Preannouncement strategy of platform-type new product for competing platforms: Technical or marketing information

Ye Jiang; Tiaojun Xiao

doi:10.3934/jimo.2020155

Article Contents

2022, Volume 18, Issue 1: 315-339. Doi: 10.3934/jimo.2020155

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Preannouncement strategy of platform-type new product for competing platforms: Technical or marketing information

Ye Jiang^1,2, and
Tiaojun Xiao^1, ,

1.
Center for Behavioral Decision and Control, School of Management and Engineering, Nanjing University, Hankou Road 22, Nanjing, Jiangsu 210093, China
2.
School of Business, Jiangsu Open University, Jiangdong North Road 399, Nanjing, Jiangsu 210036, China

^* Corresponding author: Tiaojun Xiao
^* Corresponding author: Tiaojun Xiao

Received: February 29, 2020

Revised: June 30, 2020

Early access: October 2020

Published: January 2022

This research is funded by the National Natural Science Foundation of China (No. 71871112) and Jiangsu province's "333 project" training funding project (No. BRA2019040)

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Abstract

What message should be released to consumers and developers is an important part of the preannouncement strategy of platforms' new product. From the perspectives of consumers and developers' information perceptions, we develop a game model of two-sided market, which can better describe the impacts of information preannouncement on consumers, developers, and platforms behavior in a competitive environment. There are two preannouncement strategies: Technical or marketing information. Our studies reveal that (i) when the development capabilities are heterogeneous enough, both platforms release technical information; (ii) both platforms preannounce marketing information when the heterogeneity of development capability is sufficiently small, even if it decreases total social welfare; (iii) the platform lacking competitive advantage is more inclined to adopt a strategy different from the competitive advantage platform, and competitive advantage platform is likely to change the preannouncement strategy constantly; (iv) the heterogeneity of platforms is the prerequisite for the asymmetric equilibrium, even if it may decrease the overall social welfare.

Keywords:

Mathematics Subject Classification: Primary: 91A10; Secondary: 90B60.

Citation:

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Figure 1. Game structure of the PNPP

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Figure 2. (a) SPNE change with $ t_{e} $ when $ t = 15 $ and $ f_{e} = 1 $ and (b)SPNE change with $ f_{e} $ when $ t = 1 $ and $ t_{e} = 15 $

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Figure 3. (a) SPNE distribution when $ \beta_{b} = 1.01 $ and (b)SPNE distribution when $ \beta_{b} = 5.01 $

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Figure 4. (a) Consumer price changes with $ \delta $ and (b)Developer price changes with $ \delta $

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Figure 5. (a) SPNE changes with $ f_{e} $ when $ \delta = 0.2 $ and (b)SPNE changes with $ f_{e} $ when $ \delta = 1.2 $

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Figure 6. SPNE changes with $ \delta $

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Figure 7. Total social welfare changes with $ \delta $

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Table 1. Equilibrium results under $ (M, M) $

Decisions
Consumers' price	$ p_{bi}^{MM}=t+t_{e}+\beta_{b}(1-g)/(4g)-\beta_{b}(2v_{d} +\beta_{b}+3\beta_{d})/(8gc_{d}) $
Developers' price	$ p_{di}^{MM}=[2v_{d}-2c_{d}(1-g)+\beta_{b}-\beta_{d}]/4 $
Consumers' number	$ n_{bi}^{MM}=1/2 $
Developers' number	$ n_{di}^{MM}=[2v_{d}-2c_{d}(1-g)+\beta_{b}+\beta_{d}]/(8gc_{d}) $
Equilibrium profits/total utilities
Platforms' profit	$ \Pi_{i}^{MM}=(t+t_{e})/2+(4V_{1}^2-B_{0}-2\beta_{b}\beta_{d})/(32gc_{d})-c_{M} $
Consumers' total utility	$ BS_{i}^{MM}=[4v_{b}-5(t+t_{e})]/8+[B_{0}+2(\beta_{b}+\beta_{d})V_{1}]/(16gc_{d}) $
Developers' total utility	$ DS_{i}^{MM}=(2V_{1}+\beta_{b}+\beta_{d})^2/(64gc_{d}) $

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Table 2. Nash equilibrium under $ (T, T) $

Decisions
Consumers' price	$ p_{bi}^{TT}=t+\beta_{b}(1-g)/(4g)-\beta_{b}[2(v_{d}+f_{e}) +\beta_{b}+3\beta_{d}]/(8gc_{d}) $
Developers' price	$ p_{di}^{TT}=(2v_{d}-2c_{d}+2c_{d}g+2f_{e}+\beta_{b}-\beta_{d})/4 $
Consumers' number	$ n_{bi}^{TT}=1/2 $
Developers' number	$ n_{di}^{TT}=[2v_{d}+2f_{e}+\beta_{b}+\beta_{d}-2c_{d}(1-g)]/(8gc_{d}) $
Equilibrium profits/total utilities
Platforms' profit	$ \Pi_{i}^{TT}=t/2+[4(V_{1}+f_{e})^2-B_{0}-2\beta_{b}\beta_{d}]/(32gc_{d})-c_{T} $
Consumers' total utility	$ BS_{i}^{TT}=(4v_{b}-5t)/8+[B_{0}+2(\beta_{b}+\beta_{d})(V_{1}+f_{e})]/(16gc_{d}) $
Developers' total utility	$ DS_{i}^{TT}=[2(V_{1}+f_{e})+\beta_{b}+\beta_{d}]^2/(64gc_{d}) $

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Table 3. Nash equilibrium under $ (M, T) $

Decisions
Consumers' price	$p_{bi}^{TT}=t+\beta_{b}(1-g)/(4g)-\beta_{b}[2(v_{d}+f_{e}) +\beta_{b}+3\beta_{d}]/(8gc_{d})$
Developers' price	$p_{di}^{TT}=(2v_{d}-2c_{d}+2c_{d}g+2f_{e}+\beta_{b}-\beta_{d})/4$
Consumers' number	$n_{bi}^{TT}=1/2$
Developers' number	$n_{di}^{TT}=[2v_{d}+2f_{e}+\beta_{b}+\beta_{d}-2c_{d}(1-g)]/(8gc_{d})$
Equilibrium profits/total utilities
Platforms' profit	$\Pi_{i}^{TT}=t/2+[4(V_{1}+f_{e})^2-B_{0}-2\beta_{b}\beta_{d}]/(32gc_{d})-c_{T}$
Consumers' total utility	$BS_{i}^{TT}=(4v_{b}-5t)/8+[B_{0}+2(\beta_{b}+\beta_{d})(V_{1}+f_{e})]/(16gc_{d})$
Developers' total utility	$DS_{i}^{TT}=[2(V_{1}+f_{e})+\beta_{b}+\beta_{d}]^2/(64gc_{d})$

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Table 4. Factors of effect asymmetric strategy to be a SPNE

$ t=1 $				$ c_{d}=1 $
$ c_{d} $	$ \hat{f}_{e1} $	$ \hat{f}_{e2} $	$ \hat{f}_{e2}-\hat{f}_{e1} $	$ t $	$ \hat{f}_{e1} $	$ \hat{f}_{e2} $	$ \hat{f}_{e2}-\hat{f}_{e1} $
1	0.31	0.61	0.30	1	0.31	0.61	0.30
3	0.93	1.72	0.79	3	0.34	0.58	0.24
5	1.52	2.74	1.22	5	0.36	0.56	0.20
7	2.08	3.69	1.61	7	0.37	0.54	0.17
9	2.62	4.59	1.96	9	0.38	0.53	0.15

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Table 5. Nash equilibrium of non-identical platforms

$ (M, M) $	$ (T, T) $
$p_{bi, E}^{MM}=p_{bi}^{MM}-3\beta_{b}(v_{di}-v_{d})/(12gc_{d})$ $-F(i)[(\beta_{b}+2\beta_{d})E_{2}/(24gc_{d}W_{1})-E_{3}/(12gc_{d})]$	$p_{bi, E}^{TT}=p_{bi}^{TT}-3\beta_{b}(v_{di}-v_{d})/(12gc_{d})$ $-F(i)[(\beta_{b}+2\beta_{d})E_{2}/(24gc_{d}W_{2})-E_{3}/(12gc_{d})]$
$p_{di, E}^{MM}=p_{di}^{MM}+F(i)E_{2}/W_{1}+(v_{di}-v_{d})/2$	$p_{di, E}^{TT}=p_{di}^{TT}+F(i)E_{2}/(4W_{2})+(v_{di}-v_{d})/2$
$n_{bi, E}^{MM}=n_{bi}^{MM}+F(i)E_{3}/W_{1}$	$n_{bi, E}^{TT}=n_{bi}^{TT}+F(i)E_{3}/W_{2}$
$n_{di, E}^{MM}=n_{di}^{MM}+F(i)E_{4}/W_{1}+(v_{di}-v_{d})/(4gc_{d})$	$n_{di, E}^{TT}=n_{di}^{TT}+F(i)E_{4}/W_{2}+(v_{di}-v_{d})/(4gc_{d})$
$\Pi_{i, E}^{MM}=\Pi_{i}^{MM}+E_{2}^2/(96gc_{d}W_{1}^2)+E_{3}^2/(24gc_{d}W_{1})$ $+F(i)E_{3}(\beta_{b}-\beta_{d})^2/(48gc_{d}W_{1})+E_{3}/(12gc_{d})$ $+[(v_{di}+v_{d})-2c_{d}+2c_{d}g](v_{di}-v_{d})/(8gc_{d})$}	$\Pi_{i, E}^{TT}=\Pi_{i}^{TT}+E_{2}^2/(96gc_{d}W_{1}^2)+E_{3}^2/(24gc_{d}W_{1})$ $+F(i)E_{3}(\beta_{b}+\beta_{d})^2/(48gc_{d}W_{1})+E_{3}/(12gc_{d})$ $+[(v_{di}+v_{d})-2c_{d}+2c_{d}g](v_{di}-v_{d})/(8gc_{d})$}
$(M, T)$
$p_{bi, E}^{MT}=p_{bi}^{MT}-\beta_{b}(v_{di}-v_{d})/(4gc_{d})-F(i)E_{3}(B_{2}-2W_{3})/(24gc_{d}W_{3})$
$p_{di, E}^{MT}=p_{di}^{MT}+F(i)E_{2}/(4W_{3})+(v_{di}-v_{d})/2$
$n_{bi, E}^{MT}=n_{bi}^{MT}+F(i)E_{3}/(2W_{3})$
$n_{di, E}^{MT}=n_{di}^{MT}+F(i)E_{4}/W_{3}+(v_{di}-v_{d})/(4gc_{d})$
$\Pi_{1, E}^{MT}=\Pi_{1}^{MT}+(\beta_{b}-\beta_{d})^2E_{3}(E_{3}-2R_{2})/(96gc_{d}W_{3}^2)+[8E_{3}+12(2v_{d}+\delta-2\phi)\delta]/(96gc_{d})$ $-(\beta_{b}+\beta_{d})\delta[8gc_{d}t_{e}+4f_{e}(\beta_{b}+\beta_{d})-(\beta_{b}-\beta_{d})^2-2E_{3}]/(48gc_{d}W_{3})$
$\Pi_{2, E}^{MT}=\Pi_{2}^{MT}+(\beta_{b}-\beta_{d})^2E_{3}(E_{3}-2R_{2})/(96gc_{d}W_{3}^2)+[8E_{3}+12(2v_{d}-\delta-2\phi+2f_{e})\delta]/(96gc_{d})$ $+(\beta_{b}+\beta_{d})\delta[8gc_{d}t_{e}+4f_{e}(\beta_{b}+\beta_{d})+(\beta_{b}-\beta_{d})^2-2E_{3}]/(48gc_{d}W_{3})$
$(T, M)$
$\Pi_{1, E}^{TM}=\Pi_{1, E}^{MT}+[3f_{e}^2+8gc_{d}t_{e}+f_{e}(6\delta+6V_1+4\beta_{b}+4\beta_{d})]/(24gc_{d})+(\beta_{b}-\beta_{d})R_{2}E_{4}/(3W_{3}^2)$ $+R_{2}[8\delta(\beta_{b}+\beta_{d})+(\beta_{b}-\beta_{d})^2]/(24gc_{d}W_{3})$}}
$\Pi_{2, E}^{TM}=\Pi_{2, E}^{MT}-[3f_{e}^2+8gc_{d}t_{e}+f_{e}(6\delta+6V_1+4\beta_{b}+4\beta_{d})]/(24gc_{d})+(\beta_{b}-\beta_{d})R_{2}E_{4}/(3W_{3}^2)$ $+R_{2}[(\beta_{b}-\beta_{d})^2-8\delta(\beta_{b}+\beta_{d})]/(24gc_{d}W_{3})$

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Table 1A. Mathematical abbreviation and threshold

$V_{1}=v_{d}-c_{d}(1-g)$	$B_{0}=\beta_{b}^2+\beta_{d}^2+4\beta_{b}\beta_{d}$
$B_{1}=\beta_{b}^2+\beta_{d}^2+6\beta_{b}\beta_{d}$	$\phi=c_{d}(1-g)$
$R_{1}=\beta_{b}^2-2\beta_{d}^2+\beta_{b}\beta_{d}$	$R_{2}=f_{e}(\beta_{b}+\beta_{d})+2gc_{d}t_{e}$
$R_{3}=24gc_{d}(c_{T}-c_{M})-6f_{e}[v_{d}-c_{d}(1-g)]$ $+2gc_{d}t_{e}-f_{e}(3f_{e}+2\beta_{b}+2\beta_{d})$	$R_{4}=f_{e}(\beta_{b}+\beta_{d})+5gc_{d}t_{e}$
$R_{5}=6(\beta_{b}+\beta_{d})(2v_{d}-2c_{d}+2c_{d}g+f_{e})$ $+48gc_{d}v_{b}+2\beta_{b}^2+8\beta_{b}\beta_{d}+\beta_{d}^2$	$R_{6}=2v_{d}-2c_{d}(1-g)+f_{e}+\beta_{b}+\beta_{d}$
$R_{7}=f_{e}(\beta_{b}+\beta_{d})+8gc_{d}t_{e}$	$E_{2}=2\delta(\beta_{b}^2-\beta_{d}^2)$
$E_{3}=2\delta(\beta_{b}+\beta_{d})$	$E_{4}=2\delta(\beta_{b}+\beta_{d})^2/(8gc_{d})$
$E_{5}=2v_{d}+\beta_{b}+\beta_{d}$	$W_{1}=12gc_{d}(t+t_{e})-(\beta_{b}^2+\beta_{d}^2+4\beta_{b}\beta_{d})$
$W_{2}=12gc_{d}t-(\beta_{b}^2+\beta_{d}^2+4\beta_{b}\beta_{d})$	$W_{3}=6gc_{d}(2t+t_{e})-(\beta_{b}^2+\beta_{d}^2+4\beta_{b}\beta_{d})$
$H_{1}=[6f_{e}V_{1}+3f_{e}^2+2f_{e}(\beta_{b}+\beta_{d})$ $-2gc_{d}t_{e}]/(24gc_{d})$}	$H_{2}=R_{2}[4gc_{d}t_{e}-(\beta_{b}-\beta_{d})^2$ $+2f_{e}(\beta_{b}+\beta_{d})]/(48gc_{d}W_{3})$}
$H_{3}=R_{2}[4gc_{d}t_{e}+(\beta_{b}-\beta_{d})^2$ $+2f_{e}(\beta_{b}+\beta_{d})]/(48gc_{d}W_{3})$}	$H_{4}=R_{2}^2(\beta_{b}-\beta_{d})^2/(96gc_{d}W_{3}^2)$
Threshold
$\hat{t}^{MM}=\beta_{b}\beta_{d}/(2gc_{d})-t_{e}$	$\hat{t}^{MT}=\beta_{b}\beta_{d}/(2gc_{d})-t_{e}/2$
$\hat{t}^{TT}=\beta_{b}\beta_{d}/(2gc_{d})$	$\hat{t}_{e7}=-(1+g)f_{e}(2\phi+f_{e}+E_{5})/(gc_{d})$
$\hat{f}_{e7}=\{2\phi-2v_{d}-\beta_{b}-\beta_{d}+\sqrt{(1+g)[(1+g)(E_{5}-2\phi)^2-4gc_{d}t_{e}]}/(1+g)\}/2$

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