Game Theory Sounds Fun
Vol #73 - March 18th, 2022
The silver screen has a way of romanticizing everything - even dry economics concepts.
Game theory comes alive in the movie “A Beautiful Mind”. What my college professors outlined with boxes and equations, Russell Crowe plays John Nash and illuminates the concepts in a bar played by professors and coeds.
The premise of the game is a tale as old as time. Five budding economists are sitting in a bar, and eyeing the group of girls who just walked in. There is a clear preference for the blonde, and they cite foundational economist Adam Smith to justify their competition - “the best result will come from everyone in the group doing what’s best for themselves.” Of course if they all go for the blonde, they will interfere with each other, and then lose their chances with the brunettes.
The solution presented by Nash is that they coordinate to all go for brunettes, and leave behind the blonde. While the film stylizes this as a Nash equilibrium, that’s not exactly true - this is closer to a coordination problem. It does make for good filmmaking though.
The more classic example is the Prisoner's Dilemma, where two criminals are caught, and offered deals separately. If they both deny the crime, they receive a lesser sentence of 1 year. If they rat the other out, one receives a plea deal, and the other spends three years in jail. If they both rat each other out they each get two years.
Nash equilibria exist when there is no strategy that an individual can pursue which increases their expected payoffs while others keep their strategy the same. The “expected” part is important here - it’s probabilistic. For any given game, on a given turn, an individual could cheat and end up with a better outcome. Knowing however that the other player will in turn cheat, they fall into a negative spiral with worse outcomes. Equilibria are achieved on average over time.
The dilemma here is that the Nash equilibrium exists with both players defecting. If one unilaterally decides to stay silent, they end up in a worse situation. This mutual defection is a worse outcome than both staying silent and only receiving one year.
While most of us hope to avoid the actual prisoner’s dilemma scenario, game theory finds itself everywhere. One of the other most commonly cited examples of Nash equilibria is the concept of Mutually Assured Destruction (MAD).
Since the middle of last century we have lived in a world where nuclear weapons have the potential to initiate world-altering change. While they’ve only been deployed twice in history, they have grown massively in scale, power, and distribution capabilities. The Enola Gay dropped “Little Boy” on Hiroshima which was a 15 kiloton bomb. The US currently has 9 megaton (9000 kiloton) bombs in its arsenal.
MAD is the game theory concept that says, given the immense power of these weapons, if any nuclear state were to launch them, the subsequent retaliation would mean certain destruction for both parties. Fortunately, this is a strong Nash equilibrium. While neither state has the incentive to disarm, they’re equally incentivized to NOT initiate conflict.
The monumental comedy by Stanley Kubrick “Dr. Strangelove” illustrates this mania perfectly. An American general breaks rank, initiates a strike on the Soviet Union, which is unstoppable due to a comically naïve military protocol. The US tells the Soviet Union these planes are inbound in order to stop the inevitable MAD, but the Soviets have developed their own defense mechanism that automatically retaliates when sensing plutonium. Unfortunately no one was aware of this device.
The films namesake highlights an important aspect of game theory - MAD is only effective when everyone knows about it. Information asymmetry twists the game board. Fortunately the film ends with the US finding the defected general’s communication codes and calling off the planes.
All of this seems to hit close to home as a conflict reminiscent of the ombre of the Cold War flares up again in Ukraine. While game theory and Nash equilibria are based on rational actors, there is a strong bias towards not using nuclear weapons.
Less sinister coordination problems and game theory applications exist too. Decentralized currencies present their own set of challenges, as mechanisms must be developed to induce cooperation absent communication or “real world” recourse.
Bitcoin originally solved the “Byzantine Generals Problem”, or how to coordinate agreement between separated and potentially nefarious actors. With the right mechanisms in place to validate messaging, consensus can be achieved despite competing self interest.
One of the more fascinating experiments of the last year has been the attempts of Olympus DAO to create a stablecoin based on these game theory incentives. Stablecoins are incredibly valuable in DeFi, as they provide a stable means of value store and transmission. Achieving that stability can be done through direct backed reserves (like USDC or Tether), or at the frontier of decentralization, through algorithmic cooperation mechanisms.
OHM is the token issued by Olympus DAO, that represents a claim on the treasury assets. The DAO owns its reserves, and encourages users to contribute to these by issuing discounted OHM tokens. Users can further commit to the protocol by pledging (staking) their OHM tokens and receiving the additional issuances of the protocol.
This intended flywheel was represented by the game theory notation of (3,3) implying that the greatest rewards are when both players staked. Staking means not selling, introducing scarcity, and further incentivizing new entrants to buy into the rising price at a discount.
That only works for so long as (3,3) was not a Nash equilibrium. There was a strong incentive for early entrants to cash out as new money came in. As the price rose to spectacular levels, the incentives shifted, and the cash grab was too tempting. OHM traded over $1200 on 3 separate occasions over the past year, and is now only worth $27.
Games are everywhere. Once you have the lens of game theory in place it will creep into your thinking about everything from negotiations to relationships. It’s a helpful framework to analyze how incentives drive our motives, and probabilistically frame outcomes.
A word of caution though. The cool logic of economics is not always perfectly suited to all interactions, and games must be well designed. Homo economicus is but a fictional character, and in the real world what makes us homo sapiens, is empathy and an ability to take pleasure in altruistic motives.