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Anonymous committed 571cf65

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

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 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.
 
     
     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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