在日益受到重視的平台式商業模式之中，跨邊網路效應是很關鍵的。一般而言， 一個平台會有兩邊的用戶；而平台對任一邊用戶的效用會取決於另外一邊用戶的數量。以電子錢包(如悠遊卡)為例，平台對持卡人的效用會隨著特約商店的數量遞增，對特約商店的效用也會隨著持卡人數遞增。在個體經濟的領域，跨邊網路效應的市場模型主要是建立在雙邊市場 (two-sided markets)的文獻當中。本篇論文我們以雙邊市場的理論為基礎，用電子錢包做為例子，建立一個具有跨邊網路效應的雙頭寡佔市場的代數模型，定義、推演出平台的效用函數，並進一步探討網路效應對市場中平台之間的競爭所帶來的影響。我們發現網路效應會對雙邊市場之中的雙頭寡佔競價賽局帶來一些變化。透過討論這一些賽局變化的商業意涵，我們可以得到一些經營平台所需要的商務智慧。

藉由賽局分析，隨參數變動我們可以觀察到囚犯困境賽局，循環賽局(race-around)與圈豬賽局(boxed-pigs)等多種變化。經營者可以依據觀測到的環境變數預測局勢的發展，因應各種賽局形式設定不同的競合策略，方便地將現有賽局理論的商業智慧運用到商業實務之中。依據我們的模型我們也推演出來在合作性與競爭性的商業環境之中，不同的價格彈性、用戶轉換率(churn rate)與網路效應強度之下，市場領導者與市場進入者分別可以獲致最大營收的最佳化價格。

網際網路之中平台式的商業模式越來越受重視，而跨邊網路效應相關的研究是其中很關鍵的基礎。我們的研究為平台商業模式提供一個系統性的分析方法，為以收取固定交易費用為主的平台(如電子錢包)提供具體的策略建議，同時也為更進一步的、更一般性的平台商業模式研究提供一個基礎。

Cross-sided network effect is critical to platform based business models. In general, across a platform there’re two types of users, each sitting on one side of the platform. And the platform’s utility to any user in one side depends on the number of users (or the volume of usage generated by the users) in the other side. Under the discipline of micro-economy, cross-sided network effect is modeled and analyzed in the literature of “two-sided markets”. In this article, taking eWallet (electronically stored-value payment card) service as an example, we build a model of two-sided market, define and derive the utility functions for the platforms, and design a simulation to examine the price competition games in a duopoly market. We observe that, cross-sided network effect triggers variations in duopoly price games. By elaborating the business implication of these price game variants, we provide business intelligence for competing platforms in two-sided markets.

Following the practice of game theory analysis, with our simulation we identify some famous game patterns such as prisoner’s dilemma, race-around, and varies boxed-pigs games. Depending on the game pattern presented, managers can develop their own co-opetition strategy by leveraging the existing business intelligence provided in the literature of game theory. By factoring price elasticity, churn rate, strength of network effect and market share distribution in our algebraic model, we also derive the optimized prices with which incumbents and entrants can maximize their revenue in cooperative and competitive business environments.

There’s a growing interest in platform based business models, in which cross-sided network effect plays an important role. Our work helps to provide strategic suggestion for fixed–transaction–fee platforms (such as eWallet), provide an systematic analysis methodology for platform based business models, and also provide a theoretic basics for further study in this critical area.

TABLE OF CONTENT
1 Introduction .....................................................................................................................................1
1.1 the Evolving implication of network effect and externality........................................................2
1.1.1 the Origin – negative externality.........................................................................................2
1.1.2 Network effect & positive externality – the two edge sword ...............................................3
1.1.3 Externality as a property – Coase’s theory .........................................................................4
1.1.4 Network effect as a good – the credit card business model.................................................4
1.1.5 the Winners and losers in the network ................................................................................5
1.1.6 Network effect as a non-depleted social recourse ...............................................................6
1.2 Formal definition of network effect and network externality .....................................................7
1.3 Classification of network effects.................................................................................................8
1.4 Two-sided market (TSM) and Cross sided network effect........................................................10
1.5 Initialize and internalize cross-sided network effect.................................................................12
2 Literature Review..........................................................................................................................15
2.1 Impact of cross-sided network effect (Liebowitz & Margolis) .................................................15
2.2 Two-sided networks modeling (Rochet & Tirole) ....................................................................17
2.3 Competition in two-sided networks (Caillaud & Jullien; Armstrong) ......................................19
2.3.1 Armstrong’s Work ..............................................................................................................19
2.3.2 Caillaud & Jullien’s Work .................................................................................................21
2.3.3 Competition strategy in the TSM literature.......................................................................23
3 Generic models for two-sided markets ............................................................................................24
3.1 Full blown two-sided market ....................................................................................................24
3.2 Model of 3-tier, single platform................................................................................................26
3.3 Model for 2-tier, single platform...............................................................................................28
3.4 Model for 2-tier, dual platform, single-homing ........................................................................30
3.5 Model for 2-tier, dual platform, multi-homing .........................................................................31
4 Business model for payment card service network.........................................................................34
4.1 Electronic payment card (eWallet) service network .................................................................34
4.1.1 Acquire a card...................................................................................................................35
4.1.2 Add value ..........................................................................................................................35
4.1.3 Payment transaction .........................................................................................................35
4.1.4 Return card .......................................................................................................................37
4.1.5 Risk of losing card.............................................................................................................37

4.2 Business model for payment card services ...............................................................................38
4.2.1 The Users ..........................................................................................................................38
4.2.2 The Merchants...................................................................................................................41
4.2.3 The Platform .....................................................................................................................42
5 Theoretic model for eWallet service market ................................................................................44
5.1 Duopoly market of both side multi-homing..............................................................................44
5.2 Factors of transaction revenue ..................................................................................................44
5.3 Utility function & key strategic parameters..............................................................................46
5.4 Simulation of price competition sequence ................................................................................47
5.5 Change of revenue in the price competition sequence..............................................................49
5.5.1 Revenue formulation, in case of price difference ..............................................................50
5.5.2 Revenue formulation, in case of equal price .....................................................................51
5.6 Environmental (exogenous) parameters....................................................................................52
6 Game theory analysis for non-cooperative price games..............................................................53
6.1 Static (Synchronous) game analysis .........................................................................................53
6.1.1 General setting and factoring ...........................................................................................54
6.1.2 No(low)-churn-rate situation ............................................................................................54
6.1.3 High-churn-rate situation .................................................................................................58
6.2 Dynamic (Sequential) game analysis........................................................................................61
6.2.1 Simulate price competition sequence ................................................................................61
6.2.2 Common patterns in the simulation result ........................................................................62
6.2.3 Simulation results – factoring elasticity............................................................................63
6.2.4 Simulation results – factoring churn rate..........................................................................66
6.3 Price competition scenarios in duopoly eWallet service markets .............................................68
7 Optimal Price for maximal revenue..............................................................................................71
7.1 The common multiplier for cooperative revenue......................................................................71
7.2 Optimal cooperative price and maximal cooperative revenue ..................................................74
7.3 Pricing strategy in competitive markets....................................................................................76
7.4 Optimal prices in a competitive market ....................................................................................78
7.4.1 Price optimization for the entrant platform ......................................................................80
7.4.2 Price optimization for the incumbent platform .................................................................81
8 Conclusion.........................................................................................................................................83
8.1 the systematic methodology......................................................................................................83
8.2 Key findings and the business implication ...............................................................................85
8.2.1 Revenue formulation interpretation ..................................................................................85
8.2.2 Game theory analysis........................................................................................................86
8.2.3 Price optimization.............................................................................................................87
REFERENCES....................................................................................................................................89
APPENDICES:
Appendix-A Simulation Package, Zero Churn Rate
Appendix-B Simulation Package, Unity Churn Rate
Appendix-C Simulation Package, General Conditioning
Appendix-D Algebraic Derivation for Transaction Revenues
Appendix-E Worksheet for Optimization of Competitive Price
FIGURES, CHARTS, MATRIXES & TABLES
<Figure 2-1> The Two-Sided Market Model Framework ......................................................................20
<Figure 3-1> Configuration of a full blown two-sided market ..............................................................25
<Figure 3-2> Generic model #1: 3-tier, single platform.........................................................................28
<Figure 3-3> Generic model #2: 2-tier, single platform.........................................................................29
<Figure 3-4> Generic model #3: 2-tier, 2-platform, single homing .......................................................31
<Figure 3-5> Generic model #4: 2-tier, 2-platform, Multi-homing........................................................32
<Figure 4-1> Payment Card (eWallet) Service Network........................................................................34
<Figure 4-2> Business model for payment card (eWallet) service.........................................................39
<Diagram 5-1> Duopoly two-sided market with both side multi-homing .............................................44
<Diagram 5-2> Duopoly two-sided market with both side multi-homing .............................................48
<game matrix #1> n=2, c=0, d=5%, e=0.22, X:Y:M=6:3:1 ...................................................................55
<game matrix #2> n=2, c=0, d=5%, e=0.30, X:Y:M=6:3:1 ...................................................................55
<game matrix #3> n=2, c=0, d=5%, e=0.75, X:Y:M=6:3:1 ...................................................................56
<game matrix #4> n=2, c=0, d=5%, e=1.05, X:Y:M=6:3:1 ...................................................................57
<game matrix #5> n=2, c=0, d=5%, e=1.50, X:Y:M=6:3:1 ...................................................................58
<game matrix #6> n=2, c=1, d=5%, e=0.15, X:Y:M=6:3:1 ...................................................................59
<game matrix #7> n=2, c=1, d=5%, e=0.34, X:Y:M=6:3:1 ...................................................................60
<game matrix #8> n=2, c=1, d=5%, e=0.70, X:Y:M=6:3:1 ...................................................................60
<Chart 6-1> Y initiated, n=2, d=5%, c=1, e={0, .25, .5, .75, 1, 1.25, 1.5}.............................................63
<Chart 6-2> Y initiated, n=2, d=5%, c=1, e=1 .......................................................................................65
<Chart 6-3> X initiated, n=2, d=5%, c=1, e={0, .25, .5, .75, 1, 1.25, 1.5} ............................................66
<Chart 6-4> Y initiated, n=2, d=5%, c=0.25, e=1 ..................................................................................67
<Chart 6-5> Y initiated, n=2, d=5%, c=1.25, e=1 ..................................................................................67
<Chart 7-1> Common Multiplier (1+ed)n+1(1-d), n=1.0 ........................................................................73
<Chart 7-2> Common Multiplier (1+ed)n+1(1-d), n=1.5 ........................................................................73
<Chart 7-3> Common Multiplier (1+ed)n+1(1-d), n=2.0 ........................................................................74
<Chart 7-4> Maximum revenue multiplier by elasticity & discount, n=1.0...........................................75
<Chart 7-5> Maximum revenue multiplier by elasticity & discount, n=2.0...........................................75
<Chart 7-6> Revenue gain/loss of the platform with price advantage ...................................................77
<Chart 7-7> Revenue gain/loss of the platform with price disadvantage...............................................78
<Table 7-1> Price optimization in competitive market ..........................................................................79
<Figure 8-1> Analytic methodology for two sided markets (TSM) .......................................................84

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