2-team Iterated Prisoner's Dilemma tournament

What the heck is Iterated Prisoner's Dilemma?

It's a game where each player creates a "strategy" about whether to cooperate or defect against other players based on how their history of interaction. This video does a pretty good job of describing some of the ins and outs.

Some claim that by understanding the dynamics of cooperation better, we can understand our own natures a bit better as well. Why did societies evolve cultures of cooperation? Perhaps it's not just about being nice for its own sake, but also has some links back to basic survival. Not to imply that we should cooperate with others just for our own gain, but it might help us understand how this all turned out to work for us.

Rules for this tournament:

There will be 2 teams. Initially, people will be randomly assigned to teams and given a chance to come up with a team name and a preferred method of team coordination (email, FB group, whatever).

Teams can invite others to join their team up to a max of 10 people per team for this first round, to make sure things work smoothly.

The tournament will have 12 rounds. If each team has 10 people, then, for every round every person on team A will interact with every person on team B in a round-robin format. This is different from other tournaments and is designed to model how we interact with people that aren't in our primary trusted group/tribe.

Between each round players on both teams will have a limited time to adopt the strategy of someone else on their team for the following round. They can go back to their own in later rounds, but have essentially changed their mind about what the best strategy to play is. This earns status for the player who's strategy was copied.

Each interaction between 2 players will include 100 moves. For example, if player 1 from team A is interacting with player 2 from team B, each move will include a chance for both player 1 and player 2 to choose to cooperate with, or defect against, the other. These moves will be determined automatically based on the strategy they set at the beginning of the tournament (see list below).

Scoring each move: if both players cooperate, they each player get 3 points for that move. If they both defect, they each get 1 point. If one cooperates and one defects, however, the player who cooperated gets 0 points and the player who defected gets 5 points. It looks like this:

Image result for prisoner's dilemma

The point system is balanced to make sure it's always in your immediate self-interest to defect, because if you know what the other player is going to cooperate or defect, in both cases you'll get more points by defecting than cooperating. The dilemma, however, is that the pair of both players (if you consider both players on the same team, as collaborators) will benefit most by both cooperating. That, of course, requires trust because both sides need to give up their own immediate self-interest and become vulnerable to being taken advantage of. Dilemma!

A player's score for a given interaction will be the sum of all 30 of their moves played in a row. There will be a script that does this automatically, so we don't have to do all the math ourselves.

Each team's score for a given round will be the average score of all of the players on that team. For example, if all 10 people on both teams cooperated every single time, each team would get (3pts per interaction) x (100 interactions per round) x (10 people per team) = 3,000 points for each team. The max score for a round is 5,000, and the minimum score is 0.

The tournament is won by being on the team that has the highest total score divided by the number of players on the team.

Teams will also receive a value-based rating based on the average score per turn across all players and rounds. An average score-per-turn above 3 is a Mercury rating, because some dark arts (and luck) would be required to achieve this high of a score. On the lighter side of the scale, an average score between 2.5 and 3 is a Gold rating, an average score between 2 and 2.5 is a Silver rating, an average score between 1 and 2 is a Bronze rating, and an average score between 0 and 1 is an Iron rating.

Status within each team is a twist on the classic design of this game. It's meant to represent how we both try to beat the competition, and gain status amongst our teammates in various ways. It's guaranteed to keep the game interesting! Each of the 12 rounds, the player (or players) who meet these criteria get status points:

  • Having the most points in a round earns you 1 status point.
  • Having the most cooperate-cooperate interactions that round also earns you 1 status point.
  • Having the most defect-cooperate interactions (meaning they zinged the other side) also earn 1 status point.
  • If another player chooses to switch to your strategy for one or more rounds, you earn 1 status point.

The team status game is won by being the person who has the most status (however earned) at the end of all 12 rounds.

Meta rule (optional): If your team has a proposal for a change to the game's goal, rules, or scoring system as currently described, you can make the proposal to change it in some way. If the other team accepts the proposal, we can update the game accordingly. If not, then the update doesn't happen. For example: a team could propose that the number of rounds change from 12 to some other number. As long as both teams agree to the proposal, we can update the game's rules. It's a meta form of prisoner's dilemma, since by proposing the rule you might be exposing a bit of your team's strategy, but if they agree it might benefit both sides.

What do I need to do?

  1. Sign up! To do so, just request an invite to this FB group. If it hasn't started yet, I will assign you to a team if there's still room.
  2. Find your team! If you have signed up, and know your team, you should check in with them, figure out who the captain is, etc. Details about that should be in the FB group.
  3. Pick a strategy! Some are listed below, and your teammates might have ideas as well. If you feel paralyzed, picking tit-for-tat, it's a safe bet. If you want to be ambitious, consider both the strategy you think will perform best AND the strategy that is most likely to win respect points on your team. Or, just go for the respect and forget about the other points.
  4. That's it! The rest of the game is automated. If you want, you can choose to sit back and watch what happens at this point, or you can optionally choose to switch strategies between rounds.

Tournament #1 assignments

Team Name
Team Ant 🐜
Team Beetle 🐞
CaptainSharonJessica C
David J
Jessica O
David R

List of common strategies

If you are having trouble deciding, pick one of these:

  1. Tit-for-tat: Start by cooperating, then defect whenever the other player defected last turn, but cooperate again if the player cooperated last turn.
  2. Grim trigger: Start by cooperating, then defect for the remainder of the round if the other player defects even once.

If you want to get more creative, here are a handful that do well in certain situations:

  1. Tit-for-two-tats: Like tit-for-tat but only defects if the last 2 moves by the other player were defects. A bit more forgiving.
  2. Prober: This one tries to tell if the other player is a tit-for-tatter by starting with 1 defection and 2 cooperations. If the other player cooperated in turn 2 and 3, it keeps defecting, otherwise it plays tit-for-tat.
  3. Gradual: This one has done really well in tournaments, it works like tit-for-tat but instead of only defecting once after the other player defects, it defects the number of times the other player has ever defected, then cooperates twice to reset the other player back to cooperating. So on 2nd defect, it defects twice, then cooperates twice, then goes back to responding to the previous move.
  4. Adaptive tit-for-tat: Like tit-for-tat but bases its next move on whether or not the average of all previous moves by the other player were cooperate or defect.
  5. Pavlov: This is an unintuitive one that cooperates if the last move was either cooperate-cooperate OR defect-defect.
  6. Generous tit-for-tat: Like tit-for-tat but when the player defects, you will only defect 90% of the time. This is useful if there's a chance of getting out of the always-defect sequence by being nice.

Really basic strategies that you can fall back on if you want:

  • Always cooperate: A risky strategy unless you have a lot of trust established with the other players.
  • Always defect: Not a bad strategy if you're risk adverse and just want to avoid doing terribly.
  • Random: Randomly cooperate between 1-50% of the time.
  • Pattern-based: Pick any pattern of cooperation and defection, like cooperate-cooperate-defect, and just repeat that throughout the game oblivious to what the other player does in return.

Make up your own!

  • There are a bunch more strategies on the internet. Here's a good list.
  • There are so many potential strategies out there. Part of the trick is that each strategy is attempting to optimize based on what everyone else is doing. But if you do something nobody else is expecting, they'll be less optimized!

Qualities to consider in a strategy

Here are a couple traits that seem to express themselves in strategies.

Friendliness: If I don't know anything about the other player, should I cooperate or defect? You can also decide to do a mix of them, based on a % or some other heuristic. This is a proxy for how much you trust the other teams/players to cooperate.

Provocability: How responsive to defects do you want to be? Tit-for-tat, for example, reacts immediately. Tit-for-two-tats only responds after two defects in a row. Generous tit-for-tat responds immediately 90% of the time. All of these strategies have pros and cons depending on the strategy the other player is using.

Creativity in punishment: Once a punishment is triggered, you can exact punishment however you like. It can be simple (a single move), based on some pattern, or have elements of randomness. Remember there are 100 moves per round, so the severity of your punishments will need to live within that time frame.

Creativity in forgiveness: The other half of provocability. After responding to a defect, how long do you hold a grudge? Tit-for-tat only holds a grudge for one turn, Grim trigger defects for the rest of time.

Predictability: In general, do I want to stick to my own rules 100% of time, or introduce some element of randomness? On one hand, being predictable is a part of establishing trust. On the other hand, it can get you caught in a corner.

Memory: Some people believe that the best strategy is a simple one. Like tit-for-tat... it only needs to remember the last move. But that constraint isn't required... you can do anything with the full history of a player's moves and even your own moves. Taking the average, or look for patterns, or count the number of defections, etc. Consider it all on the table, if you think this information might help you.

Team dynamics: Since everyone's on your team is trying to compete against another team's set of unknowable strategies, it makes sense to consider how your strategies might work together and reduce risk of a particular strategy wiping all of you out. For example, imagine what will happen if everyone on the other team cooperates 100%, or everyone on the team defects 100%, or if every player plays completely randomly.

Word of mouth: To make things interesting, players will have the ability to remember 1 thing from the previous round and act on it in their strategies: did the other player, on average, start new games last round in a friendly or unfriendly way, across all players? This is equivalent to reputation... the kind of thing that might get passed by word of mouth amongst your teammates... what can you do with this information?

Sometimes the simplest strategy is best. But if you wanna go complex, that's an option too. I'll add to this list based on what we learn as the tournament proceeds.