CMPS272, Winter 2007, Section 01: Project Ideas

Project ideas for Evolutionary Game Theory Class (ADD YOUR IDEA BELOW)

0. Here is the a completed group project writeup from last time. It might help you calibrate your expectations.

1. Financial market bubbles and crashes. Incorporate new realistic features into existing Netlogo simulation, e.g., rank-based incentives for portfolio managers, and liquidation of less successful funds. Alternatively, allow humans as well as agents to participate in the market simulation.

2. Veblen consumption. Existing analytics and simulation show how shock waves propagate through a population of consumers who value high rank in conspicuous consumption. Extensions would investigate realistic features like income differences and taste differences. Alternatively, allow humans as well as agents to participate in the simulation.

3. Political landscape dynamics. In an issue space of dimension 1 to 3, allow two or more political parties to compete continuously for voters? favor.

4. Contagious liquidity crises. Use a sandpile-inspired model of liquidity avalanches: Delinquent payments by one bank (or other entity) can cause their lenders to become delinquent. Sometimes it spreads widely, other times not. Investigate.

5. Parent-offspring conflict, invasion of a brood parasite.

6. Learning algorithms (Manfred style) applied to biological problems (crypsis)

7. Learning algorithms (Manfred style) applied to biological problems (aposematic-model-crypsis)

8. Various combinations of 2X2 games and the resultant effects on RPS (e.g., combining various 2x2 games and seeing which are RPS stable (e.g., a Nash equilibrium)

9. Exploring the long-term memory properties of biological learning algorithms

  • Can sex or junk DNA realize the "mixing to the past average" update
  • How does the frequency of a bad gene decay (in the long term) when we have sexual reproduction
  • Ditto when the mechanism of junk DNA is available

10. MyIdea, Name1, Name2, Name3 (make the word idea a wiki page where you flesh out the idea) Synopsis of the idea in a one liner (or two liner)

11. Sexual Conflict and Partner Manipulation in Banana Slugs- Brooke's idea. SexualConflict PLEASE LET ME KNOW IF YOU ARE INTERESTED! this is a cool project, i promise! i have a good sense of humor and really need some people who are not afraid of the wiki or of programing... or of penis chewing banana slugs for that matter. you WILL get a co-authorship on a paper if we can get this going but all YOU have to do is help me make the model! do you need a biologist? i AM a biologist. HELP ME!

12. PoliticalParties - related to idea #3. We (DanielLeavitt and AndersNyman ) were discussing how different political systems seem to yield different numbers of major political parties (2 for the US and UK, more for many social democracies.) We wondered if this might be modeled using game theory.

Maybe this could be explored by setting up two games, one parliamentary (e.g. the scandinavian countries) and one using the US system. Then you could let a number of parties compete with the same rules only modified to represent the changes in political systems. - Anders (btw, I'm gonna be away for the weekend so can't check the wiki)

13. Financial Markets: There is evidence investor behavior is a vehicle that can transmit shocks from one country to another. For example investors in the US play a role in transmitting shocks to Mexico's stock market. The project would investigate how agents form networks and how the interaction of agents transmit shocks from one country's stock market to another country's stock market. Simulations would be involved. Could be related to idea #4. Todd -

14. Understanding History of "Best" First Moves in game of Go.

  • From my limited knowledge of history, a thousand years ago the "Best First Move" in the game of go was the "4-4" points, with the goal of creating one or two large territories. A hundred years ago, the "Best First Move" in the game of Go was the "3-4", with the goal of creating several small territories.
  • In 1933, a few professional Go players caused a ruckus when they played non-traditional moves as their first few moves in tournaments, and won. These included "4-4", "3-3", and "10-10", and their goal was to be flexible. For a few years, wide experimentation ensued among professionals; almost any move was considered okay. This then settled down, and another theory of "best first moves" arose.
  • Perhaps it would be interesting to understand the development of this "New Opening" theory? Model it as competing strategies, and understand how the traditional theory could be evolutionarily stable for so long, then so quickly replaced by a mutant invader? I'm auditing, so I'm mostly suggesting this as a project for other people, but I'd be very glad to help.
  • As limited as my knowledge is of the history, my understanding of the strategy is even more limited, but here is my best attempt.
    • Explanation 1: It is easiest to make points in the corner, and hardest in the center. The traditional 3-4 strategy has both players vying for points in the corners, and neither tries for the points in the center; it would be a wasted effort. The "new" strategy delays its choice of whether to go for the corner or the center, even though this is a somewhat inefficient; even if no points are made in the center, the other player must defend against the possibility, and thus must hedge their bets, which is even more inefficient.
    • Explanation 2: If you only have 1 move to play in an area, the 3-3 is best. If you have two moves to play in an area, the 3-4 is the best first move; it has a good follow-up. If you can play 3 moves though, the 4-4 is best; it doesn't have a good single follow-up move, but 2 follow-up moves after the 4-4 are better than 2 follow-up moves after the 3-4. You can't know whether you'll be able to play 1, 2 or 3 moves in a corner, or rather, there is an opportunity-cost for doing so.
  • -- StevenScher - 14 Jan 2007

15. Evolution and Adaptation in Swarm Pursuer-Evader Games

* A pursuer-evader game is a game (usually a differential game -- i.e. one where the state space is a manifold in R^n, and the moves available to each player are supplying a set of parameters to a function which picks the time derivative of one component of the state) in which one agent, called the pursuer, attempts to reach the other agent, the evader, who is trying to escape.

* Pursuer-evader games have been fairly well-studied for games of one pursuer and one evader (often in cases where one or both players is a missile), but we propose a pursuer-evader game where some number of pursuers is trying to maximize the number of evaders each one of them "eats".

* Further we are interested in the case where after some fixed time, the surviving evaders reproduce, and the pursuers reproduce with frequency related to the amount of food (i.e. evaders) they consumed in the intervening time. After this (completely artificial) "reproduction step" the game is restarted with the new population.

* We propose that the pursuer and evader "genomes" be control laws which take, as input, the neighbors under some proximity relation and output instantaneous state derivatives, clipped to some feasible region (further restrictions could be made by putting reasonable vehicle dynamics on each player -- a common restriction is to clamp the turning radius of the pursuer, and the speed of both players)

* We are interested in whether the evaders evolve some form of cooperative swarm behavior. We are most interested in whether we can coax a simulation to produce "bait-ball" results.

* We are also interested in whether different strategies evolve under diploid versus haploid genetics. A successful strategy under diploid genetics could involve producing some number of recessive "sacrifice" offspring.

16. I attached my idea under #10 (click on that one, it is in there somewhere). Basically I am DESPERATE for a group interested in problems of social evolution. Please contact me if you want a biologist on your group or if you are another lone, groupless soul.

. Thanks!!!

17. Many of the games we have discussed in class are played among a population in the following manner: First a random set of pairs of individuals plays games. Then, according to the win/loss record of the set of pairs of individuals, a new set of individuals (some combination of originals and offspring) is produced.

The pairing of the individuals who play games can be thought of as a random graph.

How do the properties of the random graph affect the dynamics of the system?

How can we characterize the sorts of random graphs in the standard model of random interaction, and what happens when the random graphs become Erdos Renyi, Scale-free, spatially determined etc.?

How should the graph at the next reproduction step be related to the one at the current step? Should offspring be new nodes randomly connected to the graph, based on some relation to their parents neighborhood? Should the winner of each game take over the loser?

Can we characterize the degree to which graph topology affects game dynamics by using spectral analysis of the graphs? (i.e. graph Laplacian eigenvalues, adjacency matrix eigenvalues, etc)? What if the graphs are switching among a set with certain properties?

18. Analysis of Lotka-Volterra coupled with a diffusion equation as a reaction-diffusion system for describing predator-prey relations over space. (self-descriptive) (probably been done before)

19. Control of predator-prey systems.

Imagine a Lotka-Voltera system with predator and prey in which both predator and prey are extremely delicious (for instance : Tuna and Herring) Suppose we can affect the system by eating arbitrary numbers of both predator and prey. Can we use control theory to find stable equilibria which maximize our rate of fish catch?

Now suppose instead of "predator and prey" we deal with "fish genetically inclined to grow to small sizes (and thus make poor table-fish)" and "fish genetically inclined to grow to large sizes (and thus make good table-fish)". Given some growth model of each kind of fish, and limited fisherman information on which kind of fish was caught (say they only know fish size, not fish genome), can we find a stable equilibria that maximizes are long-run take of large fish?

Most sub-ideas for #19 taken from discussions with Marc Mangel's students.

20. Affirmative Action at the University level: AffirmAxn
Merrit Hoover, Ryan Shelby
We model Affirmative Action in the higher education selection process as a two player game between the university and the individual applicant(s).