How to perfectly discriminate in a crowd?

How to perfectly discriminate in a crowd A theoretical model of crowdfunding.

Wojciech Hardy

Group for Research in APplied Economics

So what is this crowdfunding I keep hearing about

„Crowdfunding is asking a crowd of people to donate a defined amount of money for a specific cause or project in exchange for

various rewards.”

- dailycrowdsource.com

various rewards.”

Previous models and my model

1. Previous theoretical models – Two stages – crowdfunding & regular sale (Belleflamme et al. 2012, Nocke

et al. 2011)

– Public good with private gifts (Varian 2013)

Complete discrimination according to Png (2002): Marginal benefit = Marginal cost

Previous models and my model

1. Previous theoretical models – Two stages – crowdfunding & regular sale (Belleflamme et al. 2012, Nocke

et al. 2011)

– Public good with private gifts (Varian 2013)

Complete discrimination according to Png (2002): Marginal benefit = Marginal cost

2. My model? – Baseline: enhancable public good, two stages (strategy planning and

crowdfunding), homogenoeus contributors.

– Simple framework with multitude of crowdfunding-related extensions.

My model: the basics - contributor

1. Consider an enhancable public good that you have to contribute anything to, to use it.

𝑈𝑐 = 𝑉𝐺 − 𝐶𝑐

2. Let the cost be subjective and related to both price and income.

𝐶𝑐 = 𝑃𝑐 ∗𝑃𝑐𝑀𝑐

3. The general value depends on the total contributions, the base value, the fixed threshold, and the rewarding scheme.

𝑉𝐺 = 𝛿 𝑃𝑖𝑁𝑖=1

𝑇∗ 𝑣0

My model: the basics

𝑼𝒄 = 𝜹 𝑷𝒊𝑵𝒊=𝟏

𝑻∗ 𝒗𝟎 − 𝑷𝒄 ∙

𝑷𝒄𝑴𝒄

𝑼𝒄 – utility of contributor c,

𝜹 – incentive parameter,

𝑵 – number of contributors,

𝑷𝒊 – price paid by contributor i,

𝑻 – fixed threshold,

𝒗𝟎 – base value of the product,

𝑴𝒄 – disposable income of contributor c.

Producer’s profit:

𝝅 = 𝑃𝑖

𝑖=1

− 𝛿 𝑃𝑖

𝑖=1

Homogeneity and two stages – simple case

Utility of homogeneous contributors:

𝑈𝑐 = −1

𝑀∗ 𝑃2 + 𝛿

𝑁𝑣0𝑇𝑃

And their optimal offer:

𝑃∗ = 𝛿𝑀𝑁𝑣02𝑇

Main extensions

Heterogeneous contributors (varying income). Producer now acts upon his expectations.

The contributors pay accordingly with their income.

Individual incentives of the 𝛿𝐼𝑃𝑐 form. Conclusions remain similar.

𝛿𝐺 is more important than 𝛿𝐼 mainly with the increasing N .

Participation incentive. Shifts the utility curve up, gives a boost to the contributions.

No production below the threshold. Producer faces 3 scenarios: A) Failure – no one contributes.

B) Overwhelming Success – contributions exceed the threshold.

C) Moderate Success – the contributions just reach the threshold.

Other considerations and future ideas

Pirates in crowdfunding. May contribute tiny amounts (even if to later download).

May contribute for the product to be there at all.

Different goal: reaching the threshold. The crowdfunding could result in losses.

Uncertainty (about M, and/or N). Risk-attitude (probability of reaching T versus maximizing

expected profit).

Uncertainty (about M, and/or N). Risk-attitude (probability of reaching T versus maximizing

expected profit).

Infinite stages in a finite period. Each new entrant faces an equilibrium.

His entrance shifts the contributions higher.

The crucial moment occurs at the end.

And so perfect discrimination is achieved!

To conclude:

Crowdfunding allows for self-imposed

complete discrimination:

Marginal benefit = Marginal cost.

Other implications follow: The incentives’ effect.

Pirates inclusion in the payments.

Dynamics of crowdfunding.

Producer’s strategy, based on the contributors’ base.

Thank you for your attention! Author: Wojciech Hardy, University of Warsaw e-mail: [email protected]

More about our research on

http://grape.uw.edu.pl

Twitter: @GrapeUW

How to perfectly discriminate in a crowd?

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