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doi: 10.3934/jimo.2022146
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Platform contract selection and coordination contract design in reward-based crowdfunding

1. 

School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China

2. 

IIF, School of Management, University of Science and Technology of China, Hefei 230026, China

3. 

College of Economics & Management, Anhui Agricultural University, Hefei 230036, China

*Corresponding author: Hongping Li

Received  September 2021 Revised  February 2022 Early access August 2022

As a new financing method, crowdfunding has alleviated the capital pressure for start-ups, and has attracted extensive attention of scholars. As an intermediary, crowdfunding platforms obtain benefits from providing services. However, the way of charging commission fees still remains a problem for platforms. This paper investigates the impacts of three service contracts, i.e., revenue sharing contract, per-unit fee contract, and fixed fee contract on the creator and platform. Using backward induction, we derive equilibrium results and get some conclusions. First, we find that under fixed fee contract, due to the trade-off between commission fee and crowdfunding success probability, the platform can only make decisions according to first-order conditions, and get partial profits from the creator. This contradicts the traditional view that the fixed fee contract allows leaders to get all the follower's profits in a stackelberg game. Further, we find that compared with revenue sharing contract and per-unit fee contract, the fixed fee contract is mostly although, not always worse (better) for the platform and system (the creator). Third, in the case of consumer homogeneity, we prove the equivalence of revenue sharing contract and per unit fee contract. However, we find that the efficiency of revenue sharing contract decreases when quality is endogenous, while when consumers are heterogeneous, the advantage of per unit fee contract for the platform decreases. In addition, we design a two-part tariff contract and prove that it can achieve coordination when the platform bears partial fixed cost. The two-part tariff contract can simultaneously improve the benefits of all parties with the appropriate parameters.

Citation: Yang Xu, Qiang Zhou, Xu Wang, Hongping Li. Platform contract selection and coordination contract design in reward-based crowdfunding. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022146
References:
[1]

A. AgrawalC. Catalini and A. Goldfarb, Some simple economics of crowdfunding, Innovation Policy and the Economy, 14 (2014), 63-97. 

[2]

V. Abhishek, K. Jerath and Z. J. Zhang, Agency selling or reselling? Channel structures in electronic retailing, Management Science, 62 (2016), 2259-2280.

[3]

P. Belleflamme, T. Lambert and A. Schwienbacher, Crowdfunding: Tapping the right crowd, Journal of Business Venturing, 29 (2014), 585-609.

[4]

G. BiB. Geng and L. Liu, On the fixed and flexible funding mechanisms in reward-based crowdfunding, European Journal of Operational Research, 279 (2019), 168-183.  doi: 10.1016/j.ejor.2019.05.019.

[5]

G. BurtchD. Gupta and P. Martin, Referral timing and fundraising success in crowdfunding, Manufacturing & Service Operations Management, 23 (2021), 676-694. 

[6]

G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. 

[7]

S. Chakraborty and R. Swinney, Signaling to the crowd: Private quality information and rewards-based crowdfunding, Manufacturing & Service Operations Management, 23 (2021), 155-169. 

[8]

G. Chemla and K. Tinn, Learning through crowdfunding, Management Science, 66 (2020), 1783-1801. 

[9]

W. Chu, Demand signalling and screening in channels of distribution, Marketing Science, 11 (1992), 327-347. 

[10]

D. J. Cumming, G. Leboeuf and A. Schwienbacher, Crowdfunding models: Keep-it-all vs. all-or-nothing, Financial Management, 2015.

[11]

J. V. Da Cruz, Beyond financing: Crowdfunding as an informational mechanism, Journal of Business Venturing, 33 (2018), 371-393. 

[12]

J. Dana and K. Spier, Revenue sharing, demand uncertainty and vertical control of competing firms, Northwestern University, working paper, 1999.

[13]

T. Dhar, Can margin differences in vertical marketing channels lead to contracts with slotting fees?, Management Science, 59 (2013), 2766-2771. 

[14]

S. DuJ. Peng and T. Nie, Pricing strategies and mechanism choice in reward-based crowdfunding, European Journal of Operational Research, 284 (2020), 951-966.  doi: 10.1016/j.ejor.2020.01.021.

[15]

Q. Gao, X. Guo, F. Yang, et al., Commitment or not? Creator's quality strategies with uncertain market in reward-based crowdfunding, International Journal of Production Research, (2021), 1-25.

[16]

A. Hagiu and J. Wright, Marketplace or reseller?, Management Science, 61 (2015), 184-203. 

[17]

M. HuX. Li and M. Shi, Product and pricing decisions in crowdfunding, Marketing Science, 34 (2015), 331-345. 

[18]

B. JiangK. Jerath and K. Srinivasan, Firm strategies in the "mid tail" of platform-based retailing, Marketing Science, 30 (2011), 757-775. 

[19]

D. Kuksov and A. Pazgal, Research note: The effects of costs and competition on slotting allowances, Marketing Science, 26 (2007), 259-267. 

[20]

P. KumarN. Langberg and D. Zvilichovsky, Crowdfunding, financing constraints, and real effects, Management Science, 66 (2020), 3561-3580. 

[21]

M. A. Lariviere and V. Padmanabhan, Slotting allowances and new product introductions, Marketing Science, 16 (1997), 112-128. 

[22]

H. Li and E. Cao, Competitive crowdfunding under asymmetric quality information, Annals of Operations Research, (2021), 1-32.

[23]

C. T. Linh and Y. Hong, Channel coordination through a revenue sharing contract in a two-period newsboy problem, European Journal of Operational Research, 198 (2009), 822-829. 

[24]

B. MantinH. Krishnan and T. Dhar, The strategic role of third-party marketplaces in retailing, Production and Operations Management, 23 (2014), 1937-1949. 

[25]

L. M. Marx and G. Shaffer, Slotting allowances and scarce shelf space, Journal of Economics & Management Strategy, 19 (2010), 575-603. 

[26]

S. Panda, Coordination of a socially responsible supply chain using revenue sharing contract, Transportation Research Part E: Logistics and Transportation Review, 67 (2014), 92-104. 

[27]

B. Pasternack, Using revenue sharing to achieve channel coordination for a newsboy type inventory model, CSU Fullerton, working paper, 1999.

[28]

J. PengJ. Zhang and T. Nie, Pricing and package size decisions in crowdfunding, Transportation Research Part E: Logistics and Transportation Review, 143 (2020), 102091. 

[29]

P. RomaE. Gal-Or and R. R. Chen, Reward-based crowdfunding campaigns: Informational value and access to venture capital, Information Systems Research, 29 (2018), 679-697. 

[30]

J. K. RyanD. Sun and X. Zhao, Competition and coordination in online marketplaces, Production and Operations Management, 21 (2012), 997-1014. 

[31]

G. Shaffer, Slotting allowances and resale price maintenance: a comparison of facilitating practices, The RAND Journal of Economics, (1991), 120-135.

[32]

Y. ShenS. P. Willems and Y. Dai, Channel selection and contracting in the presence of a retail platform, Production and Operations Management, 28 (2019), 1173-1185.  doi: 10.1016/j.ejor.2019.01.009.

[33]

R. Strausz, A theory of crowdfunding: A mechanism design approach with demand uncertainty and moral hazard, American Economic Review, 107 (2017), 1430-1476. 

[34]

M. W. Sullivan, Slotting Allowances: An Inquiry, Graduate School of Business, University of Chicago, 1989.

[35]

M. Sullivan, What Caused Slotting Allowances?, Working Paper, University of Chicago, Sullivan, 1992.

[36]

X. Tang, H. Lu, W. Huang, et al., Investment decisions and pricing strategies of crowdfunding players: In a two-sided crowdfunding market, Electronic Commerce Research, (2021), 1-32.

[37]

W. Wu, X. Huang, C. H. Wu, et al., Pricing strategy and performance investment decisions in competitive crowdfunding markets, Journal of Business Research, (2021).

[38]

F. Xu, X. Guo, G. Xiao, et al., Crowdfunding vs. bank financing: Effects of market uncertainty and word-of-mouth communication, Bank Financing: Effects of Market Uncertainty and Word-of-Mouth Communication (July 7, 2018), (2018).

[39]

G. XuB. Dan and X. Zhang, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, International Journal of Production Economics, 147 (2014), 171-179. 

[40]

Y. XuW. Song and G. Bi, The roles of crowdfunding: Financing, point provision and ex-post production, International Journal of Production Research, 59 (2021), 7037-7056. 

[41]

Y. YangG. Bi and L. Liu, Profit allocation in investment-based crowdfunding with investors of dynamic entry times, European Journal of Operational Research, 280 (2020), 323-337.  doi: 10.1016/j.ejor.2019.07.016.

[42]

Z. YaoS. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651.  doi: 10.1016/j.ejor.2007.01.049.

[43]

J. ZhangQ. Cao and X. He, Contract and product quality in platform selling, European Journal of Operational Research, 272 (2019), 928-944.  doi: 10.1016/j.ejor.2018.07.023.

[44]

W. G. ZhangJ. Fu and H. Li, Coordination of supply chain with a revenue-sharing contract under demand disruptions when retailers compete, International Journal of Production Economics, 138 (2012), 68-75.  doi: 10.1155/2014/854681.

[45]

J. Zhang and J. Huang, Deceptive advertising in a crowdfunding market, Transportation Research Part E: Logistics and Transportation Review, 135 (2020), 101892. 

[46]

Z. ZhangL. Ling and F. Yang, Pricing strategy and campaign design in flight crowdfunding: A creative way to sell flight tickets, Naval Research Logistics (NRL), 68 (2021), 795-809.  doi: 10.1002/nav.21970.

[47]

J. ZhangG. Liu and Q. Zhang, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. 

[48]

Y. Zhang and Y. Tian, Choice of pricing and marketing strategies in reward-based crowdfunding campaigns, Decision Support Systems, 144 (2021), 113520. 

[49]

T. ZhaoX. Xu and Y. Chen, Coordination of a fashion supply chain with demand disruptions, Transportation Research Part E: Logistics and Transportation Review, 134 (2020), 101838. 

[50]

H. ZhengD. Li and J. Wu, The role of multidimensional social capital in crowdfunding: A comparative study in China and US, Information & Management, 51 (2014), 488-496. 

[51]

Y. ZhouJ. Zhang and Y. Zeng, Borrowing or crowdfunding: A comparison of poverty alleviation participation modes considering altruistic preferences, International Journal of Production Research, 59 (2021), 6564-6578. 

show all references

References:
[1]

A. AgrawalC. Catalini and A. Goldfarb, Some simple economics of crowdfunding, Innovation Policy and the Economy, 14 (2014), 63-97. 

[2]

V. Abhishek, K. Jerath and Z. J. Zhang, Agency selling or reselling? Channel structures in electronic retailing, Management Science, 62 (2016), 2259-2280.

[3]

P. Belleflamme, T. Lambert and A. Schwienbacher, Crowdfunding: Tapping the right crowd, Journal of Business Venturing, 29 (2014), 585-609.

[4]

G. BiB. Geng and L. Liu, On the fixed and flexible funding mechanisms in reward-based crowdfunding, European Journal of Operational Research, 279 (2019), 168-183.  doi: 10.1016/j.ejor.2019.05.019.

[5]

G. BurtchD. Gupta and P. Martin, Referral timing and fundraising success in crowdfunding, Manufacturing & Service Operations Management, 23 (2021), 676-694. 

[6]

G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 30-44. 

[7]

S. Chakraborty and R. Swinney, Signaling to the crowd: Private quality information and rewards-based crowdfunding, Manufacturing & Service Operations Management, 23 (2021), 155-169. 

[8]

G. Chemla and K. Tinn, Learning through crowdfunding, Management Science, 66 (2020), 1783-1801. 

[9]

W. Chu, Demand signalling and screening in channels of distribution, Marketing Science, 11 (1992), 327-347. 

[10]

D. J. Cumming, G. Leboeuf and A. Schwienbacher, Crowdfunding models: Keep-it-all vs. all-or-nothing, Financial Management, 2015.

[11]

J. V. Da Cruz, Beyond financing: Crowdfunding as an informational mechanism, Journal of Business Venturing, 33 (2018), 371-393. 

[12]

J. Dana and K. Spier, Revenue sharing, demand uncertainty and vertical control of competing firms, Northwestern University, working paper, 1999.

[13]

T. Dhar, Can margin differences in vertical marketing channels lead to contracts with slotting fees?, Management Science, 59 (2013), 2766-2771. 

[14]

S. DuJ. Peng and T. Nie, Pricing strategies and mechanism choice in reward-based crowdfunding, European Journal of Operational Research, 284 (2020), 951-966.  doi: 10.1016/j.ejor.2020.01.021.

[15]

Q. Gao, X. Guo, F. Yang, et al., Commitment or not? Creator's quality strategies with uncertain market in reward-based crowdfunding, International Journal of Production Research, (2021), 1-25.

[16]

A. Hagiu and J. Wright, Marketplace or reseller?, Management Science, 61 (2015), 184-203. 

[17]

M. HuX. Li and M. Shi, Product and pricing decisions in crowdfunding, Marketing Science, 34 (2015), 331-345. 

[18]

B. JiangK. Jerath and K. Srinivasan, Firm strategies in the "mid tail" of platform-based retailing, Marketing Science, 30 (2011), 757-775. 

[19]

D. Kuksov and A. Pazgal, Research note: The effects of costs and competition on slotting allowances, Marketing Science, 26 (2007), 259-267. 

[20]

P. KumarN. Langberg and D. Zvilichovsky, Crowdfunding, financing constraints, and real effects, Management Science, 66 (2020), 3561-3580. 

[21]

M. A. Lariviere and V. Padmanabhan, Slotting allowances and new product introductions, Marketing Science, 16 (1997), 112-128. 

[22]

H. Li and E. Cao, Competitive crowdfunding under asymmetric quality information, Annals of Operations Research, (2021), 1-32.

[23]

C. T. Linh and Y. Hong, Channel coordination through a revenue sharing contract in a two-period newsboy problem, European Journal of Operational Research, 198 (2009), 822-829. 

[24]

B. MantinH. Krishnan and T. Dhar, The strategic role of third-party marketplaces in retailing, Production and Operations Management, 23 (2014), 1937-1949. 

[25]

L. M. Marx and G. Shaffer, Slotting allowances and scarce shelf space, Journal of Economics & Management Strategy, 19 (2010), 575-603. 

[26]

S. Panda, Coordination of a socially responsible supply chain using revenue sharing contract, Transportation Research Part E: Logistics and Transportation Review, 67 (2014), 92-104. 

[27]

B. Pasternack, Using revenue sharing to achieve channel coordination for a newsboy type inventory model, CSU Fullerton, working paper, 1999.

[28]

J. PengJ. Zhang and T. Nie, Pricing and package size decisions in crowdfunding, Transportation Research Part E: Logistics and Transportation Review, 143 (2020), 102091. 

[29]

P. RomaE. Gal-Or and R. R. Chen, Reward-based crowdfunding campaigns: Informational value and access to venture capital, Information Systems Research, 29 (2018), 679-697. 

[30]

J. K. RyanD. Sun and X. Zhao, Competition and coordination in online marketplaces, Production and Operations Management, 21 (2012), 997-1014. 

[31]

G. Shaffer, Slotting allowances and resale price maintenance: a comparison of facilitating practices, The RAND Journal of Economics, (1991), 120-135.

[32]

Y. ShenS. P. Willems and Y. Dai, Channel selection and contracting in the presence of a retail platform, Production and Operations Management, 28 (2019), 1173-1185.  doi: 10.1016/j.ejor.2019.01.009.

[33]

R. Strausz, A theory of crowdfunding: A mechanism design approach with demand uncertainty and moral hazard, American Economic Review, 107 (2017), 1430-1476. 

[34]

M. W. Sullivan, Slotting Allowances: An Inquiry, Graduate School of Business, University of Chicago, 1989.

[35]

M. Sullivan, What Caused Slotting Allowances?, Working Paper, University of Chicago, Sullivan, 1992.

[36]

X. Tang, H. Lu, W. Huang, et al., Investment decisions and pricing strategies of crowdfunding players: In a two-sided crowdfunding market, Electronic Commerce Research, (2021), 1-32.

[37]

W. Wu, X. Huang, C. H. Wu, et al., Pricing strategy and performance investment decisions in competitive crowdfunding markets, Journal of Business Research, (2021).

[38]

F. Xu, X. Guo, G. Xiao, et al., Crowdfunding vs. bank financing: Effects of market uncertainty and word-of-mouth communication, Bank Financing: Effects of Market Uncertainty and Word-of-Mouth Communication (July 7, 2018), (2018).

[39]

G. XuB. Dan and X. Zhang, Coordinating a dual-channel supply chain with risk-averse under a two-way revenue sharing contract, International Journal of Production Economics, 147 (2014), 171-179. 

[40]

Y. XuW. Song and G. Bi, The roles of crowdfunding: Financing, point provision and ex-post production, International Journal of Production Research, 59 (2021), 7037-7056. 

[41]

Y. YangG. Bi and L. Liu, Profit allocation in investment-based crowdfunding with investors of dynamic entry times, European Journal of Operational Research, 280 (2020), 323-337.  doi: 10.1016/j.ejor.2019.07.016.

[42]

Z. YaoS. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651.  doi: 10.1016/j.ejor.2007.01.049.

[43]

J. ZhangQ. Cao and X. He, Contract and product quality in platform selling, European Journal of Operational Research, 272 (2019), 928-944.  doi: 10.1016/j.ejor.2018.07.023.

[44]

W. G. ZhangJ. Fu and H. Li, Coordination of supply chain with a revenue-sharing contract under demand disruptions when retailers compete, International Journal of Production Economics, 138 (2012), 68-75.  doi: 10.1155/2014/854681.

[45]

J. Zhang and J. Huang, Deceptive advertising in a crowdfunding market, Transportation Research Part E: Logistics and Transportation Review, 135 (2020), 101892. 

[46]

Z. ZhangL. Ling and F. Yang, Pricing strategy and campaign design in flight crowdfunding: A creative way to sell flight tickets, Naval Research Logistics (NRL), 68 (2021), 795-809.  doi: 10.1002/nav.21970.

[47]

J. ZhangG. Liu and Q. Zhang, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49. 

[48]

Y. Zhang and Y. Tian, Choice of pricing and marketing strategies in reward-based crowdfunding campaigns, Decision Support Systems, 144 (2021), 113520. 

[49]

T. ZhaoX. Xu and Y. Chen, Coordination of a fashion supply chain with demand disruptions, Transportation Research Part E: Logistics and Transportation Review, 134 (2020), 101838. 

[50]

H. ZhengD. Li and J. Wu, The role of multidimensional social capital in crowdfunding: A comparative study in China and US, Information & Management, 51 (2014), 488-496. 

[51]

Y. ZhouJ. Zhang and Y. Zeng, Borrowing or crowdfunding: A comparison of poverty alleviation participation modes considering altruistic preferences, International Journal of Production Research, 59 (2021), 6564-6578. 

Figure 1.  The sequence of the crowdfunding campaign
Figure 2.  The profits of the platform and creator
Figure 3.  The effects of product costs and product value on total profits of each contract
Figure 4.  The effects of unit production cost, fixed production cost, and product value on efficiency of each contract
Figure 5.  The effects of technology complexity and fixed production cost on the platform and creator's optimal profit under endogenous product value
Figure 6.  The effects of technology complexity and fixed production cost on the total profits of each contract under endogenous product value
Figure 7.  The effects of technology complexity and fixed production cost on contract efficiency under endogenous product value
Figure 8.  The effects of heterogeneity on the platform and creator's optimal profits of each contract
Figure 9.  The effects of heterogeneity on the total profits of each contract
Table 1.  Literature review
Field Research Orientation Literature
Crowdfunding Pricing Hu et al., 2015; Yang et al., 2020; Peng et al., 2020; Chakraborty and Swinney, 2021; Li and Cao, 2021; Strausz, 2014; Tang et al., 2021; Wu et al., 2021
Mode Selection Belleflamme and Lambert, 2014; Bi et al., 2019; Cumming et al., 2015; Du, 2020; Gao, 2021; Zhang and Tian, 2021
Advantages Da, 2018; Xu et al., 2018; Chemla and Tinn, 2020; Kumar et al., 2020; Xu et al., 2020
Others Burtch et al., 2021; Zhang and Tian, 2021; Zhou et al., 2021
Contract Design Revenue Sharing Contract & Per-unit Fee Contract Dana and Spier, 1999; Cachon and Lariviere, 2005; Yao et al., 2008; Linh and Hong, 2009; Xu et al., 2014; Zhang et al., 2012; Zhao et al., 2020; Zhang et al., 2012; Zhao et al., 2020; Panda, 2014; Pasternack, 1999; Abhishek et al., 2016; Jiang et al., 2011; Hagiu and Wright, 2015; Mantin et al., 2014; Ryan et al., 2012; Zhang et al., 2019
Fixed Fee Contract Sullivan, 1989; Chu, 1992; Sullivan, 1992; Lariviere and Padmanabhan, 1997; Marx and Shaffer, 2010; Shaffer, 1991; Dhar, 2013; Kuksov and Pazgal, 2007
Field Research Orientation Literature
Crowdfunding Pricing Hu et al., 2015; Yang et al., 2020; Peng et al., 2020; Chakraborty and Swinney, 2021; Li and Cao, 2021; Strausz, 2014; Tang et al., 2021; Wu et al., 2021
Mode Selection Belleflamme and Lambert, 2014; Bi et al., 2019; Cumming et al., 2015; Du, 2020; Gao, 2021; Zhang and Tian, 2021
Advantages Da, 2018; Xu et al., 2018; Chemla and Tinn, 2020; Kumar et al., 2020; Xu et al., 2020
Others Burtch et al., 2021; Zhang and Tian, 2021; Zhou et al., 2021
Contract Design Revenue Sharing Contract & Per-unit Fee Contract Dana and Spier, 1999; Cachon and Lariviere, 2005; Yao et al., 2008; Linh and Hong, 2009; Xu et al., 2014; Zhang et al., 2012; Zhao et al., 2020; Zhang et al., 2012; Zhao et al., 2020; Panda, 2014; Pasternack, 1999; Abhishek et al., 2016; Jiang et al., 2011; Hagiu and Wright, 2015; Mantin et al., 2014; Ryan et al., 2012; Zhang et al., 2019
Fixed Fee Contract Sullivan, 1989; Chu, 1992; Sullivan, 1992; Lariviere and Padmanabhan, 1997; Marx and Shaffer, 2010; Shaffer, 1991; Dhar, 2013; Kuksov and Pazgal, 2007
Table 2.  Descriptions of notation
$ v $ Product value
$ c $ Unit production cost
$ K $ Fixed production cost
$ a $ Technology complexity of production
$ x $ Demand for the product, which is uniformly distributed on $ [0,1] $
$ f(x), F(x) $ Probability density function and probability distribution function of $ x $
$ G $ Crowdfunding threshold
$ \lambda $ Commission rate under revenue sharing contract
$ r $ Commission fee under per-unit fee contact
$ T $ Commission fee under fixed fee contact
$ (r_t,T_t) $ Two-part tariff contract, where $ r_t $ is the commission fee and $ T_t $ is the transfer payment
$ e $ Contract efficiency
$ \Pi_{c},\Pi_{r},\Pi_{p},\Pi_{f} $ The total profits under centralized decision, revenue sharing contract, per-unit fee contract, and fixed fee contract
$ \Pi^{ex}_{pt},\Pi^{ex}_{ct} $ Profits of the platform and creator under two-part tariff contract
$ \Pi_{pr},\Pi_{pp},\Pi_{pf} $ Platform's profits under revenue sharing contract, per-unit fee contract, and fixed fee contract
$ \Pi_{cr},\Pi_{cp},\Pi_{cf} $ Creator's profits under revenue sharing contract, per-unit fee contract, and fixed fee contract
$ v $ Product value
$ c $ Unit production cost
$ K $ Fixed production cost
$ a $ Technology complexity of production
$ x $ Demand for the product, which is uniformly distributed on $ [0,1] $
$ f(x), F(x) $ Probability density function and probability distribution function of $ x $
$ G $ Crowdfunding threshold
$ \lambda $ Commission rate under revenue sharing contract
$ r $ Commission fee under per-unit fee contact
$ T $ Commission fee under fixed fee contact
$ (r_t,T_t) $ Two-part tariff contract, where $ r_t $ is the commission fee and $ T_t $ is the transfer payment
$ e $ Contract efficiency
$ \Pi_{c},\Pi_{r},\Pi_{p},\Pi_{f} $ The total profits under centralized decision, revenue sharing contract, per-unit fee contract, and fixed fee contract
$ \Pi^{ex}_{pt},\Pi^{ex}_{ct} $ Profits of the platform and creator under two-part tariff contract
$ \Pi_{pr},\Pi_{pp},\Pi_{pf} $ Platform's profits under revenue sharing contract, per-unit fee contract, and fixed fee contract
$ \Pi_{cr},\Pi_{cp},\Pi_{cf} $ Creator's profits under revenue sharing contract, per-unit fee contract, and fixed fee contract
Table 3.  Algorithm to solve equilibrium results under heterogenous valuations (revenue sharing contract)
Input: $ v_h, v_l, c, s $ Output: $ \lambda^*, \Pi^{dv*}_{pr}, \Pi^{dv*}_{cr} $
Begin else
$ \lambda_1=argmax \; \int_{\frac{K}{s((1-\lambda)v_h-c)}}^{1} (s\lambda v_hx)f(x)dx $ $ \quad\Pi^{dv2}_{pr}=\int_{\frac{K}{((1-\lambda_2)v_l-c)}}^{1} (\lambda_2 v_lx)f(x)dx $
$ \lambda_2=argmax \; \int_{\frac{K}{((1-\lambda)v_l-c)}}^{1} (\lambda v_lx)f(x)dx $ $ \quad\lambda_l=\lambda_2 $
$ \lambda_3=solve(\Pi^{dv}_{cr}(p=v_h)=\Pi^{dv}_{cr}(p=v_l)) $ end
if $ \lambda_1>\lambda_3 $ if $ \Pi^{dv1}_{pr}>\Pi^{dv2}_{pr} $
$ \quad\Pi^{dv1}_{pr}= \int_{\frac{K}{s((1-\lambda_1)v_h-c)}}^{1} (s\lambda_1 v_hx)f(x)dx $ $ \quad\lambda^*=\lambda_h $
$ \quad\lambda_h=\lambda_1 $ $ \quad\Pi^{dv*}_{pr}=\Pi^{dv1}_{pr} $
else $ \quad\Pi^{dv*}_{cr}=\Pi^{dv}_{cr}(p=v_h, \lambda=\lambda_h) $
$ \quad\Pi^{dv1}_{pr}= \int_{\frac{K}{s((1-\lambda_3)v_h-c)}}^{1} (s\lambda_3 v_hx)f(x)dx $ else
$ \quad \lambda_h=\lambda_3 $ $ \quad\lambda^*=\lambda_l $
end $ \quad\Pi^{dv*}_{pr}=\Pi^{dv2}_{pr} $
if $ \lambda_2>\lambda_3 $ $ \quad\Pi^{dv*}_{cr}=\Pi^{dv}_{cr}(p=v_l, \lambda=\lambda_l) $
$ \quad \Pi^{dv2}_{pr}=\int_{\frac{K}{((1-\lambda_3)v_l-c)}}^{1} (\lambda_3 v_lx)f(x)dx $ end
$ \quad\lambda_l=\lambda_3 $ End
Input: $ v_h, v_l, c, s $ Output: $ \lambda^*, \Pi^{dv*}_{pr}, \Pi^{dv*}_{cr} $
Begin else
$ \lambda_1=argmax \; \int_{\frac{K}{s((1-\lambda)v_h-c)}}^{1} (s\lambda v_hx)f(x)dx $ $ \quad\Pi^{dv2}_{pr}=\int_{\frac{K}{((1-\lambda_2)v_l-c)}}^{1} (\lambda_2 v_lx)f(x)dx $
$ \lambda_2=argmax \; \int_{\frac{K}{((1-\lambda)v_l-c)}}^{1} (\lambda v_lx)f(x)dx $ $ \quad\lambda_l=\lambda_2 $
$ \lambda_3=solve(\Pi^{dv}_{cr}(p=v_h)=\Pi^{dv}_{cr}(p=v_l)) $ end
if $ \lambda_1>\lambda_3 $ if $ \Pi^{dv1}_{pr}>\Pi^{dv2}_{pr} $
$ \quad\Pi^{dv1}_{pr}= \int_{\frac{K}{s((1-\lambda_1)v_h-c)}}^{1} (s\lambda_1 v_hx)f(x)dx $ $ \quad\lambda^*=\lambda_h $
$ \quad\lambda_h=\lambda_1 $ $ \quad\Pi^{dv*}_{pr}=\Pi^{dv1}_{pr} $
else $ \quad\Pi^{dv*}_{cr}=\Pi^{dv}_{cr}(p=v_h, \lambda=\lambda_h) $
$ \quad\Pi^{dv1}_{pr}= \int_{\frac{K}{s((1-\lambda_3)v_h-c)}}^{1} (s\lambda_3 v_hx)f(x)dx $ else
$ \quad \lambda_h=\lambda_3 $ $ \quad\lambda^*=\lambda_l $
end $ \quad\Pi^{dv*}_{pr}=\Pi^{dv2}_{pr} $
if $ \lambda_2>\lambda_3 $ $ \quad\Pi^{dv*}_{cr}=\Pi^{dv}_{cr}(p=v_l, \lambda=\lambda_l) $
$ \quad \Pi^{dv2}_{pr}=\int_{\frac{K}{((1-\lambda_3)v_l-c)}}^{1} (\lambda_3 v_lx)f(x)dx $ end
$ \quad\lambda_l=\lambda_3 $ End
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