Progress so far:
I started from reading 2 chapters in game theory and evolutionary game theory respectively.
Then I moved on to some basic programming in Mathematica which could help me find best response, dominant strategy and Nash equilibrium of any game. I attempted to read the book by Weibull on evolutionary game theory, but failed.
I also tried to search for paper that build and discuss game theory models, especially those evolving dynamic games. Three papers are especially useful:
– Dynamical systems game theory and dynamics of games by Akiyama and Kaneko. This paper gave me a first view of how could we incorporate game theory with dynamic system. However, this paper is the first of its series and explained only one person DS game, which is too simple to be applied to our model.
– The Dynamic Game Models of Safe Navigation by Lisowski. This paper builds a very concrete model on navigation. It helps me to understand how to set up variables and relations. I need to read it more times for a better understanding.
– A Dynamic Game of Rand D: Patent protection and Competitive Behavior by Reinganum. This paper also builds a very concrete and detailed game theory model on competitive innovation between companies. It explains definitions, proposition, variables, and functions in a clear way. Very inspiring, but I need to read more times.
However, I wasn’t able to find any dynamic model on evolutionary game theory. In fact, the problem of how should I use evolutionary game theory instead of non-evolutionary game theory hasn’t been resolved yet.
I also read several papers in drop box on the growth, behavior and phonotypical plasticity of snails and crabs, most of which are written by Professor David Smith. These biology papers help me to construct variables and their relations in mind. I made reading notes using hand-writing, and will type up a more conclusive notes once I finished analyzing variables and discussing with professor Gole.
Here is a primitive lists of the major element of games:
General variable: Water temperature; crushing critical constant
Crab: Energy consumed per diet per time; energy gained per diet per time; cutter size; crusher size; population density; Molting function ( probable input: temperature, density of snail or some energy gain function, snail shell thickness. Output: molting time interval, increase of size)
Snails: shell size; shell thickness; upper bound of calcium formation per time; population density; shell thickening function(input: temperature, crab density. Output: shell thickness)
The game theory would probably play a role in molting function and shell thickening function.
Question: A group of related questions comes into my mind when I tried to build the model:
– Professor Smith mentioned in one of his paper that the trade-off of thickening shell and the annually fluctuation of the crabs population density in mid Main helps to explain the importance of phenotypic plasticity, which happens instead of genetic evolution. Would my model eventually helps to demonstrate such opinion?
– Unlike mid and northern Maine, green crabs are constantly prevalent in Massachusetts and Connecticut during warm temperature. Under such condition, is the thickness of snail shell majorly due to phonotypical plasticity or genetic evolution then?
– Is the thickening of crab claw/ snail shell revertible?
Following plan:
- To discuss the variables and try to construct a primitive model with professor Gole. Especially: game theory versus evolutionary game theory; how to define players; in which part to use game theory.
- To finish the 2 readings on model constructing.
- Find another book Evolutionary Games and Equilibrium Selection by Samuelson, which seems easier to understand. Try if I can dig more information and method on evolutionary game theory from this book.
- Answer the above questions.
I would like to attach note books and reading notes, but it seems that I am not allowed to do so…..