# Commits

committed 571cf65

make the culture and knowledge vectors symmetric for ease of re-scaling

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• Parent commits fdb0c17

# File docs/dan.pdf

Binary file modified.

# File docs/dan.tex

 be replaced by a new firm with different hiring rules. This is not yet
 implemented.

-Let performance of a firm $k$ be given
+Now we stipulate the performance of firms. Let $n^k=|W^k|$, i.e. the number of agents employed by firm $F^k$.

-$E^k=B^kC^k$
+Then we calculate the performance of a firm $k$ by
+
+$E^k=B^kC^kn^k$

 or if you want to raise these factors to an arbitrary power because you have
 reason to suppose some kind of nonlinear scaling.

-$R_k=(B^k)^g(C^k)^h$
+$R_k=(B^k)^g(C^k)^h n^k$

 You could even enforce
 $g+h=1$
-and make this a weighted geometric mean, if you'd like.
+and make this a weighted geometric mean, if you'd like. Since $B^k$ and $C^k$ have both been specified to have range between 0 and 1, this allows a pleasing symmetry.

-For now, I presume, to the contrary, that $g = h = 1$.
+For now, I presume, to the contrary, that $g = h = 1$, as it simplifies creating estimates of the marginal benefit of a given agent with a given knowledge factor.

 Now, we need to define the culture multiplier
 $C_i^k$. We associate a matrix $\kappa^k$ with each firm at each time step,
 comprised of the vertically stacked horizontal culture vectors of the agents
 employed at that firm. Then we calculate a culture factor from the column
-means. Let $n^k=|W^k|$, i.e. the number of agents employed by firm $F^k$.
+means.

 \begin{align*}
 C_i^k &= 0, & n^k=0 \\

 In general, asymmetric functions might be useful too.

-We give the knowledge multiplier more simply:
+We give the knowledge multiplier more simply as the mean of the vector of all employee knowledge values.

-$B_k=\sum_j b_j$
+$B_k=\frac{1}{|W_k|}\sum_j b_j$

 Workers are assigned, each turn, a canonical'' performance measure
 $p_i^j$, based on a share of their firm's market distribution, attributed
 imputes a mean valuation coefficient to all pairwise changes in employment.

 Symbolically we write
-$v(f^k, w^j, i+1) := V_{f(j,i),F^k}p_i^k$
+$v(f^k, w^j, i+1) := V_{f(j,i),F^k}p_i^k$

 where $V_{x,y}$ is a matrix of these pairwise firm coefficients.


# File src/fns.py


     for firm in world.firms:
         firm.competitiveness = (
-            (1.0 + firm_culture_fn(firm, params)) ** params.culture_exponent *
-            firm_knowledge_fn(firm, params) ** params.knowledge_exponent
+            firm_culture_fn(firm, params) ** params.culture_exponent *
+            firm_knowledge_fn(firm, params) ** params.knowledge_exponent *
+            len(firm.workers)
         )

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