In the fourth article of the game theory series, we build on the Saudis out-bluffing OPEC and The Joker forcing the good people of Gotham to choose between game theory and Batman. In this installment, you will learn how blood thirsty, treasure hunting pirates might just explain the ridiculously large wage gaps in modern day corporations. To set the stage, one must think like a pirate, indeed be the pirate. I do not mean the rum soaked debauchery of commercially suggestible women in a tavern named Hurricane. What I mean when I say ‘think like a pirate’ is think selfishly. That’s what successful senior executives do. Isn’t it?
Consider three pirates: Lloyd, Jamie and Vikram. For the purposes of this scenario, the pirates adhere to a strict hierarchy. Lloyd is top, next is Jamie and finally there is Vikram. The pirates have just plundered some treasure. Let’s say they sold a pension fund some credit default swaps referenced to a portfolio of goats, then got paid by a San Francisco hedge fund to shoot the goats. After manipulating the London inter-bank goat swap reference rate and provisioning $200 billion of shareholder money against legal claims, the pirates made off with 100 gold coins. The question that immediately presents itself is: how does the treasure get distributed?
Following the pirate code the most senior pirate, Lloyd, suggests a split of the treasure. Everybody, including Lloyd, then votes. In general, if there is a tied vote then the most senior pirate has the casting vote. If a majority votes to accept Lloyd’s split then they go ahead with it. If not, Lloyd is shot (up or out!) and then the game is run again with the next most senior pirate suggesting a split, in this case Jamie.
At first glance you might think that Lloyd would have to give most, if not all, of his gold away so as to avoid getting shot by the other two pirates ganging up on him. But if you thought that, it would be because you did not go to Pirate School, the secret 9th Ivy, where the game theoretic analysis of treasure sharing is one of the most coveted courses (the modern day equivalent is called compensation theory). No self respecting pirate would ever deign to allow HR to handle compensation negotiations for him. This, by the way, explains the prevalence of fencing as a sport in the Ivy League. So why is gut instinct wrong?
Let’s look at what happens if Lloyd picks an unacceptable split and is shot. That leaves Jamie as senior to Vikram. Remember, in a tied vote the senior pirate has the casting vote. That means that Jamie can suggest 100 gold coins for himself, zero for Vikram, then vote for himself and he will get all the coins and Vikram will get none. Logically, therefore, Vikram wants at all costs to not have Jamie become senior pirate. It follows that if Lloyd offers him just 1 gold coin on the split that Vikram will vote for it since it is better than zero, which is what Jamie will force on him.
This analysis can be extended to the case of 100 pirates (I think the collective is investment bank). In that case, the logical split that the senior pirate should make is 49 coins, 1 each to the odd numbered pirates, and he gets to keep 51 coins. I won’t bore you with the math.
This analysis shows beautifully how a forced hierarchy, even with democratic like voting, can still result in a massive pay gap with the senior pirate taking home 51% of the pay! The analogy is not exact to a modern day corporation, but the concepts are. Especially the blood thirsty part.
Again, we see that logic does contradict certain natural human behaviour such as sharing and team work. On the other hand, it brutally explains reality. Being able to arrive at unintuitive but powerfully accurate conclusions can give one a great advantage in business.
- The first post in the series, The Bluff: An Important Strategy Tool looks at the role of randomized strategies in business.
- The second post in the series, Game Theory’s Relevance to Investing: The Basics is self descriptive.
- The third post in the series, Gotham Game Theory: The Joker’s Dilemma, uses an example from the Batman film The Dark Knight to further describe game theory and its uses.