Deciding on the best way to divvy up a business when the owners decide to go their own ways can be tricky. It has to be fair in the eyes of everyone involved, but what if everyone has different expectations?

When people first form a business partnership, they’re often advised to sign a binding contract that specifies how the assets will be divided in the event of death, disability, divorce or departure. This is similar to a prenuptial agreement couples sign before they get married.

However it’s often not practical to sell the business to a third party and divide the proceeds. The partners may have skills or knowledge that make the business less valuable to a third party than to them.

So we’ve developed another way of dissolving business relationships - through an auction.

The different ways of dividing

In the United States the most common exit mechanism for two-person, equal-share partnerships is the “Texas shootout”. The partner who wishes to dissolve the partnership triggers a shootout by naming their price. The other partner is then compelled to either buy out their partner or sell their own interest at that price.

A Texas shootout is like a “divide and choose” mechanism used by parents everywhere to split a piece of cake between two children. This is where one child divides the cake and the other child chooses which piece to take.

Divide and choose has the compelling feature that each child can guarantee themselves at least half the cake. By cutting the cake in what he regards as two equal pieces, the divider gets half the cake. By choosing the “larger” piece, the chooser gets what she regards to be at least half the cake.

Likewise, in a Texas shootout each partner can guarantee they capture at least half of the value they place on the whole partnership. A partner who names a price that leaves him indifferent to whether his partner buys or sells is guaranteed to receive half of his value on the partnership. Likewise, his partner, by simply taking the best deal cannot leave with less than 50% of her value.

However, the Texas shootout is unattractive for a number of reasons. For starters, the procedure does not easily scale if there are more than two joint owners. Nor does it treat the partners symmetrically.

This point can be illustrated with a simple example. Suppose that Ann’s value for the partnership is $10, Bob’s value for the partnership is $16, and suppose, further, that each knows the other’s value.

If Ann triggers the shootout, she should propose a price of $8. Bob will buy her out, and she gets $8. On the other hand, if Bob triggers the shootout, he should propose a price of $5, which Ann should accept.

This way Ann is better off if she triggers the shootout, because she captures $8 rather than $5 – which may lead Ann to trigger the shootout if she fears Bob will trigger it.

Finally, if each partner is uncertain of how highly the other values the partnership, then the buyer in the shootout may not be the partner who values it most highly.

Suppose Ann, for example, knows that Bob values the partnership more highly than she does but is uncertain of what that value is. If there’s a possibility that Bob values the partnership very highly, it may be optimal for Ann to name a price so high that there is some risk Bob will choose to sell rather than buy.

The auction method

So, we have developed a new method – called a “compensation auction” – which avoids the negative features of the Texas shootout while retaining the attractive feature that each partner can guarantee themselves an equal share of the value for the business.

The auction takes place over several rounds. At the beginning of each round, the amount of compensation is set to zero.

Compensation is then increased continuously, until one of the partners agrees to take this amount of compensation in return for giving up his claim to the business. This partner exits, and a new round begins.

The process is then repeated until only one partner remains. That partner is awarded the business and he pays each of the others their individualised compensation.

For example, suppose that Ann, Bob and Cathy wish to dissolve their business partnership. In the first round of the auction, compensation rises until Ann becomes the first to drop out, at $8. She surrenders her claim to the partnership and receives $8. Bob and Cathy remain to participate in the second round.

Compensation is set to zero and then increases continuously. Suppose Bob then agrees to accept compensation when it reaches $6. Cathy buys the business, paying $14 in compensation – $8 to Ann and $6 to Bob.

The rules of the compensation auction treat the partners symmetrically, with no partner having a special role. The auction accommodates any number of players and is also efficient.

In addition, each partner can also guarantee themselves an equal share of his or her value for the business. To illustrate, suppose in the example above that Ann’s value for the business is $15 and she follows the plan of accepting compensation if it reaches $5 (that is, a third of her value).

There are two possible outcomes: the first is that she accepts compensation of $5 at either the first or second round, getting a third of her value; the alternative is that she buys the partnership after Bob and Cathy have both dropped out, each having accepted less than $5 as compensation.

In the latter case, Ann gets the business (which she values at $15) and pays at most $10 in compensation, obtaining a net value of at least $5.

The compensation auction therefore ensures each partner can capture an equal share of their value for the partnership. The compensation auction is “fair” in that it treats the partners symmetrically, takes into account any number of partners and is efficient.

Wooders is grateful for financial support from the Australian Research Councilís Discovery Projects funding scheme (project number DP140103566).

Matt Van Essen does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond the academic appointment above.