Risk sensitive scheduling strategies of production studios on the US movie market: An agent-based simulation

Bertolotti, Francesco; Roman, Sabin

doi:10.3233/ia-210123

Cited by 6 publications

(6 citation statements)

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“…The social sciences also offer numerous examples of power law distributions [ 44 ] that naturally evolve in time (but whose time dependence has not necessarily been quantified), such as the range of time between two deaths in serial killers’ behavioural patterns [ 45 ], in narrative structure [ 46 ] or in the budget distribution of movies [ 47 ]. In economics, they mainly derive from aggregation and rich-get-richer processes.…”

Section: Discussionmentioning

confidence: 99%

A master equation for power laws

Roman

Bertolotti²

2022

R. Soc. open sci.

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We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker–Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson’s Law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value. In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log–log plots in the frequency and rank distributions.

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Section: Discussionmentioning

confidence: 99%

A master equation for power laws

Roman

Bertolotti²

2022

R. Soc. open sci.

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“…The social sciences also offer numerous examples of power laws distributions [38] that naturally evolve in time (but whose time dependence has not necessarily been quantified), such as the range of time between two deaths in serial killers' behavioural patterns [39], in narrative structure [40] or in the budget distribution of movies [41]. In economics, they mainly derive from aggregation and rich-get-richer processes.…”

Section: Discussionmentioning

confidence: 99%

A Master Equation for Power Laws

Roman¹,

Bertolotti²

2022

Preprint

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We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power laws that describes how the number of cascades changes over time (cascades are consecutive transitions that end when the initial state is reached). The partial differential equation has a closed form solution which gives an explicit dependence of the number of cascades on their size and on time. Furthermore, the power law solution has a natural cut-off, a feature often seen in empirical data. This is due to the finite size a cascade can have in a finite time horizon. The derivation of the equation provides a justification for an exponent equal to 2, which agrees well with several empirical distributions, including Richardson's law on the size and frequency of deadly conflicts. Nevertheless, the equation can be solved for any exponent value.In addition, we propose an urn model where the number of consecutive ball extractions follows a power law. In all cases, the power law is manifest over the entire range of cascade sizes, as shown through log-log plots in the frequency and rank distributions.

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“…The third paper of the special issue extends [1] and discusses the risk sensitive scheduling strategies of production studios on the US movie market exploiting agent-based simulation. In particular the paper analyses the time series of the number of movies on release each week and the box office results of the top 10 ranking movies (ranked for box office) on the US movie market highlighting that are in counterphase and repeatedly intersect with a seasonal trend.…”

Section: About This Special Issuementioning

confidence: 99%