2.23. Lecture 17: Evolution of cooperation

Before this class you should:

  • Read Think Complexity, Chapter 12

Before next class you should:

  • Make sure you have a copy of The Alignment Problem

Note taker: Rich Hawkins

2.23.1. Overview

  • This lecture explores the evolution of cooperation and trust through the use of game theory

  • Examines the problem of altruism and how it conflicts with natural selection

  • We discuss the Prisoner’s Dilemma and its implications for cooperation

2.23.2. The Problem of Altruism

Altruism refers to selfless behavior that benefits others at a cost to oneself. This is in conflict with the idea of natural selection, which suggests that individuals should act in their own self-interest to maximize their chances of survival and reproduction. This contradiction illustrates the problem of altruism, which has been a topic of debate among scientists and philosophers.

It is a debate about human nature. Are humans inherently good, evil, or shaped by their environment? During class we explored this topic through a discussion and a simulation called the game of trust, which highlighted the importance of cooperation and trust in human interactions.

2.23.3. The Prisoner’s Dilemma

The Prisoner’s Dilemma is a classic example of a game that illustrates the conflict between individual rationality and collective benefit. It is often used to study cooperation and trust in social interactions.

How Does the Game Work?

Two prisoners are arrested and interrogated separately. They can either betray each other or remain silent. Neither knows what the other will do. The outcomes depend on their choices:

  • If both betray, they each get a moderate sentence.

  • If one betrays and the other remains silent, the betrayer goes free while the silent one gets a heavy sentence.

  • If both remain silent, they both get a light sentence.

Key Findings:

  • In a single round of the Prisoner’s Dilemma, the rational choice for both players is to betray, leading to a worse outcome for both compared to if they had cooperated.

  • However, in repeated interactions (Iterated Prisoner’s Dilemma), cooperation can emerge as a stable strategy, especially when players can build trust over time.

Conclusions:

The best strategy for the Prisoner’s Dilemma is tit for tat

  • Start by cooperating, then replicate your partner’s previous move

  • This strategy promotes mutual cooperation and can lead to better outcomes over time

2.23.4. Game of Trust

In class we used an interactive exercise that used an agent model to explore different strategies in the Prisoner’s Dilemma. Checkout the Game: <https://ncase.me/trust/>

History / Background

  • On Christmas during the First World War, Peace Broke Out

  • Soldiers from opposing sides temporarily ceased hostilities and fraternized

  • Crossing No Man’s Land to bury their dead, exchange gifts, and play games

  • This event demonstrated the potential for cooperation and trust in the midst of conflict

  • But why in the modern age, where we have been at peace for decades, do we still struggle with trust and cooperation?

Rules of the Game

  • Similar to the Prisoner’s Dilemma, agents are paired against another agent and must decide whether to cooperate (pay a coin) or betray (not pay a coin).

  • The payoffs are as follows:

    • If both players cooperate, they both receive 2 points.

    • If one player betrays and the other cooperates, the betrayer receives 3 points while the cooperator loses 1 point.

    • If both players betray, they both receive 0 points.

Agents and Strategies

These are the agents used in the game and their behaviors:

  • Copycat: Always copies the opponent’s last move. If the opponent payed a coin last round, the Copycat pays a coin this round, and if the opponent did not pay a coin last round, the Copycat will not pay a coin this round.

  • Always Cooperate: Never cheats and always cooperates. It always pays a coin no matter if the opponent paid a coin or not in the last round.

  • Always Cheats: Never cooperates and always cheats. It never pays a coin no matter if the opponent paid a coin or not in the last round.

  • Grudger: Cooperates until the opponent cheats, then always cheats. It starts by paying a coin, but if the opponent ever fails to pay a coin, the Grudger will never pay a coin again.

  • Detective: Starts with a specific sequence of moves to test the opponent’s strategy before settling into a pattern. The sequence is: Cooperate, Cheat, Cooperate, Cooperate. After this sequence, if the opponent ever cheated, the Detective will switch to copying the opponent’s last move. If the opponent never cheated, the Detective will always cheat.

  • Copykitten: Similar to Copycat but only cheats back after being cheated on twice. It is more forgiving than the Copycat, as it allows for one mistake before retaliating.

  • Simpleton: Starts by cooperating, if oppenent cooperates, it does the same thing as last round, if opponent cheats, it does the opposite of its move in the last round.

  • Random: Chooses to cooperate or cheat randomly each round with a 50/50 chance.

The class was split up into groups to explore the game ourselves, stopping after key rounds to discuss strategies and outcomes.

One Tournament Simulation

This is a simulation where each Agent plays against each opponent (a different Agent) for 10 rounds, and the total points are tallied to determine the winner.

This simulation was only ran with the Copycat, Grudger, Detective, Always Cheat, and Always Cooperate Agents. The results were as follows:

  • The Copycat Agent won the tournament, followed by the Grudger Agent, then a tie between the Detective Agent and the Always Cheat Agent, and finally the Always Cooperate Agent.

  • This proves our conclusion from the Prisoner’s Dilemma that tit for tat is the best strategy.

Multiple Tournaments Simulation

This simulation extends the One Tournament Simulation by running multiple tournaments in succession. After each tournament, the five worst agents are eliminated and replaced by five clones of the winner.

This simulation also allowed testing how many rounds were played against each opponent as well as adjusting the payoffs, to see what results that may produce. It was only ran with the Copycat, Always Cheat, and Always Cooperate Agents. The results were as follows:

  • The Always Cheats Agent quickly overpowers and eliminates the Always Cooperate agent regardless of how many rounds per match.

  • Once the Always Cooperate Agent is eliminated, the Copycat Agent dominates the Always Cheat Agent but only when there are more than 5 rounds per match.

  • When there are 5 rounds or less per match, the Always Cheat Agent dominates the Copycat Agent.

  • By changing the payoffs/rewards of the game, different strategies can become more or less effective

Mistakes

The game of trust also explores the impact of random accidents. For example what happens if a person accidentally cheats when it meant to cooperate? What if a somebody meant to put a coin in but tripped and missed?

By running the multiple tournament simulation with the addition of the Copykitten, Simpleton, and Random agents while adjusting the mistake probability, we can see how different strategies perform when there is a chance of an agent making a mistake. The results were as follows:

  • The Simpleton agent is able to exploit Always Cooperate, because if the Simpleton agent makes a mistake and cheats, it will keep cheating the Always Cooperate agent.

  • If the chance of a mistake is between 1% and 9%, the Copykitten agent can outperform everyone, but it is so forgiving it never wipes out the Copycat agent.

  • If the chance of a mistake is between 10% and 49%, the Always Cheat agent will dominate and eliminate every other agent.

  • If the chance of a mistake is above 50%, no stable winner emerges.

Conclusions

Through the use of the Game of Trust, we can see how different strategies can evolve and compete in a social environment. The outcomes of the game are influenced by several factors:

  • Repeat Interactions: Trusting is a successful strategy so long has there is enough repeated interactions

  • Payoffs: The rewards and penalties of the game can influence which strategies are most effective. Must be a non zero sum game to promote cooperation, i.e., both players can win at the same time.

  • Mistakes: With few mistakes, forgiveness can thrive, but with too many mistakes, trust can break down and lead to widespread cheating.

The Big Lesson: The Environment and Context of the game can have a significant impact on the evolution of cooperation and trust. By understanding these factors, we can better design systems and policies that promote cooperation and trust in society.

2.23.5. Robert Axelrod

Robert Axelrod was a political scientist who conducted extensive research on the evolution of cooperation using the Prisoner’s Dilemma. He ran tournaments where people submitted their strategies for the game, and he analyzed the results to understand which strategies were most successful and published his findings in the book “The Evolution of Cooperation”. His work has had a significant impact on the field of game theory and our understanding of cooperation in social interactions.

At the start he found that the tit for tat strategy was the most successful, highlighting a few key properties contributing to success:

  • Being nice: Starting by cooperating and never defecting first.

  • Being retaliatory: Responding to defection with defection.

  • Being forgiving: Being too vindictive can be counterproductive.

  • Being non-envious: Not focusing on outscoring opponents, but doing well enough against a large variety of opponents.

These findings offer a possible partial solution to the problem of altruism. Showing that it is probable that the genes for altruism are prevalent because they are adaptive. Meaning they provide a survival advantage. But the strategies in this tournament were developed by people so they didn’t evolve from nothing. Therefore what initialized or created the genes for altruism? Was it a mutation or a product of the environment? Therefore not giving a full solution to nature vs. nurture.