1. Introduction
Crowdfunding is a form of fundraising whereby groups of people pool money, typically (very) small individual contributions, to support a particular goal (
Ahlers et al. (
2015)). It is usually performed online. There are different types of crowdfunding. Our focus in this paper is on reward-based crowdfunding,
1 where investors count on some extra-benefits from the company such as future product discounts. Reward-based crowdfunding campaigns are commonly offered in one of two models. The ”All-Or-Nothing” (AON) model involves establishing a fundraising goal. If the goal is not achieved, the money are returned to investors/funders. The ”Keep-It-All” (KIA) model assumes keeping the entire amount raised unconditionally.
The two largest crowdfunding platforms are Kickstarter and Indiegogo. Kickstarter follows an AON model. Since its creation in 2008, it hosted 473,941 campaigns, among which 176,497 successfully funded for a total amount raised of more than
$4.5 billion.
2 Indiegogo is the second largest crowdfunding platform. It hosted more than 800,000 campaigns, among which about 9% successfully funded for a total amount raised of more than
$1.6 billion (
Smith (
2020)
3). On Indiegogo entrepreneurs can choose between a KIA model and an AON model. The platforms charge fees that can range from 3% to 9% of the volume of funds raised.
Compared to Kickstarter, Indiegogo is a more open platform that can be used by any company for any product.
4 It launched several strategic projects in 2017–2018 helping crowdfunding firms develop their business after a campaign. For example, it introduced Indiegogo Marketplace/InDemand where firms sell their products initially financed through crowdfunding and compete against other firms which may not have necessarily used crowdfunding to launch their products (
Schleifer (
2017);
Rear (
2018)). In a similar spirit, both Kickstarter and Indiegogo have teamed up with Amazon to create an Amazon Launchpad project. It makes it easy for startups to launch, market, and distribute their products to millions of Amazon customers around the globe. The program offers a number of services for entrepreneurs such as custom product pages and comprehensive marketing packages. It helps firms overcome many of the problems associated with starting new businesses. Both Marketplace and Amazon Launchpad help creating an environment where firms that have used crowdfunding compete against firms that have not. Among other examples note that Australian farmers seem to have started using crowdfunding to improve traditional market structures like duopolies which are often the case (
Askew (
2016)).
Several interesting features of the previously discussed trends seem to have emerged. First, platform fees related to the projects described above are relatively high. For example, Indiegogo takes 10%-15% of every sale made through Marketplace (
Mogg (
2017)). Secondly, launching a crowdfunding campaign prior to spot sales has become a part of the strategy for not only “unknown” start-up firms but also for established, reputable firms. David Mandelbrot, CEO of Indiegogo, said the following (
Takahashi (
2018)): “The other trend we’re seeing is more and more companies using Indiegogo as a way to engage with their audience early. In the last year we’ve had campaigns from companies like Procter and Gamble, Honeywell, and Bose. They’re big, public companies...but they’re using Indiegogo to validate the products coming out of their... divisions and launch those products to an audience they can engage with directly.”
Moreover one can now see cases where products offered by firms who used InDemand or AmazonLaunchpad and had crowdfunding experience previously seem to have a higher quality compared to firms that did not use either. For example the company Prynt, founded in 2014, raised more than
$1.5 million from more than 9000 backers on Kickstarter before launching the The Prynt Case on Amazon Launchpad, with customers already purchasing enough cases and photo packs to print more than 120,000 instant photos.
5 Prior to launching their crowdfunding campaign, its founders had a good level of belief in the high potential of their product. After showing off their product in early 2016 at the Consumer Electronics Show in Las Vegas, Prynt had a couple of notable write-ups under their belt. “...a [Kickstarter] campaign requires a lot of anticipation and dedication...,” said Clément Perrot, CEO and Co-Founder of Prynt (
Cunningham (
2016)). He also said that before you hit the launch button, you have to be ready with updates, posts, pictures and images. Shortly after their crowdfunding campaign, an independent author covering innovations mentioned: ”...there are a whole slew of services that let you order prints right from your smartphone with incredible ease and equally incredible quality. There are even apps that channel the wind-and-click days of only getting one shot without any edits. However, compared to Prynt, those innovations start to look like novelty gimmicks.” (
Cunningham (
2016)). Furthermore it seems like on Amazon the ratings, prices and customer feedback of Prynt are relatively high, and higher for example than that those of firms that did not use crowdfunding.
6 “Participating in the Amazon Launchpad program has been wonderful—from their awesome team to all of the resources they make easily available to startups,” Perrot said in another interview.
7 “The marketing support in particular is huge in helping us stand out, and our sales have been excellent. It’s great to know that we have a team at Amazon focused on making sure our product is a success!” Recently an expert company specializing in rankings on portable printer named Prynt as the best printer in the iPhone category: “...we’ve chosen to highlight the iPhone-only Prynt Pocket due to its novel and highly-portable design that sets it apart from most other smartphone printers out there...” (
Hesse (
2019)).
One should also mention the Kickstarter Collection project related to Amazon Launchpad. It features products and projects that had successful crowdfunding experiences with Kickstarter and are now available for purchase on Amazon.com. “...Working with Kickstarter is a great way for us to hear directly from customers what products they care about, since they truly hold the power to bring these products to life...,” said Jim Adkins, Vice President of Amazon.
8 Companies in the Kickstarter Collection include Piper, Zivix, MudWatt and the above mentioned Prynt among others. Most of these companies are very successful. Note for example Piper’s award winning product “The Piper Computer Kit”.
9In our model, a firm decides whether to use crowdfunding for the pre-sale stage or just use spot price sales. The crowdfunding campaign has the following features: (1) no arbitrage condition; in equilibrium, the crowdfunding pre-sale price and the spot price are equal; (2) the firm provides rewards to funders; (3) the crowdfunding decision is publicly observable.
10 We first demonstrate that in a monopoly setting, without making any additional assumptions such as community benefits to funders, crowdfunding is never used and firms prefer to just use the spot market since crowdfunding involves a cost in the form of rewards. Then we consider a duopoly. When information between firms is symmetric a situation where both duopolists do not use crowdfunding, and only use the spot market, is not an equilibrium because each firm has an incentive to deviate and use a crowdfunding campaign prior to its spot sales. Early commitment of a firm increases its production, makes the product price lower and forces the other firm out of its optimal quantity. When information between firms is asymmetric, we find that the only signalling equilibrium that exists is when high-quality (high demand) firms are likely to chose reward-based crowdfunding strategically as a signal of quality. Low-quality firms are less likely to mimic high-quality firms (by chosing crowdfunding), as this would imply an additional cost related to rewards, and prefer spot sales exclusively instead. On the other hand an equilibrium where low-quality firms select crowdfunding and high-quality firms do not does not exist. If the uninformed competitor perceives the firm that uses a crowdfunding campaign as a low-quality/low-demand firm, it will be pessimistic about the price and will concede the market. A high-quality firm can benefit from this situation by mimicking the strategy of low-quality firms during the crowdfunding stage. The existence and uniqueness of the signalling equilibrium allows us to generate empirical predictions about the connections between crowdfunding and firm quality/demand.
The model provides several implications that have not yet been tested e.g., firms can use crowdfunding strategically to signal a high level of demand for their products; (reward-based) crowdfunding is procyclical; a higher platform fee may lead to higher firm profits in equilibrium; competition increases the chances of using crowdfunding compared to the monopoly case; a non-monotonic relationship exists between the risk of crowdfunding campaign failure and firm profit.
The rest of the paper is organized as follows.
Section 2 presents the review of related lietarture.
Section 3 presents the basic model and some preliminary analysis.
Section 4 analyzes a model with competition.
Section 5 provides the main results of the duopoly analysis under asymmetric information.
Section 6 summarizes the model’s results and predictions.
Section 7 discusses the model’s robustness and its potential extensions and
Section 8 provides a conclusion to the study.
2. Literature Review
Petruzzelli et al. (
2019) identify five aspects of research on crowdfunding: platform, backers, campaign, entrepreneurs and outcome. In ”campaign” area they point out the importance of the problem of choosing the right campaign type. Similarly,
Miglo and Miglo (
2019) mentioned that the literature on crowdfunding still lacks a full understanding of how entrepreneurs choose between different types of crowdfunding and how they decide whether to use crowdfunding or other types of financing. Among papers in this area note the following.
Belleflamme et al. (
2014) compare reward-based and equity-based crowdfunding. As the authors mentioned, further research is required.
Miglo and Miglo (
2019) consider the choice between the different types of crowdfunding and traditional financing under different types of market imperfections.
Fairchild et al. (
2017) analyze an entrepreneur’s choice between venture capital financing and crowdfunding in order to finance a new innovative start-up.
Petruzzelli et al. (
2019) suggest several propostions regarding the choice between sustainability-driven crowdfunding campaigns (mostly donations-based crowdfunding) and commercial-based campaigns.
In the present paper we analyze the choice between crowdfunding and spot sales, which has not been analyzed previously.
Some papers analyze links between the crowdfunding campaign and the aspects of firm activity beyond the campaign itself. One line of research looks at this connection from funders/backers point of view. For example,
Gleasure and Feller (
2016) suggest a “pay-to-partcipate” concept. This concept describes a desire to be part of the community responsible for some project. Similarly,
Gerber et al. (
2012) noted backers’ desires to “engage and contribute to a trusting and creative community”.
Beaulieu et al. (
2015) suggest that crowdfunding is a form of relationship building because of a desire to construct shared meaning.
Zvilichovsky et al. (
2013) noted the reciprocal social capital created by this relationship.
Gambardella (
2012) suggest that in general investors may wish to participate because they wish to learn new knowledge or skills and enjoy the opportunity to observe a project unfold. In a similar spirit the concept of erosion of organisations’ financial boundaries focuses on funders’ expectations to access firm records, digital resources, and other valuable information.
Gambardella (
2012) provide some examples related to this concept (see also
Kuo and Gerber (
2012);
Frydrych et al. (
2014);
Mollick (
2014);
Gleasure (
2015) and
Chaney (
2019)).
A connected line of research looks at links between crowdfunding campaign and “after-campaign” scenarios from the firm/entrepreneur point of view. For example
Cumming et al. (
2019) point to the importance of determining success chances of firm projects beyond the crowdfunding campaign success.
Mollick (
2014) reports that 75% of projects successfully funded on Kickstarter deliver late.
Cumming et al. (
2019) suggest that one might expect that this percentage varies according to the fundraising model (KIA versus AON) used during the campaign, since the latter is related to the amount raised. Projects that are started with sufficient funds are more likely to produce the promised product and eventually deliver on time, something that is worthwhile investigating in future research.
Belleflamme et al. (
2014) argued that crowdfunding allowed a form of price discrimination between pre-ordering consumers (crowdfunders) and other consumers that could mitigate risk and up-front costs, provided fundraising did not exceed the threshold at which it cannibalises post-production sales. Similar observations were made by authors such as
Singer et al. (
2011);
Gerber et al. (
2012); and
Sung-Min (
2012), who highlighted the benefits of crowdfunding in allowing creators to engage with potential users earlier in development during a fund-seeking campaign, such as additional opportunities for feedback and experimentation.
Our paper mostly contributes to crowdfunding literature from the previous paragrapth namely by looking at the benefits of crowdfunding for a production and spot sales following a crowdfunding campaign from an entrepreneur’s point of view. For example, we highlight the strategic role of crowdfunding as a marketing tool and a signalling device for a firm when it competes against other firms and how the usage of crowdfunding shapes the outcome of a competition between rivals not only in crowdfunding itself but in production and spot sales of products in an “after-campaign” state.
Some papers analyze the role of information in crowdfunding. One line of research focuses on the role of asymmetric information between founders and funders. Although most researchers agree that crowdfunding can play an important role in markets with asymmetric information (see, among others,
Ahlers et al. (
2015);
Kleinert et al. (
2020);
Hildebrand et al. (
2016);
Vismara (
2018a) and
Vismara (
2018b), researchers often disagree on the exact nature of this role, e.g., what type of crowdfunding can be used as a signal of a firm’s quality, what signals are sent to potential investors if a firm selects crowdfunding instead of the other types of financing etc.
Belleflamme et al. (
2014) argue that the value of equity-based crowdfunding can be higher under asymmetric information than under symmetric information.
Miglo and Miglo (
2019) consider the choice between reward-based crowdfunding and equity-based crowdfunding and find that high-quality firms prefer reward-based crowdfunding and use it as a signal of quality.
Chakraborty and Swinney (
2019) consider a crowdfunding model where product quality is known to the entrepreneur but not to some contributors. They find that a larger campaign target can be used by high-quality firms as a signalling device. At the same time,
Miglo and Miglo (
2019) find that the relationship between a firm’s quality and the campaign goal is non-linear. More specifically they argue that the threshold should be neither very low nor very high. To some extent it is consistent with the spirit of the results of some papers in that higher targets do not necessarily signal a higher quality. For example,
Mollick (
2014) and
Cordova and Dolci (
2015) find that setting higher thresholds does not lead to higher campaign success rates.
Another line of literature looks at the aspects of funders behaviour in terms of monitoring and collecting information about the campaign.
Burtch et al. (
2013) suggest that crowdfunding participants pay attention to information and information plays a strategic role in crowdfunding.
Agrawal et al. (
2015) analyze what types of funders pay more attention to previous information in crowdfunding.
In this paper the analyze the role of imperfect information in a competitive environment with crowdfunding, which is a new direction in this line of research.
Finally note that when talking about crowdfunding the media and internet usually provide examples of firms that use it for funding extremely innovative and often very sophisticated Apple-esque
11 products (see, for example,
Kumar et al. (
2015)). Examples include 3D-printers, electric cars, smart watches etc. In this case firms retain monopoly power during the development stage and sale of the project (see
Santos (
2017) among others). Less attention is paid to companies that use crowdfunding for financing more traditional products and services such as handbags, perfumes, toys etc.
12 In this case the level of competition with producers of similar products increases. Theoretical research on crowdfunding has generally followed this trend and has mostly assumed that crowdfunding is used under monopoly conditions (see, for example,
Belleflamme et al. (
2014);
Chang (
2016);
Strausz (
2017);
Chemla and Tinn (
2019) or
Miglo and Miglo (
2019)). However, much less is known about the role of crowdfunding in explaining the behaviour of entrepreneurs operating in competitive markets including cases when entrepreneurs who use crowdfunding compete against entrepreneurs who do not. In this article we compare the role and the importance of crowdfunding in a competitve environment and in the monopoly case.
3. Crowdfunding and Monopoly
We begin by considering a traditional framework where an entrepreneurial firm has monopoly power over its product or service. The production is
q (all variables are described in
Table 1).
The firm trades on the spot market (the price is
p) and (prior to that) it can use a crowdfunding campaign (the crowdfunding or pre-sale price is denoted by
). Let
c and
s denote crowdfunding pre-sales and spot sales respectively:
. If a firm uses crowdfunding, the funders (those who pre-order the product during the pre-sale/crowdfunding stage) expect to receive an extra-benefit (reward)
from the firm.
13 so the total cost of these benefits for the firm equals
. Everybody is risk-neutral and the risk-free interest rate equals zero.
The sequence of events is as follows.
Price determination is driven by the following rules: (1) ; parameter a reflects the magnitude of the demand and a higher price leads to a lower demand; (2) , where represents the market’s expectation regarding the spot sale price (non-arbitrage condition). We assume that is just large enough to compensate funders for the waiting time between the pre-sale stage and the actual sale of the product so the non-arbitrage condition holds.
An equilibrium is a situation where the following hold: (1)
(rational expectations); (2) during the spot sale period the firm selects
s to maximize
(spot sale incentive constraint);
14 (3) during the crowdfunding campaign the firm selects
c to maximize its total profit over two periods
(crowdfunding incentive constraint). Here
represents the firm’s expectation of
s. In equilibrium we should have
.
We start the solution by working backwards. When selecting s, the firm maximizes .
Also
When selecting
c, the firm maximizes
. The market participants can rationally anticipate the spot price and sales using (
1) and (
2). This implies that when selecting
c, the firm maximizes
. The solution is
Lemma 1. Under a monopoly, crowdfunding is not used.
In
Belleflamme et al. (
2014), a monopoly is facing individual customers with different demand functions. A potential consumer’s surplus from buying the product is
, where
p is the price and
v is the consumer’s product valuation. Each consumer only needs one unit of the product/service. The valuation from consuming an extra-unit is zero. Consumers buy/order the product/service as long as they have a non-negative surplus
, where
p is the price.
v is uniformly distributed between 0 and
a. In this setting if the price equals
p, all consumers with
v greater than
p will buy the product making the demand
like in our model. Further, on the spot market, the remaining customers (who did not order during crowdfunding) will buy if
, where
is the spot price. If
, no customers will buy on the spot market because they already ordered during crowdfunding, so the crowdfunding model becomes essentially just a spot market model (i.e., there is no special role for crowdfunding: similar to our result in Lemma 1). The only case that makes sense is the case
. However this case contradicts the no-arbitrage condition for the equilibrium concept: why would consumers buy for a higher price during crowdfunding and not wait until the spot sales begin? To overcome this problem the authors introduce non-monetary benefits for funders participating in crowdfunding. Although some researchers support the significance of these benefits (see, for example,
Schwartz (
2015)), others find that their role seems to be negligible (see, for example,
Cholakova and Clarysse (
2015)).
4. A Market with Competition
Suppose that there are two firms each producing one product/service. The production of Firm 1 is and that of Firm 2 is . Let and denote crowdfunding pre-sales and spot sales respectively for Firm i, : . The sequence of events in the game is as follows.
Firms decide whether to use crowdfunding (this strategy will be denoted CF) or not (S).
Firms observe each other’s decisions.
Firms choose . is determined.
Firms choose . p is determined.
Price determination is driven by the following rules: (1) ; (2) , where represents the market participants’ expectations regarding the spot sale price.
An equilibrium is a situation where the following hold: (1) ; (2) during the spot sale Firm i, selects to maximize for a given choice of by Firm j, ; (3) during the crowdfunding campaign Firm i, selects to maximize its total profit over two periods for a given choice of by Firm j, . Here is a firm’s expectation of . In equilibrium we should have ; (4) In stage 1 each firm selects strategy S or CF which maximizes its payoff given the choice of the other firm.
Note that in addition to the non-arbitrage and rational expectation conditions, which are similar to the ones that we used in the monopoly analysis, here we also use a Nash equilibrium concept (similar to traditional literature on duopoly) to analyze the outcomes of the different stages of competition.
In stage 1 the following situations can occur: both firms select S; both firms select CF; Firm 1 selects CF and Firm 2 selects S; Firm 2 selects CF and Firm 1 selects S. If both firms select S, the equilibrium outcome is
and
. Indeed Firm 1 chooses
to maximize
, which makes:
Similarly, for Firm 2 we get
Solving (
3) and (
4) produces
Also
The firm’s profit (and supply) increases with a (the intercept of the demand function).
Now consider a situation where both firms select CF. We begin the solution by working backwards. On the spot market, Firm 1 chooses
to maximize
, which makes:
Similarly for Firm 2 we get
Solving (
6) and (
7) produces
During crowdfunding Firm 1 maximizes
subject (
8). This gives us:
Similarly for Firm 2:
This implies
15:
(
8) and (
9) imply that the prices equal
The firms’ profits then equal
Now consider a situation where one firm (for instance, Firm 1) selects CF and the other one selects S. In this case .
Since
, (
8) implies:
During crowdfunding Firm 1 maximizes
subject (
10). This gives us:
Accordingly we have
Proposition 1. (1) If . the equilibrium is (S,S); (2) Otherwise the equilibrium is (CF,CF).
Proof. Consider the matrix of payoffs.
The case
was discussed in footnote 15. Consider
. It follows from
Figure 1 that switching to crowdfunding from the case (S,S) improves the payoff of Firm 1. Early committment of Firm 1 makes the product price lower, increases the production of Firm 1 and forces Firm 2 out of its optimal quantity. So (S,S) is not an equilibrium. Indeed the profit of Firm 1 in the case (S,CF) is greater than it is in the case (S,S) if:
This holds because it can be written as
As follows from the matrix of payoffs, whether the equilibrium is (S,CF) or (CF,CF) depends on the following:
If this holds, the equilibrium is (CF,CF) and vice versa. (
12) can be written as
which holds because
so (CF,CF) is an equilibrium. ☐
This section demonstrates that crowdfunding will be used in equilibrium. A situation where both competitors do not use crowdfunding, and only use the spot market, is not an equilibrium because each firm has an incentive to deviate and use a crowdfunding campaign prior to its spot sales. Early commitment of a firm increases its production, makes the product price lower and forces the other firm out of its optimal quantity. As a result, firms fight agressively for market share by using crowdfunding. This is a new result because it argues that in an environment without any non-monetary benefits (as in
Belleflamme et al. (
2014)), moral hazard issues (as in
Strausz (
2017) or
Chemla and Tinn (
2019)) or other imperfections (as in
Miglo and Miglo (
2019)), crowdfunding can still provide value for firms in a competitve environment. This contrasts the monopoly case discussed in the previous section. As was mentioned previously crowdfunding has never been introduced/analyzed in a competitive model so this is a new result. We provide more discussion in
Section 7.
The next step in the analysis is based on the following observations. First, for some values of
, crowdfunding is not used in equilibrium. Second, in many cases equilibria with crowdfunding are not Pareto-efficient.
16 Because of that and also because our model is the first to analyze the role of crowdfunding in a competitive environment, it is interesting and important to analyze other aspects of crowdfunding in shaping the outcome of competition. So far it has been assumed that information is complete and perfect. In the next section we will analyze the model with imperfect information and demonstrate some interesting results related to the use of crowdfunding.
5. Imperfect Information
Suppose that in our model firms face demand uncertainty: with probability and otherwise , . Two cases are possible. One where the demand is unknown to both competitors and one where one of competitors receives private information about demand (without loss of generally let this be Firm 1). We begin by considering the latter. Firm 1 knows the demand and respectively Firm 1 can be two types depending on its knowledge: for type h and for type l. Firm 1 knows the value of a while Firm 2 does not (although Firm 2 believes that Firm 1 is type h with probability ). The analysis of this scenario is interesting and useful for at least two reasons. The uninformed party receives information through two channels: one is related to its own effort (e.g., conducting a crowdfunding campaign and then analyzing the demand) and the second channel is observing the actions of the informed party (Firm 1). Our analysis will help to understand the interaction of both channels and their impact on the outcome of competition. Secondly it is interesting to analyze the actions of the different types of the informed player (Firm 1) because it can generate predictions about the connections between the firm’s strategy and its qualities. It is an important part of crowdfunding research as well as other literature dealing with different ways of rasing funds by firms.
An equilibrium is a situation where no type has an incentive to deviate. It is characterized by the actions (strategies) undertaken by each type of Firm 1, the beliefs of Firm 2 about Firm 1’s type after observing different actions (on equilibrium path and off-equilibrium path) and the actions undertaken by Firm 2. We first focus on separating equilibria which help to generate predictions about the signalling power of crowdfunding. It is an equilibrium where the different types of Firm 1 select different strategies. Two possible separating equilibria may exist. One where type l uses crowdfunding and type h does not and another where type h uses it and l does not.
Proposition 2. (1) A separating equilibrium where type l selects CF and type h selects S does not exist; (2) if and only if β is sufficiently small, a separating equilibrium exists where type h selects CF and type l selects S.
To illustrate Proposition 2, consider the case . The matrix of payoffs for the case of perfect information for each type of Firm 1 is as follows.
The candidate for a separating equilibrium is the case where Firm 2 selects CF and the different types of Firm 1 select different strategies. The situation where Firm 2 selects S cannot be an equilibrium because looking at the matrix of payoffs we can see that Firm 2 would deviate to CF. One can show that a separating equilibrium where type
h selects CF and type
l selects S exists and a separating equilibrium where type
l selects CF and type
h selects S does not exist. Consider a situation where Firm 1 selects CF only if it is type
l and selects S otherwise. Firm 2 believes that the Firm 1’s type is
l when observing CF and
h when observing S. From
Figure 2 the profits of each type are
Suppose that
h mimics
l and uses crowdfunding. (
9) implies
After learning new information about demand from observing the results of the crowdfunding stage Firm 2 realizes that its rival is type
h (i.e., the demand is high), and so it chooses
to maximize
, which makes:
Similarly for Firm 1 we get
Solving (
15) and (
16) produces
Also
During crowdfunding Firm 1 maximizes
. This gives us:
Firm 1’s profit then equals
Comparing this with (
14) we find that it is smaller if
This does not hold since is smaller than and we know . So this equilibrium does not exist. If Firm 2 perceives a firm that uses a crowdfunding campaign to be a low demand firm, it will be pessimistic about the price and will concede the market. Type h can benefit from this situation by mimicking the strategy of type l during the crowdfunding stage.
Now consider an equilibrium where type
h uses crowdfunding and
l does not. The equilibrium payoffs are:
Suppose that
h mimics
l and does not use crowdfunding. Similarly to (
11) we get
17:
After learning information about demand, Firm 2 chooses
to maximize
, which makes:
Similarly for Firm 1 we get
Solving (
21) and (
22) produces
Also
Comparing this with (
19) we find that it is smaller if
Suppose that
l mimics
h and uses crowdfunding. The calculations are similar to the previously analyzed equilibrium case where type
h plays CF and type
l mimics
h. Therefore (
17) implies
Comparing this with (
20) we find that it is smaller if
Note that conditions (
24) and (
25) can hold simultaneously because
. Therefore an equilibrium where type
h uses crowdfunding and type
l does not may exist.
The main result of Proposition 2 is that the only signalling equilibrium that can exist is the one where the high-demand type selects crowdfunding (and the low-demand type selects spot sales).
Next we analyze the pooling equilibria. We define a pooling equilbrium as one where both types of Firm 1 select the same strategy. We will also check that the off-equilibrium beliefs of Firm 2 survive the intuitive criterion of
Cho and Kreps (
1987). This condition means that Firm 2’s off-equilibrium path beliefs are reasonable in the sense that if for any Firm 1 type its maximal payoff from deviation is not greater than its equilibrium payoff then Firm 2 should place a probability of 0 on this firm making a deviation. The definitions above are consistent with the standard perfect bayesian equilibrium definition (see, for instance,
Fudenberg and Tirole (
1991)) with the addition of the intuitive criterion, which is quite common in these types of games involving financing, i.e., when firms raise funds from external investors (see, for instance,
Nachman and Noe (
1994)). If multiple equilibria exist we will use the mispricing criterion to indicate the one that is most likely to exist. We use the standard concept of mispricing that can be found, for example, in
Nachman and Noe (
1994). The magnitude of mispricing (usually it is the difference between a firm’s value under symmetric information and its equilibrium value) in a given equilibrium is equal to that of the undervalued type(s). The mispricing of the overvalued type(s) does not matter.
Proposition 3. (1) A pooling equilibrium where both types of Firm 1 and Firm 2 use crowdfunding may exist; (2) If it does, it is dominated, according to the mispricing criterion, by the separating equilibrium where h selects CF if and only if μ is sufficiently high.
The following explains some ideas behind Proposition 3. First a pooling equilibrium with crowdfunding does not always exist. If it does though it should be compared with the separating equilbrium using the mispricing criterion. First note that compared to the symmetric information case, the low-demand firm (type
l) loses under the pooling equilibrium because its payoff is less than it is under symmetric information. This is because in the case of pooling, Firm 2 is more aggressive compared to the symmetric information case for type
l, since Firm 2 has higher expectations about product demand. So type
l’s profit is reduced. To compare the two equilibria using the mispricing criterion we will compare the payoffs of type
l, which is equal to the firm’s value for its founders, in each equilibria. To illustrate this consider the case
. The outcome of
l under the separating equilibrium (see (
20)) equals
. As shown in
Appendix A.2, under pooling its payoff is
It can be seen that the firms’ payoff under the pooling equilibrium decreases with
because if Firm 2 perceives Firm 1 to be a high-demand firm with a higher probability it increases its volume of crowdfunding which ultimately reduces the total outcome.
18 This leads to the following condition. The payoff under the separating equilibrium is higher for type
l than it is under the pooling equilibrium if
This implies that the separating equilibrium prevails or that signalling opportunities for high-demand firms are more relevant when the economy is performing well ( is high). As a result, our model suggests that the usage of crowdfunding by entrepreneurial firms for signalling is procyclical.
Finally consider the case when demand is unknown by both competitors. We find that in this case the outcome is similar to Proposition 1 except that the likelihood of equilibrium with crowdfunding increases because it adds value to firms by revealing information about the demand during the crowdfunding stage. The following proposition considers the case when neither firm knows the demand, i.e., the value of a. As before we assume that with probability and otherwise , where .
Proposition 4. (1) If β is sufficiently small, the equilibrium is (CF,CF); (2) If not, the equilibrium is (CF,CF) if the difference between and is large enough. Otherwise, the equilibrium is (S,S).
Proposition 4 confirms the results in Proposition 1 to some extent. Crowdfunding is used when is sufficiently low. The last part has an interesting interpretation: a large degree of uncertainty about the demand makes crowdfunding more likely to appear in equilibrium. The result is intuitive. If uncertainty about demand is high, using crowdfunding prior to spot sales helps the firm learn demand and hence helps it in making production decisions later.
6. The Main Implications of The Model and Its Contribution to The Literature
Our paper has several implications for a firm’s choice of crowdfunding.
Proposition 1 explains the value of crowdfunding for firms. Under monopoly (and without any additional assumptions such as non-monetary benefits, market imperfections, moral hazard problems etc.), crowdfunding is not used. If the non-argbitrage condition holds, the firm should compensate its buyers for waiting by offering rewards, which makes crowdfunding a more expensive option. However in the case of a duopoly firms may select crowdfunding in favor of just spot price sales. Except some extreme cases when is large and we have a corner solution where crowdfunding is not a feasible option, a situation where both firms do not use crowdfunding is never an equilibrium. Firms have an incentive to use crowdfunding and consequently force the second firm out of the market to some extent. Early commitment from one firm (i.e., using crowdfunding) makes the product price lower, increases its production and forces the other firm out of its optimal quantity. Furthermore Proposition 4 implies that the likelihood of using crowdfunding increases with demand uncertainty. This is intuitive. A higher level of uncertainty increases the value for the firm to engage with customers early which can have a positive effect on future production and spot sales decisions.
Proposition 2 implies that high-demand firms can use crowdfunding to signal their quality. If an uninformed firm perceives a firm that uses a crowdfunding campaign to be a low-demand firm, it will be pessimistic about the price and will concede the market. A high-demand firm can benefit from this situation by mimicking the strategy of the low-demand firm during the crowdfunding stage. So an equilibrium where the low-demand firm uses crowdfunding and the high-demand firm does not does not exist. However, we show that the opposite is true and an equilibrium where a high-demand firm uses crowdfunding can exist. The uninformed firm (Firm 2) perceives crowdfunding to be a high-demand product with high prices so Firm 2 also increases its production, which may reduce prices implying that a low-demand firm will lose profits if it mimics this strategy. This prediction has not been directly tested but is consistent with the spirit of the results found in
Ahlers et al. (
2015);
Cumming et al. (
2019) and
Mollick (
2014) (the firm’s financing choice can serve as a signal of a project’s quality).
Proposition 3 implies that the separating equilibrium prevails or that signalling opportunities for high-demand firms are more relevant when the economy is performing well (
is high). As a result, our model suggests that the usage of crowdfunding by entrepreneurial firms for signalling is procyclical. To the best of our knowledge, no empirical research exists testing this prediction directly. Further research is expected.
Rampini (
2004) is probably closest to the spirit of this prediction since it suggests that entrepreneurial activity is procyclical (see
Llopis et al. (
2015) for a review of related literature). Also note that,
Dushnitsky et al. (
2016), for example, find that crowdfunding development is closely related to the level of entrepreneurial activities.
Crowdfunding can also be viewed as an example of a firm’s capital structure decision. In light of capital structure literature (see, for example,
Harris and Raviv (
1991) for a review) our paper falls into the branch where capital structure decisions are connected with production decisions in a competitive setting.
Brander and Lewis (
1986);
Bolton and Scharfstein (
1990) and
Williams (
1995) consider the role of capital structure in improving a firm’s competitive position and find that the level of a firm’s debt is strongly related to its level of agressiveness on the product market. Our paper makes two contributions. First it introduces reward-based crowdfunding as a financing choice for a firm. Existing literature usually focuses on the traditional debt/equity choice. Second, to the best of knowledge this literature does not analyze the role of asymmetric information, which is a major part of our model.
8. Conclusions
Crowdfunding is a growing area of interest among practitioners and theorists (see, e.g.,
Ahlstrom et al. (
2018)). It is especially important for small businesses, innovative businesses and start-up businesses because for them financing is a crucial factor of success. Unlike large or established businesses, they do not typically have a long and successful credit history and do not own a large amount of tangible assets in order to successfully negotiate traditional forms of financing such as bank loans. It is not surprising then that these firms are often considered pioneers in finding new ways of funding their projects including private equity in the 1940s, business incubators in the 1950s, venture capital finance in the 1960s, angel finance in the 1970s and seed accelerators in the 2000s. Crowdfunding in its modern form (performed online) is one of the newest ideas in this area and is sometimes credited as a top 10 invention of the 21st century.
26 In the last 10-15 years, crowdfunding has been playing a significant role in enhancing entrepreneurial potential for innovation and economic growth (
Belleflamme et al. (
2015);
Estrin et al. (
2018)).
Existing literature has discovered many reasons for why raising funds is difficult for entrepreneurial companies including asymmetries of information, high bankruptcy costs, transactions costs, moral hazard issues and many others. Our paper contributes to the growing literature on crowdfunding in particular to the branch that focuses on the role of crowdfunding in mitigating asymmetric information problems. Theoretical literature on crowdfunding usually considers a monopoly setting. It is not surprising given that crowdfunding was originally used to fund highly innovative projects where firms retain monopoly power during the development and sale of the given products. Recently, however, companies have begun to use crowdfunding to finance more traditional products and services where they compete against other sellers of similar products. Our main contribution is that we consider the role of crowdfunding in a competitive setting.
27 This paper offers a model of a duopoly where firms can use crowdfunding prior to direct sales. The model is based on asymmetric information between competitors regarding the demand for the product.
We first demonstrate that in a monopoly setting, without making any additional assumptions such as community benefits to funders, crowdfunding is never used and firms prefer to just use the spot market since crowdfunding involves a cost in the form of rewards. Then we consider a duopoly.
Our paper also contributes to the literature that analyzes different marketing tools for a firm operating in a competitive environment. This encompasses forward trading, advanced sales, social coupons, price discrimination etc. It is known that competition weakens or eliminates the effectiveness of many marketing strategies (e.g., bundling, price discrimination). In our paper, competition does not diminish the advantage of crowdfunding (comparing duopoly and monopoly cases for example) because, unlike price discrimination, consumer reward applies to all consumers in the pre-sale period so one seller is unable to focus his/her attention on only one group of consumers (i.e., those being discriminated against).
In
Section 4 and
Section 5 both competition and imperfect information including information asymmetry are present and their interaction and implications for crowdfunding decisions are analyzed. As was mentioned previously, existing theoretical literature focuses on crowdfunding in a monopoly setting. The main deficiency of this line of research and its value for entrepreneurial firms is that it undermines the importance of competition. An increasingly important aspect of competition is information management, which includes, on one hand, acquiring information about competitors and on the other hand managing a firm’s own information and developing a strategy of sharing its own information with the outside world etc. (see, among others,
Dixon (
1992);
Lubit (
2001);
Wang and Ellinger (
2011);
Jeitschko et al. (
2016) and
Chen et al. (
2017)). Furthermore, at the highest levels of competition, firms may have an incentive to deliberately distort their actions to undermine the ability of their rivals to make inferences about their underlying private information (
Jeitschko et al. (
2016)). We argue that crowdfunding can play a strategic role in competitive markets. For example we find that high-demand firms can use crowdfunding to signal their quality. Hence our paper also contributes to the literature on oligopolistic competition under asymmetric information. As was previously mentioned, this literature has analyzed many issues including, for example, firm strategy regarding information acquisition, consumer satisfaction, confidentiality and the social value of information but not in regards to crowdfunding. Crowdfunding literature dicusses some asymmetric information problems in a monopoly setting but it has not analyzed the role of asymmetric information between rivals.
Our paper also contributes to the capital structure literature that connects firm financing decisions and production decisions in a competitive setting (for a recent review see, for example,
Li and Wang (
2019)). Our paper is the first to introduce reward-based crowdfunding as a financing choice for a firm. We also analyze the role of asymmetric information. Both of these aspects (crowdfunding and asymmetric infromation) have not yet been significantly considered in papers in this field of capital structure analysis (see, for example,
Brander and Lewis (
1986);
Bolton and Scharfstein (
1990) and
Williams (
1995)). As discussed in
Section 6, we leave many interesting topics for future research, such as: considering heterogeneity of consumers’ preferences and other modifications of the demand function, introducing different types of crowdfunding and other types of financing into the model, and considering dynamic extensions of the model.