The Ultimatum Game is a fairly commonly used game to study people’s behaviour, cooperation, social capital, etc. Participants are divided into pairs, and one half of the pair is given a sum of money, say Rs. 100. The objective of this player (let’s call her A) is to divide this money between herself and her partner for the game (whom we shall call B). There are no rules in terms of how A can divide the money, except that both sums need to be non-negative and add up to the total (Rs. 100 here).
After A has decided the division, B has an option to either accept or reject it. If B accepts the division, then both players get the amounts as per the division. If B rejects the division, both players get nothing.
Now, classical economics dictates that as long as B gets any amount that is strictly greater than zero, she should accept it, for she is strictly better off in such a circumstance than if she rejects it (by the amount that A has offered her). Yet, several studies have found that B often rejects the offer. This is to do with a sense of “unfairness”, that A has been unfair to her. Sociologists have found that certain societies are much more likely to accept an “unfair division” than others. And so forth.
The analogy isn’t perfect, but the way co-foundes of a startup split equity can be likened to a kind of an ultimatum game. Let’s say that there are two people with complementary and reasonably unique skills (the latter condition implies that such people are not easily replaceable), who are looking to get together to start a business. Right up front, there is the issue of who gets how much equity in the venture.
The thing with equity divisions between co-founders is that there is usually not much room for negotiation – if you end up negotiating too hard, it creates unnecessary bad blood up front between the founders which can affect the performance of the company, so you would want to get done with the negotiations as soon as possible. It should also be kept in mind that if one of the two parties is unhappy about his ownership, it can affect company performance later on.
So how do the founders decide the equity split in this light? Initially there will be feelers they send to each other on how much they are expecting. After that let us say that one of the founders (call him the proposer) proposes an equity division. Now it is up to the other founder (call him the acceptor) to either accept or reject this division. Considering that too much negotiation is not ideal, and that the proposer’s offer is an indication of his approximate demand, we can assume that there will be no further negotiation. If the acceptor doesn’t accept the division that the proposer has proposed, based on the above (wholly reasonable) conditions we can assume that the deal has fallen through.
So now it is clear how this is like an ultimatum game. We have a total sum of equity (100% – this is the very founding of the company, so we can assume that equity for venture investors, ESOPs, etc. will come later), which the proposer needs to split between himself and the acceptor, and in a way that the acceptor is happy with the offer that he has got. If the acceptor accepts, the company gets formed and the respective parties get their respective equity shares (of course both parties will then have to put in significant work to make that equity share worth something – this is where this “game” differs from the ultimatum game). If the acceptor rejects, however, the company doesn’t get formed (we had assumed that neither founder is perfectly replaceable, so whatever either of them starts is something completely different).
Some pairs of founders simply decide to split equally (the “fairest”) to avoid the deal falling through. The more replaceable a founder or commoditised his skill set is, the less he can be offered (demand-supply). But there are not too many such rules in place. Finally it all boils down to a rather hard behavioural problem!
Thinking about it, can we model pre-nuptial agreements also as ultimatum games? Think about it!