# Fairness in Game Theory

This article discusses fairness in game theory. The fair commission model(FCM) assumes that buyers and sellers of businesses with goodwill will seek to find a price that meets their criteria of fairness. Click here for a description of these criteria. Some may think that fairness criteria of value have no place in the hard-headed world of seller and buyer negotiation of equity exchanges. These skeptics may paraphrase the famous Donna Summers song and ask “What does fairness have to do with it?” Modern game theory and behavioral economics answers: “a lot”.

## Fairness in Game Theory: The Ultimatum Game

One famous well studied game is known as the Ultimatum Game. While this game is not precisely like an equity exchange negotiation, there are similarities that are relevant and the manner in which people have been found to play the game underscores the importance of fairness.

In the Ultimatum Game two players are to divide a sum of money. The first player proposes an allocation of a fixed sum of money. The other player cannot counter the proposed allocation by the first player, but that player can accept or reject the first player’s offer. If the second player rejects the offer neither party gets to keep any of the sum.

For example, suppose \$100 is to be divided. If the first player chooses to keep \$75 the other player is allocated \$25, or the first player might choose a \$50 split and so forth. Again all the second player can do is accept or reject.

This is a cooperative game because in order for both players to gain anything they each have to agree to the proposed allocation. Now if fairness considerations did not play any role in how the game was played, the second player would always accept the proposed allocation as long as the first player did not allocate the entire sum just to themselves.

So for example, if the first player allocated \$99 to them self and \$1 to the second player, the second player should accept the \$1 because the alternative is to reject the offer and receive nothing. Since \$1 is better than \$0 a player not under the influence of any sense of fairness would accept this skewed allocation. But almost all readers putting themselves in the position of the second player would do what? If they are like most human beings, they will reject the offer leaving themselves \$1 worse off. And why? Because the proposed allocation was so unfair. Empirical research on real Ultimatum Game players shows that first offers in the 20% range are rejected about half the time.

## Fairness in Game Theory: The Dictator Game

Fairness considerations are also exhibited in a variant of the Ultimatum Game known as the Dictator Game. In this variant the first player, the dictator makes a proposed allocation. However, the second player has no right of refusal. In other words, the first player can allocate a fixed sum anyway he or she chooses and the second player must accept. There are no negative economic consequences to the dictator even if the allocation proposed is 100% in their own favor.

Standard economic theory predicts that under these circumstances a sum of say \$100 will be appropriated entirely to the dictator in almost every circumstance. Ok readers, quiz time again. Suppose you are the dictator and \$100 is to be divided. What do you do? What do you think most other people will do? According to various empirical studies most dictators offered on average 20% to the second player. Only 30 to 40% of the dictators took all the money. Here again, we have evidence that considerations of fairness play an important role in the allocation of money.

## Equity Negotiations as Two Person Games

Neither the Ultimatum Game nor the Dictator Game precisely mirrors the form of a negotiation for the equity exchange of a closely held firm. Yet there are important similarities. There are usually only a few qualified and motivated buyers and only a few opportunities to acquire successful closely held businesses in local service sector markets.

As a prelude to a serious negotiation, there is a vetting process formally called “due diligence” that must take place. The potential buyer must determine that the seller has in fact a successful business that can provide immediate access to customers, clients, patients (CCPs) that the buyer would otherwise have to compete for. The seller also has to insure that the potential buyer has the resources, skills and experience to finance the acquisition and operate the business successfully. This vetting process is time consuming and often involves out of pocket expenses.

For all these reasons both parties are usually heavily invested in a successful outcome and that negotiation very much looks like an Ultimatum Game. Of course a positive outcome is more likely than in an Ultimatum Game because the negotiators have the opportunity to in effect play the game multiple times. Offer can be met with counter offer more than once. However, the value ultimately agreed upon must conform to what both parties deem to be a fair allocation of the competitive advantage offered by the seller. And it is for this reason that the fairness criteria in a buyer/seller negotiation must be made explicit.

Often sales of closely held firms are sold on special terms called “earn outs” these sale terms embed the fairness criteria outlined in the fair commission model of goodwill. Click here for a description of “earn out” sales terms.

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