creativity::belief::Profit Class Reference

This class represents an author's belief about the lifetime profitability of a work. More...

#include <creativity/belief/Profit.hpp>

Public Member Functions
	Profit ()
	Construct a noninformative profit model. More...
template<typename ... Args>
	Profit (Args &&...args)
	Constructs a profit model with the given parameter information. More...
virtual unsigned int	fixedModelSize () const override
	Returns parameters()
double	predict (unsigned int draws, double q, unsigned long previousBooks, unsigned long marketBooks)
	Given a set of model parameters, this returns an expected value \(\Pi_b\), the lifetime profit of the book. More...
std::pair< double, double >	argmaxL (unsigned int draws, const std::function< double(const double &)> q, unsigned long previousBooks, unsigned long marketBooks, double l_min, double l_max)
	Given previousBooks and marketBooks parameters, a function \(q(\ell)\) that returns expected quality for a given value \(\ell\), and \(\ell_{max}\), this numerically determines the value of l in \([0, max_l]\) that maximizes the profit less effort. More...
virtual std::string	display_name () const override
	Returns "Profit", the name of this model.

Static Public Member Functions
static unsigned int	parameters ()
	Returns the number of parameters of this model (4)
static Eigen::RowVectorXd	profitRow (double quality, int previous_books, int avg_market_books)
	Builds an X matrix row of profit data for a book. More...

Detailed Description

This class represents an author's belief about the lifetime profitability of a work.

The model is:

\(\pi_b = \beta_0 + \beta_1 q_b + \beta_2 q_b^2 + \beta_3 marketBooks + u\)

Specifically, the fields above are:

• \(\pi_b\) is the lifetime profits of the book without considering the initial creation effort
• \(q_b\) is the (non-negative) quality of the book.
• \(marketBooks\) is the average number of books on the market in the past creation_time periods (so that it includes one full creation cycle). Ideally we'd want books in the current period can't be used because it is unknown at the time the reader is making the decision of whether or not to create.

Although a \(\beta_3 \leq 0\) restriction would make some intuitive sense (more competition means lower profit), it isn't imposed because doing so induces volatile creation cycles: readers decide to create in low-book periods, which results in an immediate surge in on-market books, which induces readers to not create in the next period, and so on. Not imposing it still often has it be significant for many readers, but seems to avoid the strong behavioural cycles.

The model uses a natural conjugate prior for the purposes of updating the beliefs via Bayesian econometrics.

Constructor & Destructor Documentation

Profit() [1/2]

creativity::belief::Profit::Profit ( )

inline

Construct a noninformative profit model.

See also

eris::learning::BayesianLinear::BayesianLinear

Profit() [2/2]

template<typename ... Args>

creativity::belief::Profit::Profit ( Args &&...  args )

inlineexplicit

Constructs a profit model with the given parameter information.

Parameters

args	prior arguments to forward to the base BayesianLinear constructor.

See also

BayesianLinear::BayesianLinear

Member Function Documentation

argmaxL()

std::pair<double, double> creativity::belief::Profit::argmaxL	(	unsigned int	draws,
		const std::function< double(const double &)>	q,
		unsigned long	previousBooks,
		unsigned long	marketBooks,
		double	l_min,
		double	l_max
	)

Given previousBooks and marketBooks parameters, a function \(q(\ell)\) that returns expected quality for a given value \(\ell\), and \(\ell_{max}\), this numerically determines the value of l in \([0, max_l]\) that maximizes the profit less effort.

Initial fixed creation cost is not included.

Parameters

draws	the number of beta draws to use for prediction
q	A function, lambda or similar object that takes a double and returns the quality associated with that double. If the function returns a negative value, 0 will be substituted instead.
previousBooks	the previous books of the author
marketBooks	the books on the market in the previous period
l_min	the minimum value of l to consider. The value is typically at least the effort level associated with book of quality = MC + distancePenalty(0) + sizePenalty(1): as long as they can observe the quality, no reader would ever buy a book with lower quality. (Note, however, that this assumes readers directly observe the quality and have identical penalty functions).
l_max	the maximum value of l to consider. This is typically the reader's money (income) on hand.

Returns

a pair of double values: the first is the double value \(\ell\) that maximizes expected net profit; the second is the maximized profit value after subtracting the maximizing \(ell\), but before subtracting fixed creation costs.

See also

eris::single_peak_search for the numerical algorithm used.

predict()

double creativity::belief::Profit::predict	(	unsigned int	draws,
		double	q,
		unsigned long	previousBooks,
		unsigned long	marketBooks
	)

Given a set of model parameters, this returns an expected value \(\Pi_b\), the lifetime profit of the book.

Parameters

draws	the number of draws to use for prediction
q	the quality of the book
previousBooks	the number of previous books created by this book's author. This parameter also determines the firstBook dummy (= 1 iff previousBooks == 0).
marketBooks	the number of books on the market last period

profitRow()

static Eigen::RowVectorXd creativity::belief::Profit::profitRow ( double  quality, int  previous_books, int  avg_market_books  )

static

Builds an X matrix row of profit data for a book.

This needs to be called after the period has advanced: typically in the inter-period optimization stage.

This method should only be called in periods \(t=3\) and later (because otherwise the lagged value is not useful: the first books are created in \(t=1\), and so the lagged value will be 0 at the beginning of \(t=2\), thus need to wait until the beginning of \(t=3\)).

Parameters

previous_books	the number of previous books written by the same author
quality	the mean quality of the book as determined at creation time by the book's author. Must be non-negative.
avg_market_books	the average number of books on the market over the previous creation time periods

Returns

a row containing the book's information as used for this model

Inheritance diagram for creativity::belief::Profit:

Collaboration diagram for creativity::belief::Profit:

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The documentation for this class was generated from the following file:

• creativity/belief/Profit.hpp