adiwajshing / cs2378-final

CS 2378 Final Project

Simulating the gross revenue generated by a collective of entities, given the copyright term were X years.

An explanation of the simulation

Note: the variable names mentioned in the brackets are the corresponding names in the variables.json document

• $y =$ the number of years since the start of the simulation, and $Y=$ years of simulation (simulationYears)
• $E =$ number of entities in the simulation (contentProducingEntities).
• $P_{avg}$ is the average profitability of a copyrighted work
• $C =$ the copyright term in years (copyrightTerm)
• $R_v() \in {0,1}$ is a random value generating function (Math.random)

Pure revenue generated of work = $R_w(y)$

Is modelled using a gaussian bell curve. $R_w(y) = floor( m_w e^{-\frac{(y - p_w)^2}{2m_w^2}} )$

$p_w$ is the year of peak profitability of this work

• Let $Y_{max}$ be the max years it takes for a work to be profitable (maxYearsTillMaxProfitability).
• It is computed as $p_l = { 3R_v()\ \ if R_v() < 0.5 \ \ else \ \ Y_{max}R_v() }$

$m_w$ is the profit generated in the most profitable year

• Let $d_w$ be the derivative value of the work.
  • i.e. if the work is original, $d_w = 0$
  • If the work was derived from an (public domain) original work, $d_w = 1$
  • Else, $d_w = d_{w2} + 1$ (derivative value of the work it is derived from + 1)
• $D_f$ is the derivative factor (derivativeFactor). It models how does being a derivative work affect revenue generated from the newly generated work.
• It is modelled as $m_w = (R_v() + 0.5 + d_w*0.1)0.5P_{avg}$

Loss due to piracy

Is modelled as a product of already existing revenue $R(y)$ and $C$ with a multiplying factor $p_l$ (piracyMultiplier)

Loss due to piracy in any given year ($y$) = $L_w(y) = \sigma(({\sum}_{i=1}^{y-1} R_w(i)) * C * p_l)$

• The sigmoid function is used to limit the range to (0,1)

Revenue of a work, adjusted for piracy

$S_w(y) = R_w(i) * (1 - L_w(i))$

Total revenue generated by an entity = $R_e(y)$

$R_e(y) =$ total revenue generated by an entity $e$ till year $y$

Max Works possibly generated by an entity = $M_w(e, y)$

$M(e)$ is the initial work production capacity.

• $S$ is a constant describing the max works any entity can produce at any given point in Time (maxWorksPerEntity).
• $I$ is the inequality factor $\in {0,1}$ (initialInequality). 0 means a fully equal design, all entities can produce the same amount of work from the very start.
• It is modelled as $M(e) = ceil( e^{(x/S)I + 1} ) * S$

Now, $M_w(e, y) = R_e(y-1)*0.01 + M(e)$

Probability of generating a new work in a given year = $P_g(e, y)$

• $W$ is work generating constant. Higher the value, more the content produced in a year.
• $P(y) =$ set of all publicly available content in year $y$
• $W_p$ is public work "inspiration" constant. Lower the value, more the content produced via public domain content in a year
• $P_g(e, y) =$
  • $0 \ \ if |W(e)| >= M_w(e, y)$ (limit number of works that can be copyrighted by an entity at any given time)
  • $1 \ \ if \ \ R_v() < W * max(R_e(y-1), 10)$
  • $1 \ \ if \ \ R_v() < \frac{|P(y)|}{W_p}$
  • $0 \ \ otherwise$

Gross revenue generated ($LR$)

$LR =$

• Initialize $LR = 0$
• Initialize $W_e(1) ={}$. (No works in the first year)
• $for \ \ y \ \ in \ \ {1,Y}$
  • $for \ \ e \ \ in \ \ {1,E}$:
  • $if \ \ P_g(e, y) = 1$:
  • $W_e(y) = W_e(y-1) + W()$ (add a new copyrighted work for this entity)
  • $LR += {\sum}_w^{W_e(y)}R_w(y)$
  • $for \ \ w \ \ in \ \ {1,W}$:
    • if $y - C_r(w) > C$: (if copyright term expired)
    • $P(y) = P(y) + w$ (make public work)
    • $W_e(y) -= w$ (remove as copyrighted work)