often, I am in a meeting with a bombastic person who must be “the smartest guy in the room.” This person tends to suck the oxygen out of the conversation, causes everyone to clam up, thereby hindering the open dialog. On the other hand, if you lower defenses and share information, you will create an open dialog and learn what you need to know more efficiently.

  • Avoid the phrase “Deal Breaker” Of course, deals reach impasses, most of which are resolvable, others are not. But, for every action, there is an equal and opposite reaction. Saying “deal-breaker” causes the other side to dig in. When you reach an impasse, check your ego at the door, reach out to the other side and say, “we have a tricky issue I need your help resolving.” Discuss each party’s concerns and ways to address them. Often, you will find a solution.

The Nash Score Card

OK, Back to Dr. Nash.

Once you have established an open dialog, don’t be afraid to ask direct questions. For example, “besides valuation, what other criteria are you factoring into your decision?” Also, be an active listener by asking pertinent follow questions (e.g. why is employee retention important to you?).

You then create a Nash Score Card (a term I coined), which is a list of acquisition/sale criteria list in terms of importance to the relative party. Here is an example:





Employee Retention


Employee Retention





Once you have the score card, the structure of the transaction becomes apparent. In the example above, the seller looks willing to compromise on Price in exchange for Employee Retention which aligns well with the buyer’s priorities.

Real-Life Example: Healthcare Service Company*

My investment banking firm, River Corporate Advisors, advised a healthcare services company that was 50/50 owned by two brothers. After the marketing process, we obtained an offer that was acceptable to both brothers. However, prior to executing the letter of intent, one brother (call him “Brother 1”) informed the team that he believed that he had a greater role in growing the business over its 10-year history and, therefore, deserved a greater share of the sale proceeds. Brother 2 did not agree with the premise of that statement and stated that “a deal’s a deal.” 

Rock meet hard place.

I tried to broker a deal between the brothers. Would you take 55/45, 53/47, 52/48? No, no and no! I defaulted to zero-sum game negotiations and failed.

Fortunately, the company’s Chief Operating Officer, and long-time counselor of the brothers’ family, intervened. He had a vital piece of information:  the brothers owned a piece of real estate with their two sisters, each owning 25% of the building. Brother 1 had lost interest in the real estate holding long ago.

 So, the Nash Score Card was as follows:

Brother 1

Majority Ownership

Real Estate

Brother 2

Real Estate
Equal Ownership

The COO found Nash’s Equilibrium by swapping Brother 1’s real estate interest for an extra 3% of the healthcare services company. 

Neither brother changed his strategy (Nash’s Equilibrium) and we closed the transaction.

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