Variation of the Prisoner's Dilemma

For those that already know of the dilemma, skip on down to see it’s relation to this ranking system. For the others: Here is a simple explanation of the dilemma given my understanding.

There are two people that commit a crime. They each know the way the law works. Below are the outcomes:

  1. Nobody confesses=each gets 2 years
  2. Prisoner A confesses= Prisoner A goes free, Prisoner B gets 10 years
  3. Prisoner B confesses= Prisoner B goes free, Prisoner A gets 10 years
  4. Both confess=Both get 5 years in prison

Now, they can’t talk to each other and are faced with this decision. What do they do? Well, prisoner A wants what is best for him. If he doesn’t confess, he could get either 2 or 10 years. If he does confess, he could either go free or get 5 years. Given these rules, his selfish nature, and distrust of his fellow criminal: he confesses. Prisoner B makes the same decision making the outcome to be 5 years each. Neither wins.

On to the application to FIRST:

This year there is a similar choice. Score on your opponent or yourself. I’m going to assume that alliance A scores 4 and alliance B scores 6. Each gets 2 points of penalty.

  1. Both score on A:
    Pre-penalty: 10-0
    Final: 8-0
    Seed points: 8-10
  2. Score on opponent:
    Pre-penalty: 6-4
    Final: 4-2
    Seed points:8-6
  3. Score on self:
    Pre-penalty: 4-6
    Final: 2-4
    Seed points: 6-8
  4. Both score on B:
    Pre-penalty: 0-10
    Final: 0-8
    Seed points: 10-8

Now, we are going to assume you want a high rank, don’t communicate with the opposing alliance, and understand these outcomes. If your team A, you can choose to score on yourself and get 6 or 8 seed points. Or you can choose to score on B and get 8 or 10 seed points. Given our assumptions, you would choose to score on team B. If your team B, you can choose to score on yourself and get 8 seed points. Or you can choose to score on A and get 6 or 10 seed points. Team B would choose to score on themselves.

This means that both teams should score on the team that is going to score most. It doesn’t matter if your scoring on yourself or your opponent.

I know I threw alot of stuff out there…sorry for the long post. I just find this intriguing and wonder if the GDC had been inspired by this game theory. Any thoughts? Feel free to correct any of my numbers or assertions. I probably missed something, but thought that this was worth getting up fast.

As I understood it, the point of the prisoner’s dilemma game was that if each party made the best choice they could in terms of expected value, then they would both end up with a bad outcome for both of them. In the scenario you are describing for Breakaway, each party acting in their own self interest leads to the best outcome for both parties. Thus, the payoff matrix you used is not really a prisoner’s dilemma because nobody would change their strategy if they knew what the opponent would do. That’s not to say that there aren’t scores and penalties for teams A and B that can make this a prisoner’s dilemma, but the ones stated here certainly do not.

Also, Molten, I’m sure you realize this, but both the assumption that you can’t communicate as well as the assumption that both parties understand the outcomes are a stretch, to say the least. When people don’t even understand the seeding system, they’re probably not framing the situation in terms of game theory.

I did a little analysis at kickoff, and I came to the conclusion that the robots would never score on the same alliance, since it is more profitable to score on whichever team the opponent isn’t scoring on, both if they are losing or winning (as long as there is a good difference between scores. If they are tied, trying to win is better).

The cycle would go like so (assuming team A can score better than B):

A scoring points for A
B scoring points for B

A gains a good lead

A scores points for B, go get a higher number of points
B scores points for A, to maximize their points

B catches up to A, since A is a better and is scoring for them

A scores points for A, to regain their lead
B scores points for B, to try and take a lead

back to start

If B knows A is better, then they might just keep scoring for A, but they generally do not know this.

6v0 matches split the points evenly, but the total number of points given remains constant (assuming no defense). I remember 1519 came to 20’s pits, asking that we don’t play defense. I agreed with them, since that is (imo) the best way to maximize points while seeing how well the robots perform.

From our perspective, not playing defense during the qualification rounds was a very evident conclusion; nearly everybody within 1519 was agreed on this point, and we believed that we could convince other teams (both alliance members and our alliance opponents) that the “no defense in qualification matches” approach was a better strategy than playing defense. Attached is a “No Defense Briefing Sheet” that we wrote and distributed well in advance of each qualification match in which we participated – first to our alliance members to get their buy-in, and then to our alliance opponents. At least half of the alliance opponents we talked to about this thought we were trying to “pull a fast one” with them on this matter.

In all honesty, I was amazed at how few teams had seriously pondered the ranking strategies before the tournament and didn’t realize that win/loss was no longer used for determining seeding rankings (even low-numbered veterans; team 20 was one of the rare exceptions that had clearly thought the matter through beforehand). At least half of the drive teams we spoke with had no knowledge of the new seeding approach and were hearing it from us for the first time, even into Saturday morning.

Internally, our team is split on whether the collective best strategy for qualification matches is to play a “3v3” match with no team playing defense, or to have all 6 teams collude to play a “6v0” match. Personally, I believe that the “6v0” match will likely be better for all teams, given two significant assumptions: (1) that in a “no defense” 3v3 match, average qualification round scores would be around 6-5, and (2) that in a “collusion” 6v0 match, the total number of goals scored would increase by about 30-50% over a “no defense” 3v3 match, since all balls are always going in the same direction, and specific roles can be assigned to all 6 teams to work together, to play to the strengths of each of the 6 robots.

Given the above assumptions, in a 3v3 match resulting in a 6-5 score, the winners would receive a total of 16 points for ranking, and the losers would receive 6 points. However, if the same teams played 6v0, I think they would score approximately 40% extra goals, resulting in a total of around 15-0, giving 15 points to all 6 teams. In such a scenario, I personally would advocate the 6 teams work together to get that 15-0 match.

We had wanted to be in a 6v0 match at the Granite State Regional. However, we encountered enough trouble trying to convince 5 other teams to not play defense that getting all teams in a match to collude on a single coopertition strategy was right out of the question.

I’m hoping that by the time we get to the North Carolina Regional (week 5), we’ll be able to participate in a few 6v0 matches!

PS: Oh, and by the way, as was clearly evidenced in the GSR finals, we don’t suggest a “no defense” approach in the elimination rounds…

FRC-1519-No-Defense-Briefing.pdf (138 KB)

FRC-1519-No-Defense-Briefing.pdf (138 KB)

The outcomes are unrealistic in this day and age. We all know how the law works today. One of them would turn State’s evidence, rat-out the other, and get off scott free.

That too has applications to FIRST - I.E. Being late to Coopertate is not in your best interest!

I think the NO DEFENSE strategy will not work entirely. In order to get the coopertition bonus, you have to win or tie. Therefore, when it comes down to which alliance will get the bonus defense will come into play. Preventing a team access to the tower prior to the 20 seconds, stop the other team from scoring when the score is close, etc… The best outcome for all teams is a high score tie. A 8-8 game (no penalties) will give all teams 24 seeding points. A 8-7 game will give winners 22 points and losers 8. If you are maximizing the points for your own alliance, then WIN and keep the score close. Let your opponents score some points.

Coaches and Drivers will have to keep a close eye on the score, use minimum defense, but not NO defense.

The game changes in the elimination rounds.
Each team will want to do their best to show off their robot’s capability during the qualification matches, because come the alliance selection, you are going to want to have the teams that handle the ball well and can score. Your third robot may be a pure defensive robot. The scout teams will be very important, the rankings will not give the best evidence of the “best” robots when picking your alliance.