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tidy up documentation

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# File docs/dan.pdf

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# File docs/dan.tex

 but the culture vector is visible to other agents only by its effects on productivity.

 $c_j$ is binary, of length, say, $8$.
-$b_j$ is chosen uniformly from the interval [0,1],
+$b_j$ is scalar, chosen uniformly from the interval $[0,1]$,
 and the elements of $c_k$ are chosen by i.i.d. fair coin-toss from $\{0,1\}$.

 There is a fixed finite market whose per-turn returns are fixed at unity.

 Each firm, $F_k$ is associated with a set $W_k(t)$ of workers at each timestep $t$,
 which partition the workforce, i.e. each worker has at most one employer.
-It pays each worker a wage $\omega_j(t)$, determined by means that will be
+Each firm pays each worker a wage $\omega_j(t)$, determined by means that will be
 expanded momentarily.
 We denote by $f(n, t)$ the index of the firm whose
 worker set contains $w_n$ at time $t$.
-(We sometimes omit the $t$ parameter in
-this function, and the $t$ parameters in series variables, when the timestep
-may be assumed from context.)
+(We sometimes omit the $t$ parameter in this function, and the $t$ parameters in series variables,
+when the timestep may be assumed from context.)

 Workers are initially assigned to firms at random with zero wages.


 $R_k = \frac{E_k}{\sum_m E_m}$

-Firm profit, $P^k$ is given $P^k=R_k-\sum_{j \in W_k} \omega_j(t)$ - that is,
+Firm profit, $P_k(t)$ is given $P_k(t)=R_k(t)-\sum_{j \in W_k} \omega_j(t)$ - that is,
 the profitability is income minus expenses, where expenses are assumed to be
 comprised only of worker wages.

 Firm funds, $\Phi_k$, are given
 $\Phi_k(t) = \sum_{i=1}^t P_k(t) + \Phi_k(0)$ for $\Phi_k(0)$ the startup capital.

-When a firm has no funds it may not spend any money. It could optionally
-be replaced by a new firm with different hiring rules. This is not yet
-implemented.
+When a firm has no funds it may not spend any money.
+It could optionally be replaced by a new firm with different hiring rules.
+This is not yet implemented.

-Now we stipulate the performance of firms. Let $n_k=|W_k|$, i.e. the number of
-agents employed by firm $F_k$.
+Now we stipulate the performance of firms.
+Let $n_k=|W_k|$, i.e. the number of agents employed by firm $F_k$.

-Then we calculate the performance of a firm $k$ by
+We calculate the performance of a firm $k$ by
 \footnote{
 or if you wanted, you might raise these factors to an arbitrary power because you have
 reason to suppose as a kind of nonlinear scaling.
 }
 $E_k=B_kC_kn_k$

-Now, we need to define the culture multiplier $C_i^k$.
+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 stacked (horizontal) culture vectors of the agents
 employed at that firm.
-Then we calculate a culture factor from the column
-means.
+Then we calculate a culture factor from the column means.

 \begin{align*}
 C_k(t) &= 0, & n_k=0 \\

 $d(x) := 2 |x - 1/2|$

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

 Will come back to that.

 In any case, I'm still nutting out the precise form for it.
-Basically, if the
-employment at firms over time remains similar, the difference in culture
+Basically, if the employment at firms over time remains similar, the difference in culture
 matrices and hence value of given workers between them might be sufficiently
 well approximated by this to improve bidding performance.
-I'm thinking of
-taking the means in the log domain so that they decay naturally to 1 in the
+I'm thinking of taking the means in the log domain so that they decay naturally to 1 in the
 absence of new data points.

 \end{document}