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machine visualisation

(this post is in a series of evolutionary game stuff, i'll try to weave them together better after all of them has been materialised, for now i'll just write them in messy fragments)

mathematica is a tool that solves specific domain problems, an expensive tool in the toolset that is used for particular purpose. do you have a tool to only cut apples (or round-shape apple-size stone-fruit) in your kitchen? or a banana-only slicer? or an avocado-only slicer? that's mathematica.

(wolfram is a weird person, what you do when you watch his video or read his book is that you discount completely his self introduction and hyper self praise, you go directly to the functional part.)

racket is the plain knife that i use for all purposes. of course no one makes thing that is strictly dominated by another. so things like this coexist for its reasons. (you may try R, python)

mathematica doesnt really matter for grad student at general level because it is expensive, requires background knowledge, costs a lot to learn syntax. but anyway, here is how to draw a horrid all-defection machine for the repeated prisoner dilemma game:

all defection

the best illustration for a machine is its selfie:

i know that it's a horrid selfie, but that's the best i can do in mathematica. first i define the machine as a discrete markov process: (well i dont know other ways, i search on google and they say they draw machines like this)

AllD = DiscreteMarkovProcess[1, {{1}}];

when you type function DiscreteMarkovProcess, mathematica will suggest a help menu -> you click that menu icon (the hamburger icon) and try to read the Details and the Example part.

• in the above sentence, number 1 means it starts with state 1

• {{1}} is the way transition matrix is written in mathematica (if you use wolfram calculator online). this all-defection machine has only one state.

now after defining it, we draw it, this is the simplest working graph of the machine:

AllDPic = Graph[{"D"}, AllD, EdgeLabels -> "C/D"];

if you shift+Enter to execute this line, you kinda understand the syntax right? function Graph will draw the label "D" on the only state of object AllD (previously defined), we add the EdgeLabels as "C/D".

however, it still looks untolerable, i add more details in the Graph function:

AllDPic = Graph[{"D"}, AllD, EdgeLabels -> "C/D",
  VertexStyle -> Pink, VertexSize -> Tiny, GraphStyle -> "Automatic"]

I add VertexStyle, VertexSize, GraphStyle keywords. and tadaa!! the thing about mathematica is that when it's a built-in stuff, it'll suggest a menu icon when you are typing -> you click that menu icon to open help windows and you read the Details and Example part in that pop-up window.

now i search google how to export graph in mathematica:

Export["allD.png", AllDPic]

tit for tat

this is another exapmle for tit for tat:

code:

TitForTat = DiscreteMarkovProcess[1, {{1/2, 1/2}, {1/2, 1/2}}];
TFTPic = Graph[{"C", "D"}, TitForTat,
   VertexStyle -> Pink, VertexSize -> Medium,
   GraphStyle -> "Automatic"];
Export["tft.png", TFTPic]

well this time i use the same value Tiny for keyword VertexSize but it turns out real tiny so i use Medium and it works, the shape is magically circle again. please dont ask me why there is no EdgeLabels keyword.