Friday, January 18, 2013

Game Theory

Games of Life are really interesting and very simple but it seems to be a field somewhat lacking. With the computational power and the minds we have today why are people stuck on things such as Conway's Game of Life?

Yesterday, i spent lots of time reading on game theory and thinking of different ways to invite new games. The most cool thought experiment game I found was The Pirate Game . I really like the logic and reasoning behind the results.

Ok so what to do.. I was thinking about applying Statistical Mechanics to decision making processes and seeing how that led to self-organization or equilibrium behaviour. Simulated actions would be described by probability distribution. The problem is I keep thinking that I am just coming back to molecular dynamics.

Strategies is also an interesting part of Game Theory. As in finding optimal strategies for simple games.

I am more inclined towards the simulation part though. I just have not been able to figure out how to distill things down to a simple simulation.

Conway's Game of Life was interesting to people because it only had 4 rules even though they were completely arbitrary:

  1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overcrowding.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
I guess it would be interesting to find out how many rules are needed for self-organization. I guess the problem with these games is that there is really no probabilities or random variables. There are sets of defined variables and that is it.
How much randomness or stochasticity would it take to ruin a self-organized system?
 What does it take for a self-organized system to stay self-organized even with X amount of noise or stochasticity?

I need more time to think and maybe more time to drink. It's Friday and almost time for graduate student seminar.