Economics students today probably hear John Nash’s name more than any other economist. He was awarded the Nobel Prize in 1994 and was the subject of the movie ‘A Beautiful Mind’ starring a schizophrenic Russel Crowe. But outside of economics his theory and it’s application is not widely understood.

Before Nash, economic solutions, or equilibria, existed for zero-sum games. Games where one person’s gain is another person’s loss. Which is fine in poker or coin tossing but not much use in every day life.

But Nash showed a solution could be found in any game with a finite number of players and a finite number of moves to choose from. This simple concept is important because it’s applicability extends well beyond economics.

Choices like deciding which side of the road to drive on are a Nash equilibrium. At any time there’s a set number of people and only a few choices to choose from (left or right). Your decision to obey your local driving rules and stick to the correct side gives you the best chance of getting to your destination alive. And since the same logic applies to everyone else, everybody does the same thing.

Repeated games extend Nash’s equilibrium. The best known is the Prisoner’s Dilemma. This game
offers two prisoners a choice. Betraying their criminal partner (and going free) or remaining silent (and staying in prison for a short period of time). For a single game the optimal outcome for each individual is that they betray each other. The result is that they both serve longer prison time than if they had remained silent. But when the game repeats, cooperative behaviour appears and the criminals stop ratting on each other. Any acts of betrayal are best met with one off retribution. Keeping them in the game. But reminding them of the rules.

Beyond prison walls we see repeated games in telco’s. The British government’s auction of 3G mobile operating licences in 2000 raised £22.5 billion because of Nash Equilibrium. Auction designers treated the auction as a game, setting rules so that the best strategy for bidders was to make bullish bids. Although winning bidders were less than pleased with the outcome.

In business procurement. Every time a tender is issued or reverse auction run buyer’s and seller’s are tempted to defect. Buyer’s could renege on their selection criteria . Sellers could rescind their offer. But this one-off behaviour is rarely seen.

Procurement professionals understand the long game. Contracts are usually renegotiated before people change companies. People remember past behaviour. And it’s taken into account at the next contract negotiation. Impacting prices and risk weightings. Thanks to Nash’s work we know that it’s not just rules creates effective procurement. Retribution promises make markets work.