My Game Theory YouTube Playlist and other resources

I just added Graham Poll's awesome +YouTube playlist (http://goo.gl/UZ1Ws) to my "reading" list for my Game Theory course that I'm teaching on Monday and thought that I should also include the humble videos related to Game Theory that I have on my channel:



I also thought I could get away with making a blog post about this. The playlist above has them in 'last in first out' order but here they are in the order that I made them:

1. "An introduction to mixed strategies using Sage math's interact page."

A video that looks at the 'battle of the sexes' game and also shows of a +Sage Mathematical Software System interact.

2.  "Selfish Behaviour in Queueing Systems"

A video close to my research interests which look at the intersection of Game Theory and Queueing Theory. This video is actually voiced by +Jason Young who was doing his first research internship at the time with me and will be starting his PhD at the beginning of the 2014/2015 academic year.

3. "Pigou's Example"

A video describing a type of Game called a 'routing game'. Pigou's example is a particular game that shows the damaging effect of selfish (rational) behaviour in a congestion affected system. This video also comes with a bit of +Sage Mathematical Software System code.

4. "Calculating a Tax Fare using the Shapley Value"

This is one of my most popular videos despite the error that +Brandon Hurr pointed out at 3:51. It describes a basic aspect of Cooperative Game Theory and uses the familiar example of needing to share a taxi fare as an illustration.

5. "Using agent based modelling to identify emergent behaviour in game theory"

This video shows off some Python code that I've put online that allows the creation of a population of players/agents that play any given normal form game. There are some neat animations showing the players choosing different strategies as they go.

6. "OR in Schools - Game Theory activity"

This isn't actually a video of mine. It is on +LearnAboutOR 's channel but it's a 1hr video of one of the outreach events I do which gets kids/students using Game Theory.

7. "Selfish behaviour in a single server queue"

I built a simulation of a queue (Python code here) with a graphical representation (so you see dots going across the screen). This video simply shows what it can do but also shows how selfish behaviour can have a damaging effect in queues.

I'm going to be putting together (fingers crossed: time is short) a bunch more over the coming term.

Selfish behaviour in queues and some open source graphical simulation software

In 1969 Naor, wrote a really nice paper called 'The Regulation of Queue Size by Levying Tolls'. In this paper Naor considered a system with a single server queue:

• With an arrival rate $\lambda$ (customers per time unit)
• A service rate $\mu$ (customers per time unit)
• and a reward and cost for service that can actually just be considered as a "value for service": $\beta$

Naor then considered two types of customers: Selfish and Optimal.

It is relatively straightforward to see that Selfish customers should join if and only if:

$$\frac{n+1}{\mu}\leq \beta$$

where $n$ is the number of other customers in the system upon arrival.

What is slightly less straightforward is that Optimal customers should join if and only if $n\leq n^*$ where:

\[\frac{n^*(1-\rho)-\rho(1-\rho^{n^*})}{(1-\rho)^2}\leq \beta \mu < \frac{(n^*+1)(1-\rho)-\rho(1-\rho^{n^*+1})}{(1-\rho)^2}\]

(where $\rho=\lambda/\mu$)

It's a really cool result and one that has given rise to a lot more research (including what I mainly enjoy looking at).

I was asked recently be a colleague to give a 15 minute talk about my research to her second year OR class who will have just seen some queueing theory. I decided to talk about Naor's paper and thought that it would be nice if I could give a graphical representation of the customers arriving at the queue (similar to the DES package: +SIMUL8). So I spent some time writing a simulation engine and using the in built +Python Turtle library to get some graphics. A part from some of the optional plotting (matplotlib), this only uses base python libraries. Here's a gif from an early prototype:

Here's a video discussing Naor's result and showing demonstrating everything with my simulation model:

The code is all up on github and it really could do with some improving so it would be great if anyone wanted to contribute: https://github.com/drvinceknight/Simulating_Queues

Blog/YouTube Channel

I don't post to my blog very often yet I have started making a few more videos on my YouTube channel in one of three categories I guess:

- "Tech" (for want of a better name) how to's (or more exactly how I've figure out how to do stuff which might not be the best way...)
- "Education" (for want of a better name) stuff
- Research presentations

I've decided that I'll also throw those videos on here when I put them together (not too sure why, perhaps the best reason is "why not?"). To get started here are 3 past videos:

- Using GitHub to host a website:

- Simulating a Queue: Basic Discrete Event Simulation

- A game theoretical approach to the EMV ED interface