[macosxnerd101]

A lot of the foundations require a good bit of real analysis. Proving the existence of a mixed strategies Nash equilibrium leverages Kakutani's Fixed Point Theorem (von Neumann dismissed the NE as "just a fixed point theorem" actually), but getting to fixed points requires some building blocks. What I really do are auctions and algorithmic mechanism design. Things like shortest path auctions, flow auctions, matching mechanisms, etc.

I see what I'm doing as a branch of applied math. Unfortunately, applied mathematicians don't agree, given that it doesn't involve numerical methods or differential equations.

[ishkabible]

Looking up Kakutani's fixed point theorem is part of what got me interested in topology (I'm just starting to learn about it)! Also I'm not (again) reminded that John Nash just died. I've heard about from different sources so many times recently.

On another note, what exactly is mechanism design? I looked it up and I don't really understand it. The wikipedia article didn't give me any examples but rather the general definition and a bunch of thermos. About all I have gathered is that it is the opposite of regular game theory. My (possibly incorrect) understanding is this: Rather than being given the payoff matrix and deciding on a strategy, you instead are given the strategy and are asked to design a game (that maximizes what? expected payoff of one of the strategies?). How close am I?

I also realized that this actually makes a lot of sense for you given your interest in economics and computer science. It's like computational physics for Dogstopper.

[macosxnerd101]

Mechanism design is designing a game to achieve a desired result. Basically, how do you incentivize players to behave in a certain manner. Can players manipulate the mechanism to increase their payoff? How stable is the mechanism? How do two different mechanisms compare?

One example of algorithmic mechanism design is the Gale-Shapley algorithm to solve the stable marriage problem. The Gale-Shapley mechanism is stable (all allocations are in the core), and it incentivizes the proposers to honestly report their preferences. The acceptors can lie about their preferences and improve their payoffs, however.

Auction theory is a subset of mechanism design.

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I also realized that this actually makes a lot of sense for you given your interest in economics and computer science.

Computational economics tends to be more applied- more on the macro side. Algorithmic mechanism design is definitely at the interface of CS, graph theory, combinatorics, and economics. It's a relatively new area and quite interesting!

Edit: Also, shameless plug for my tutorial on the Stable Marriage Problem. I'll hopefully have a tutorial by the end of the week on the Top-Trading Cycle Procedure (another algorithmic mechanism).

[ishkabible]

Ah interesting. So governments (and many other interested parties) can actually properly design economic incentives.

I'll have to look at this more. Situations with multiple games to design; mainly I was trying to see if a replicator dynamic type thing cropped up. Unfortunately my thoughts are getting rather muttled (partly because I don't understand what I am reading very well and partly because it is 1:15 in the morning)

Basically say you were in a situation where you had to repeatedly make decisions about a payoff matrix and so do other people. You then play each others games in some mannar such that how you play each game depends on the way other games were designed.

[macosxnerd101]

Yes. It is possible to design an incentives system.

I wouldn't intuit this as a payoff matrix. More, I would think that each player will seek to maximize utility (or expected utility) and play accordingly.