evolutionary game Q&A
i want to write this for some reasons (i started long time ago but couldnt progress to finish because i fucked up. but i discover that from now on i have this unit test: if i'm unable to articulate stuff in a blog post, i dont understand it):
for the sake of clarification to the ones who wasnt able to refute me when i was narrow in scope.
the main purpose is for ones who ask: what do you study to do evolutionary game and simulation and stuff. i write this as an insufficient answer[1].
btw hopefully create a side-effect: lure students that doing this is fun, which it is, 5% of the time, statistically significant
[1] the problem with insufficient and narrow encounter is that it makes you cling on with deep and isolated idea and think that it's all there is. a wrong model itself is not harmful, but a wrong model in isolation without constant update and fixing bugs can cause quite much systematic trouble.
1. small talks
neither cooperative game theory nor noncooperative game theory will go away. they live to validate the existence of each other. it's like 2 sides: some situation assumes that moral is to be taken for granted and some others believe that moral traits has functional and evolutionary explanation.
saying about dividing the pie, in the realm of what should be, nash's barganining solution is the ultimate of what-should-be. you want perfect world, the solution he proposes is invariant to everything, you want no-discrimimation, it is under the veil of ignorance blah blah..
in the parallel school of what really happens, nash defines an equilibrium based on best response regarding to own interest. if it's in our interest to do anything, we do it. the result may be perceived to be sweet and touching as we love each other we trust this world... it doesnt really matter. after the result materialises, observers can decorate it with fancy moral subjectively whatever they want. we believe in trust in love in righteousness in the color of the bright eyes of each other whatever.. but if we push the rationale to the core of it, the drive of the action is singlehandedly to our own interest, strictly speaking, to our best interest. based on our own belief of the world.
(there is a dangerous temptation to interpret after maths manipulation. the result is the maths result, making it sound culturally relevant may get sympathy from readers but try to keep in mind that it isnt necessarily to be that. )
back to NE, nash equilibrium is always right, it is right by definition. it's a self-fulfilling prophecy. and it is very broad concept because it bases only on belief, not necessarily on what's real. if the expectation converges in equilibrium + the action is consistent in equilibrium, then what wasnt real before becomes real now. pause at that to feel the profound. what wasnt justified before becomes justified now and only now (in equilibrium), as everything (expectation and action) converges neatly.
(i doubt if i understand correctly Wittgenstein says language doesnt have exogenous meaning, its meaning is created endogenously IN the equiblibrium, not out of it. first time people said languages define our world, restrict our imagination, restrain our thought, i was quite surprised. how is that even possible, language is a tool and a tool isnt supposed to have that much power on our mind. i mean it can affect to some extent but i never thought it can dictate what we are. but it does.)
anyway, back to NE, the inherent issue is that concept is a bit too large in general. certainly it is. i never see common sense that is strict. common sense needs to be general and flexible enough to be interpreted with common sense in a large number of cases. hence, many giants have tried to develop stricter concept of equilibrium, mostly founded on nash equilibrium. NE concept is so fundamental it is like the unit test for any kind of equilibrium concept you would like to build.
the essence of these refinements is usually to test the robustness of the NE with some criterion. it's like you let the NEs under push and pull to see how tough it is. different refinements are trembling hands while you pick strategy, pertube payoff, proper mistake... evolutionary stable and stochastic.. jargons blah blah..
[skip a big part of explaining refinement concepts and stuff]
[skip because i dont fully grasp it, maybe i give it a try next time]
the thing about these refinements is that they are created by giants. so they inherit the mega-rationality from their creators. these nobel laureates & colleagues create mega-rationality assumption for their players plus infinite recursive thinking of common knowledge! so of course people rebel. successful spin offs are behavioral, experimental, neuro-economics, psychological economics.. people have different toys and there is no way mega-theorists can get all the fun.
2. fun times
Maynard Smith (biologist?) brings in evolution concept in game theory (not-surprising, Nash mentioned this idea too). the good thing about this refinement is that it doesnt even need the slightest assumption of rationality but it still narrows down the NE set significantly, in some case achieving the same rationality amount as other refinements, in some case even more strict.
first let's set this baby-step convention, we call players in game, and we call agents in population of simulation. (i read this in a paper and cant let go).
until this point i seriously think that this post unfolds to be a series. to my best hope, this can be useful for my thesis because i fucked up so bad i havent even written a single word of it yet!!!
so my plan is let run some simulations of 2x2 repeated games for fun. and in the process, hopefully i can deliver the illustration of these following concepts:
replicator dynamics (which is basically a vector field, describing law of motion)
agents and their spectrum of sophistication
code the machines[2]
the survival of fittest mechanism (let run prisoner dilemma)
the round-robin mechanism (let run hawk-dove game)
[2]: i embrace the narrow set of machines: deterministic (when they move, they move pure strategy, not mixed) and not even stochastic, so we can cover them all =))
hope you dont mind the future that one day, you look at 0 0 0 1 0 and you yell out happily: TWEEDLE DEE!!!