0
$\begingroup$

I'll write an introduction. This problem came to me while I was doing an experiment with the prisoners dilemma. I'm codifing the agents behavior in genes (I want to measure the correlation between the "stability/peace" of the system and many characteristics of the agents.

But there are three characteristics that are the most important in my experiment:

  • Memory capacity (how many past games can remember the agents). Every "memory slot" represents a variable in the polinomial (which can be 0 or 1).
  • Recognition of other individuals (another form of memory capacity). In case there are recognition of individuals, every game we associate a new variable to every memory slot to indicate if the current adversary was the adversary in the past game associated with the memory slot. Evidently, the values are again 0 or 1.
  • "Cognitive sofistication": This is... the grade of the polynomial. Yes, this is not a good representation of cognitive sofistication, but it's better than nothing. In any case, I prefer polynomials over boolean operators because the "mutations" can be smoother, I can capture more complex behaviors and I can work with probabilistic values.

Then, the problem:

It's possible to find the characterization of n-grade, m-variables polynomials $P$ over $\mathbb{R}$, with $P(x_1,\ldots,x_m)\in [0,1]$ if $\forall x_i \in [0,1]$ ?

Thanks in advance :) .

  • 0
    I've chose$n$ polynomials because I can simulate boolean operators using the real algebra. But with the possibility of non strict decisions (more human than a deterministic mechanism). Also, the mutations in the genes induce smoother changes in behavior than if I were using boolean operators).2012-10-13

0 Answers 0