# Possibility: Contests for Algorithms, Pedagogy

Proposal: Game Theory

## Algorithms

My introduction to game theory was Axelrod's Evolution of Cooperation, in which he introduces a computer tournament for the iterated prisoner's dilemma with an uncertain ending. As you may know, his paper/book touts Tit-for-Tat, but there have been other strategies introduced since: Tit-for-2Tats, Win-Stay Lose-Shift, Grim Trigger, zero-determinant strategies, etc.

I think a StackExchange site dedicated to game theory could host tournaments like this.

That is, it could clearly explain the rules, have people submit algorithms, let people vote as they see fit, run the tournament (someone would have to do this on their local computer), and then mark the winner as the answer (which may or may not have the most votes). It would be akin to the Code Golf StackExchange.

I've been reading up on what makes a good StackExchange, and one of the articles, "Real Questions Have Answers, not items or ideas or opinions" made me wonder whether this would be within scope (of any StackExchange, but particularly this one)?

So is this a good idea? Or is my exuberance blinding me?

## Pedagogy

Wikipedia is a great resources for learning about concepts in game theory, as is YouTube, online videos, and textbooks. But these methods depend on self-interest (intrinsic or extrinsic), whereas I feel as though game theory is one of the few subjects that can be experienced. After all, humans are strategic decision makers, so they can generally be put in the situtations we study. So one tag we might have is a pedagogy tag for

How Best to Explain [this Concept] to an Undergraduate

While most questions of this nature garner a couple answers and multitude of votes, it would be more advantageous for the future visitors if there was a horde of answers and a swarm of votes allowing the best answers to flow to the top. Then, visitors can read from best down the different ways to understand and teach different concepts (through illustrative examples, stories, playable games). We could encourage this behavior by offering a bounty (say of +200), just to let people know that we're not looking for the first answer that is "good enough" but for many answers tailored to different types of learners (and teachers).

Specific Example: How Best to Explain Incentive Compatibility in a Second Price Auction?

This is important pedagogically, but also practically. When people play a second price auction, there is evidence that (without explanation) they treat it as a first price auction and shade their bids slightly (but slightly less so than if it actually was a first price auction). In general, behavioral results in games may deviate from the expected behavior (even accounting for risk aversion and other behavioral quirks) because they're using heuristics and learning in a haphazard environment. Imagine if we could show something graphical or change the game form such that the solution is obvious.

Crowdsourcing for answers is one thing StackExchange is good for; maybe collaborating to share and create new pedagogical tools is another.

Another Example: Teaching Mixed Strategy Nash Equilibrium to Undergraduates

Does this sound palatable?

## On Algorithms

I'm going to argue YES, from that article Real Questions Have Answers:

Constructive subjective questions:

1. inspire answers that explain “why” and “how”.
2. tend to have long, not short, answers.
3. have a constructive, fair, and impartial tone.
4. invite sharing experiences over opinions.
5. insist that opinion be backed up with facts and references.
6. are more than just mindless social fun.

Let's say the competition is to submit a learning algorithm for a double auction:

1. Answers should be an algorithm and an explanation why it would work
2. They should be long (maybe not the length of a paper, but certainly a paragraph for each interesting feature
3. Pssht. We collectively use the word "we" even when there is only a single author. Science'd.
4. Opinion has nothing to do with it; strategies either succeed in certain contexts or they don't; you'd be sharing your expertise, insight and experience rather than your opinion.
5. In science (and hopefully practice), references/facts are part of the game
6. They are fun, but they ain't mindless. Also, it could definitely be something more - like a paper or two papers or a book. Or a semi-accurate model for predicting real-world events.

How frequently these could be run is a different matter - maybe quarterly; depends on interest.

I'm going to have to argue NO on both counts. Not because I don't think they are interesting idea, just because I don't think they'll fit on StackExchange.

## Algorithms

Just to clarify - So you want algorithms to be submitted (presumably not publicly, at first) and ran by some third party (presumably the question asker) in a tournament.

These are some problems I see:

• Posts are public - if they are kept public, this could allow other people to simply write an algorithm to counter it. If they are private at first that will just complicate everything
• Forcing someone to run tons of code to get an answer seems ... wrong
• StackExchange is a network of Q&A sites to help people learn, this doesn't seem like it is doing that
• How will voting work? Will answer score be purely based on performance or will users still be allowed to vote? Or does the winner just get the accepted answer and possibly a bounty-like award and voting as normal? If voting as normal does this make sense? This would mean the worst solution can get voted to the top because it 'has a nice idea' or 'looks pretty' or something.

StackExchange will require major fundamental changes for this to work.

Now if someone would be willing to host a third-party machine dedicated to receiving and running the code, followed by posting it to the site, we may be getting somewhere (still the voting problem), but it's still unlikely to fit well into how StackExchange currently works.

## Pedagogy

Isn't

``````How Best to Explain Incentive Compatibility in a Second Price Auction?
``````

basically the same as this?

``````How does Incentive Compatibility in a Second Price Auction work?
``````

I don't really see the difference. In the latter, you can also state your current level of knowledge in the question and hopefully get an appropriate answer. Or you can get a wide range of answers greatly differing in knowledge required, which would be less localized.