Emergence of Cooperation
Thomas Hobbes declares in 1651, 'the State of Nature is a state of war of all against all.' If indeed everyone were perpetually at war, how was it ever possible for cooperation to emerge? We take a closer look at contemporary political scientist Robert Axelrod's work answering this puzzle.
The Prisoner's Dilemma
The Prisoner's Dilemma is a thought experiment that illustrates the balance of cooperation and defection.
In the classic setup, two suspects are arrested and held separately. Each has two choices: cooperate with the other by remaining silent, or defect by testifying against the other.
The payoff matrix shown here will impress upon you, no matter what your opponent does, it is better to defect. The conclusion remains the same for your opponent as well. Thus both end up choosing defection over cooperation!
| Points Scored | Opponent Cooperates 🤝 | Opponent Defects 👊 |
|---|---|---|
| You Cooperate 🤝 | 3 You | Opponent: 3 | 0 You | Opponent: 5 |
| You Defect 👊 | 5 You | Opponent: 0 | 1 You | Opponent: 1 |
Lets play a 5-Round Game
Challenge three different opponents. Choose to Cooperate (🤝) or Attack (👊) each round.
What Did You Discover?
Bully strategy
The bully attacks, always. Your best response is attacking back (adopting their strategy). This would earn you a mere 5 points.
Random Strategy
Your opponent will randomly choose cooperation and attack. On an average you would expect to get 15 points but in reality the results will fluctuate.
Fair Strategy (Tit-for-Tat)
Your opponent will cooperate first, and then mirror your last move. Your best score is 15 points by cooperating in all rounds.
As an opponent you would like to select a Fair opponent and adopt their strategy while playing to maximize your scores.
Lets make these characters play each other
The tournament involves bullies, fair and random strategy being played against each other (including themselves). 3 players adopting random, bully and fair strategy will each play 400 games against each of the 3 strategies. Each game consists of 5 rounds.
Population Evolution
Unlike a sport where one emerges a winner and one a loser, life is all about long-term thinking. When humans interact, they adapt to their surroundings. They build rapport with others and observe how well they pair with others. Let's simulate this: starting with equal proportions (33% each) of bullies, randoms, and fair strategies. Each tournament runs games proportionally - strategies that make up more of the population play more games. After each tournament, we update proportions based on performance: successful strategies grow their population share, while less successful ones decline. This runs for 50 tournaments and we will see evolutionary trends.
Ok, you are a cynic!
You do not believe that world is equal parts bully, fair and random. Fair enough, choose the initial population composition and simulate the trends:
Current Proportions
But wait! The emerging frontier
There is a flaw in the previous simulation. You are likely to choose opponents from your surroundings instead of randomly selecting anyone. Lets create a 100x100 grid with a bully at each of those grid points except for 5 grid points right in the middle who would start with Fair strategy. Each player on the grid plays 10 games against their 4 neighbors (fewer if they are on the boundary) and we will keep their mean scores. After the games are done, each grid point will adopt the best strategy in their neighborhoods based on mean score. We will run this 2 step process for 200 generations and see what happens.
Parting words
Human progress was built on cooperation. It was built because long time ago someone thought of offering cooperation without expecting the same back.
If you just take a look at the 2x2 payoff matrix at the top of the page, as a rational you would not choose to cooperate. But as an unreasonable man, you could...
- George Bernard Shaw