Network Game Theory Models of Services and Quality Competition with Applications to Future Internet Architectures and Supply Chains

Transcription

1 Network Game Theory Models of Services and Quality Competition with Applications to Future Internet Architectures and Supply Chains Sara Saberi Doctoral Dissertation Defense Isenberg School of Management University of Massachusetts Amherst, Massachusetts August 12, 2016 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

2 Acknowledgments This research was supported by the National Science Foundation (NSF) grant: CISE # , NeTS: Large: Collaborative Research: Network Innovation Through Choice, awarded to the University of Massachusetts Amherst. This support is gratefully acknowledged. I would also like to acknowledge the support from two Isenberg Scholar Awards. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

3 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

4 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

5 Main Contribution In this dissertation, I contribute to the modelling, analysis, and design of the communication and supply chain networks with a focus on quality of service and price competition between decision-makers in the Internet and supply chain networks. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

6 Networks All networks provide the infrastructure for connectivity and operations for service providers in our societies. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

7 Networks All networks provide the infrastructure for connectivity and operations for service providers in our societies. Communication Networks Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

8 Networks All networks provide the infrastructure for connectivity and operations for service providers in our societies. Communication Networks Supply Chain Networks Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

9 Networks Challenges Large-scale nature and complexity, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

10 Networks Challenges Large-scale nature and complexity, Increasing congestion, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

11 Networks Challenges Large-scale nature and complexity, Increasing congestion, The alternative behaviors of the networks users, which can lead to paradoxical phenomena, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

12 Networks Challenges Large-scale nature and complexity, Increasing congestion, The alternative behaviors of the networks users, which can lead to paradoxical phenomena, To maintain an edge, every business needs to achieve optimum levels of efficiency, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

13 Networks Challenges Large-scale nature and complexity, Increasing congestion, The alternative behaviors of the networks users, which can lead to paradoxical phenomena, To maintain an edge, every business needs to achieve optimum levels of efficiency, Creating a variety of products and taking into consideration quality of products. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

14 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

15 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

16 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Chapter 4 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

17 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Chapter 4 How will the quality and the duration of Internet network contracts affect the pricing of services? Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

18 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Chapter 4 How will the quality and the duration of Internet network contracts affect the pricing of services? Chapter 5 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

19 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Chapter 4 How will the quality and the duration of Internet network contracts affect the pricing of services? Chapter 5 Considering the similarities between supply chain networks and communication networks, how to handle both price and quality competition with multiple modes of shipment for carriers and manufacturers in a supply chain? Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

20 Overview In this dissertation, I address the following questions for service-oriented networks. How to find the equilibrium prices and quality levels in an oligopoly market of service providers in a service-oriented Internet which provides quality-based services from both equilibrium and dynamic perspectives? Chapter 3 Chapter 4 How will the quality and the duration of Internet network contracts affect the pricing of services? Chapter 5 Considering the similarities between supply chain networks and communication networks, how to handle both price and quality competition with multiple modes of shipment for carriers and manufacturers in a supply chain? Chapter 6 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

21 Methodologies Optimization Theory Network Theory Variational Inequality Theory Projected Dynamical Systems Game Theory Algorithm - Euler Method Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

22 Variational Inequality Theory Definition 2.1 The finite-dimensional variational inequality problem, VI(F, K), is to determine a vector X K R n, such that F(X ), X X 0, X K, where F is a given continuous function from K to R n, K is a given closed convex set, and, denotes the inner product in n-dimensional Euclidean space and, F (X ), X X = n i=1 F i (X ) (X i X i ). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

23 Proposition 2.1: The Relationship between Variational Inequalities and Optimization Problems Let X be a solution to the optimization problem: Minimize f (X) subject to: X K, where f is continuously differentiable and K is closed and convex. Then X is a solution of the variational inequality problem: f (X ), X X 0, X K, where f (X) is the gradient vector of f with respect to X, that is f (X) X 1 f (X) f (X) = X f (X) X n Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

24 Projected Dynamical Systems The class of ordinary differential equations (ODE(F, K)) that are of concern in this dissertation take on the following form: Ẋ = Π K(X, F(X)), X(0) = X 0 K, where Ẋ denotes the rate of change of vector X, K is closed convex set, corresponding to the constraint set in a particular application, and F(X) is a vector field defined on K. Theorem 2.6 Assume that K is a convex polyhedron. Then the equilibrium points of the PDS(F, K) coincide with the solutions of VI(F, K). Therefore, X K satisfies Ẋ = 0 = Π K(X, F (X )) also satisfies F(X ), X X 0, X K. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

25 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

26 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

27 This section corresponds to Chapter 3 of the dissertation, and is based on the following paper: Saberi, S., Nagurney, A., Wolf, T., A network economic game theory model of a service-oriented Internet with price and quality competition in both content and network provision. Service Science 6(4), The paper has been cited in: Behzad, B., Jacobson, S.H., Asymmetric Bertrand-Edgeworth-Chamberlin competition with linear demand: A pediatric vaccine pricing model. Service Science 8(1), among other references. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

28 Global Internet 3.4 billion Internet users out of a global population of 7.3 billion. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

29 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

30 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

31 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

32 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Networking research community is designing new architectures for the next generation Internet. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

33 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Networking research community is designing new architectures for the next generation Internet. Economic relationships are far more mysterious than the underlying technology, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

34 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Networking research community is designing new architectures for the next generation Internet. Economic relationships are far more mysterious than the underlying technology, Future Internet includes multi-tier service providers Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

35 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Networking research community is designing new architectures for the next generation Internet. Economic relationships are far more mysterious than the underlying technology, Future Internet includes multi-tier service providers Content Service Providers Content Provider (CP), Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

36 Background and Motivation Advances in the Internet and other telecommunication networks bring about new applications and services, Key challenge is how to price and bill, Price is not the only factor and Quality of Service (QoS) comes into play, Networking research community is designing new architectures for the next generation Internet. Economic relationships are far more mysterious than the underlying technology, Future Internet includes multi-tier service providers Content Service Providers Content Provider (CP), Network Service Providers Network Provider (NP). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

37 Literature Review Addressing the Nash equilibrium Zhang, Z.L., Nabipay, P., Odlyzko, A., Guerin, R., Interactions, competition and innovation in a service-oriented Internet: An economic model. Proceedings of IEEE INFOCOM San Diego, CA, Nagurney, A., Li, D., Wolf, T., Saberi, S., 2013a. A network economic game theory model of a service-oriented Internet with choices and quality competition. Netnomics 14, Nagurney, A., Wolf, T., A Cournot-Nash-Bertrand game theory model of a service-oriented Internet with price and quality competition among network transport providers. Computational Management Science 11(4), Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

38 Literature Review Studied two-sided payments effects in the NGI Laffont, J., Marcus, S., Rey, P., Tirole, J., Internet interconnection and the off-net-cost pricing principle. The RAND Journal of Economics 34(2), Hermalin, B.E., Katz, M.L., The economics of product-line restrictions with an application to the network neutrality debate. Information Economics and Policy 19(2), Musacchio, J., Schwartz, G., Walrand, J., Network economics: Neutrality, competition, and service differentiation. In Next-Generation Internet Architectures and Protocols, Ramamurthy, B., Rouskas, G., Sivalingam, K., (Editors). Cambridge University Press, Cambridge, England, Economides, N., Tag, J., Network neutrality on the internet: A two-sided market analysis. Information Economics and Policy 24(1), Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

39 Overview This research contributes to the literature as: I include quality levels, in addition to prices, for both network and content providers. However, Altman, Legout, and Xu (2011) considered only quality level for network providers, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

40 Overview This research contributes to the literature as: I include quality levels, in addition to prices, for both network and content providers. However, Altman, Legout, and Xu (2011) considered only quality level for network providers, Consumers have more choices in that they can select network and content providers. However, El Azouzi, Altman, and Wynter (2003) have only one choice of network provider for customers. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

41 The Network of Oligopoly Model Content Flows Network Content Providers CP 1 CP i CP m NP 1 NP j NP n u 1 u k u o Users at Demand Markets Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

42 The Network of Oligopoly Model Content Flows Network Payments Flows Network Content Providers Content Providers CP 1 CP i CP m CP 1 CP i CP m p cm p t1 NP 1 NP j NP n p tn p c1 p t1 p t2 p tn p cm p c1 Network Providers NP 1 NP j NP p n c2 p p sn s1 p sn u 1 u k u o u 1 u k u o Users at Demand Markets Users at Demand Markets Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

43 The Network of Oligopoly Model Content Flows Network Payments Flows Network Content Providers Content Providers CP 1 CP i CP m CP 1 CP i CP m p cm p t1 NP 1 NP j NP n p tn p c1 p t1 p t2 p tn p cm p c1 Network Providers NP 1 NP j NP p n c2 p p sn s1 p sn u 1 u k u o u 1 u k u o Users at Demand Markets Demand function Users at Demand Markets Demand for Content produced by CP i and transmitted by NP j to u k : d ijk = d ijk (p s, q s, p c, q c), i, j, k. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

44 Content providers Behavior Each CP i has a production cost CC i : CC i = CC i (SCP i, q ci ), i = 1,..., M. The utility of CP i : U CPi = N O (p ci p tj ) d ijk CC i (SCP i, q ci ). j=1 k=1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

45 Content providers Behavior Each CP i has a production cost CC i : CC i = CC i (SCP i, q ci ), i = 1,..., M. The utility of CP i : U CPi = N O (p ci p tj ) d ijk CC i (SCP i, q ci ). j=1 k=1 Network providers Behavior Each NP j incurs a transmission cost CS j : CS j = CS j (TNP j, q sj ), j = 1,..., N. The utility of NP j : M O U NPj = (p sj + p tj )( d ijk ) CS j (TNP j, q sj ). i=1 k=1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

46 Definition 3.2: Nash Equilibrium in Price and Quality A price and quality level pattern (p c, q c, p s, q s ) K 3 m i=1 K1 i n j=1 K2 j, is said to constitute a Nash equilibrium if for each content provider CP i ; i = 1,..., m: where U CPi (p c i, ˆ p c i, q c i, ˆ q c i, p s, q s ) U CPi (p ci, ˆ p c i, q ci, ˆ q c i, p s, q s ), (p ci, q ci ) K 1 i, pˆ c i (pc 1,..., pc i 1, pc i+1,..., pc m ) and qˆ c i (qc 1,..., qc i 1, qc i+1,..., qc m ). and if for each network provider NP j ; j = 1,..., n: where U NPj (pc, qc, ps j, pˆ s j, qs j, qˆ s j ) U NPj (p sj, p ˆ c, qc, ps j, q sj, qˆ s j ), (p sj, q sj ) Kj 2, pˆ s j (ps 1,..., ps j 1, ps j+1,..., ps n ) and qˆ s j (qs 1,..., qs j 1, qs j+1,..., qs n ). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

47 Theorem 3.4: Variational Inequality Formulations of Nash Equilibrium for the Service-Oriented Internet Assume that the provider utility functions are concave, continuous, and continuously differentiable: M i=1 + [ N j=1 N O N O d ijk j=1 k=1 [ + + M i=1 i=1 k=1 [ j=1 k=1 N O j=1 k=1 M O M O d ijk N j=1 [ N i=1 k=1 O j=1 k=1 d ijk q sj d ijk (pc p i p tj ) + fc (SCP i i, qc i ) SCP ] i (p ci pc ci SCP i p i ) ci d ijk (pc q i p tj ) + fc (SCP i i, q ] c i ) (q ci qc ci q i ) ci d ijk p sj (ps j + p tj ) + fs (TNP j j, qs j ) TNP ] j (p sj ps TNP j p j ) sj (p s j + p tj ) + fs j (TNP j, q q sj s j ) (p c, q c, p s, q s) K 3. ] (q sj q s j ) 0, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

48 This variational inequality can be put into standard form: determine X K 3 such that: F(X ), X X 0, X K F pci = CC i(scp i, q ci ) SCP i SCP i p ci F qci = CC i(scp i, q ci ) q ci F psj = CS j(tnp j, q sj ) TNP j TNP j p sj F qsj = CS j(tnp j, q sj ) q sj where K = K 3 and N = 2m + 2n. n j=1 k=1 o d ijk n o j=1 k=1 i=1 k=1 n o j=1 k=1 d ijk q ci (p ci p tj ), m o m o d ijk m o i=1 k=1 i=1 k=1 d ijk q sj (p sj + p tj ), d ijk p ci (p ci p tj ), d ijk p sj (p sj + p tj ), Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

49 Algorithm We recall the Euler method for the solution of the Variational Inequality Problem. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

50 Algorithm We recall the Euler method for the solution of the Variational Inequality Problem. Explicit formulae for the Euler method p τ+1 c i { n = max 0, pc τ i + a τ ( q τ+1 c i o n o d ijk + j=1 k=1 { n = max 0, qc τ i + a τ ( j=1 k=1 o j=1 k=1 d ijk (pc τ p i p tj ) CC i (SCP i, qc τ i ) SCP } i ), ci SCP i p ci d ijk (pc τ q i p tj ) CC i (SCP i, q τ } c i ) ), ci q ci p τ+1 s j { m = max 0, ps τ j + a τ ( q τ+1 s j o m o d ijk + i=1 k=1 { m = max 0, qs τ j + a τ ( i=1 k=1 o i=1 k=1 d ijk (ps τ p j + p tj ) CS j (TNP j, qτ sj ) TNP } j ), sj TNP j p sj d ijk (ps τ q j + p tj ) CS j (TNP j, qτ sj ) } ). sj q sj Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

51 Example 3.2 CP NPs DM CP 1 NP 1 NP 2 u 1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

52 Example 3.2 The demand functions: CP NPs DM CP 1 NP 1 NP 2 u 1 d 111 = p s1 +.5p s2 1.83p c q s1.6q s q c1, d 121 = p s1 1.5p s2 1.83p c1.6q s q s q c1. The cost functions: CS 1 = 1.7(d q 2 s ), CS 1 2 = 1.8(d q 2 s ). 2 CC 1 = 1.84 [ d d q 2 ] c. 1 The utility functions, with p t1 = p t2 = 0: U CP1 = (p c1 p t1 )d (p c1 p t2 )d 121 CC 1. U NP1 = (p s1 + p t1 )d 111 CS 1, U NP2 = (p s2 + p t2 )d 121 CS 2. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

53 Example 3.2 The demand functions: CP NPs DM CP 1 NP 1 NP 2 u 1 d 111 = p s1 +.5p s2 1.83p c q s1.6q s q c1, d 121 = p s1 1.5p s2 1.83p c1.6q s q s q c1. The cost functions: CS 1 = 1.7(d q 2 s ), CS 1 2 = 1.8(d q 2 s ). 2 CC 1 = 1.84 [ d d q 2 ] c. 1 The utility functions, with p t1 = p t2 = 0: U CP1 = (p c1 p t1 )d (p c1 p t2 )d 121 CC 1. U NP1 = (p s1 + p t1 )d 111 CS 1, U NP2 = (p s2 + p t2 )d 121 CS 2. The equilibrium solution: p c 1 = 29.19, p s 1 = 27.66, p s 2 = 37.38, q c 1 = 18.43, q s 1 = 12.14, q s 2 = Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

54 Example 3.2: Sensitivity Analysis The value of both p t1 and p t2 increase simultaneously from 0 to 40. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

55 Example 3.3 CPs CP 1 CP 2 NPs NP 1 NP 2 Ms u 1 u2 u3 The utility functions of the content providers: U CP1 = (p c1 p t1 )(d d d 113 ) + (p c1 p t2 )(d d d 123 ) CC 1, U CP2 = (p c2 p t1 )(d d d 213 ) + (p c2 p t2 )(d d d 223 ) CC 2. The utility functions, with p t1 = 23 and p t2 = 21: U NP1 = (p s1 + p t1 )(d d d d d d 213 ) CS 1, U NP2 = (p s2 + p t2 )(d d d d d d 223 ) CS 2. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

56 Example 3.3 CPs CP 1 CP 2 NPs NP 1 NP 2 Ms u 1 u2 u3 The utility functions of the content providers: U CP1 = (p c1 p t1 )(d d d 113 ) + (p c1 p t2 )(d d d 123 ) CC 1, U CP2 = (p c2 p t1 )(d d d 213 ) + (p c2 p t2 )(d d d 223 ) CC 2. The utility functions, with p t1 = 23 and p t2 = 21: U NP1 = (p s1 + p t1 )(d d d d d d 213 ) CS 1, U NP2 = (p s2 + p t2 )(d d d d d d 223 ) CS 2. The equilibrium solution: p c 1 = 40.57, p c 2 = 41.49, p s 1 = 8.76, p s 2 = 5.35, q c 1 = 13.96, q c 2 = q s 1 = 36.67, q s 2 = 12.15, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

57 Example 3.3: Sensitivity Analysis I let p t1 + p t2 = 40, so that p t1 starts at 40 and decreases to 0 while p t2 starts at 0 and increases to 40 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

58 Example 3.3: Sensitivity Analysis Examining with n = 30, n = 50, and n = 60 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

59 Summary and Conclusions I modeled the competition for monopoly content and a single network provider. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

60 Summary and Conclusions I modeled the competition for monopoly content and a single network provider. I modeled an oligopoly market of multi-tier providers. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

61 Summary and Conclusions I modeled the competition for monopoly content and a single network provider. I modeled an oligopoly market of multi-tier providers. All providers are noncooperative and are assumed to be utility maximizers. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

62 Summary and Conclusions I modeled the competition for monopoly content and a single network provider. I modeled an oligopoly market of multi-tier providers. All providers are noncooperative and are assumed to be utility maximizers. The users reflect their preferences for the services produced by content providers and shipped by network providers through the demand functions. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

63 Summary and Conclusions I modeled the competition for monopoly content and a single network provider. I modeled an oligopoly market of multi-tier providers. All providers are noncooperative and are assumed to be utility maximizers. The users reflect their preferences for the services produced by content providers and shipped by network providers through the demand functions. Sensitivity analysis shows that the overall effect of implementing network neutrality regulations (e.g., having p tj = 0) may still be both positive and negative depending on the parameter values and the model structure. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

64 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

65 This section corresponds to Chapter 4 of the dissertation, and is based on the paper: Nagurney, A., Li, D., Saberi, S., Wolf, T., A dynamic network economic model of a service-oriented Internet with price and quality competition. In Network Models in Economics and Finance, Kalyagin, V.A., Pardalos, P.M., Rassias, T.M. (Editors). Springer International Publishing Switzerland, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

66 Research Contributions This research completes the general model in Chapter 3. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

67 Research Contributions This research completes the general model in Chapter 3. Motivation I study and analyze the underlying dynamics of the various economic decision-makers involved. Novel insights into the networks structures is obtained by taking into account the associated economic models and equilibrium conditions among provider. I capture the dynamics of oligopolistic competition in service-oriented networks. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

68 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

69 This section corresponds to Chapter 5 of the dissertation, and is based on the paper: Nagurney, A., Saberi, S., Wolf, T., Nagurney, L.S., A game theory model for a differentiated service-oriented Internet with duration-based contracts. Proceedings of the ICS 2015: Operations Research and Computing: Algorithms and Software for Analytics, Borchers, B., Brooks, J.P., McLay, L. (Editors). Richmond, VA, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

70 Service-Oriented Internet with Duration-Based Contracts Online video consumption almost doubled in the US from 2012 to 2013, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

71 Service-Oriented Internet with Duration-Based Contracts Online video consumption almost doubled in the US from 2012 to 2013, It may result in network congestion that leads to a degradation in the quality of transmission. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

72 Current Internet Limitations Quality and price concerns, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

73 Current Internet Limitations Quality and price concerns, Customers are locked-in for extended periods of time. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

74 Literature Review Early mathematical models with duration and quality of services P.J. Bailey, I. Gamvros, and S. Raghavan. Ex-post Internet charging: an effective bandwidth model. In E.K. Baker, A. Joseph, A. Mehrotra, and M.A. Trick, editors, Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Springer, US, , C. Courcoubetisaib and V.A. Siris. Managing and pricing service level agreements for differentiated services. Proceedings of the Seventh International Workshop on Quality of Service, London, England, , J. Hwang, H.J. Kim, and M.B.H. Weiss. Interprovider differentiated service interconnection management models in the internet bandwidth commodity markets. Telematics and Informatics, 19(4): , J. Jormakka, I. Grgic, and V. Siris. Methods for monitoring, controlling and charging QoS in IP networks. Telektronikk, 97(2/3): , Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

75 Literature Review Early mathematical models with duration and quality of services P.J. Bailey, I. Gamvros, and S. Raghavan. Ex-post Internet charging: an effective bandwidth model. In E.K. Baker, A. Joseph, A. Mehrotra, and M.A. Trick, editors, Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Springer, US, , C. Courcoubetisaib and V.A. Siris. Managing and pricing service level agreements for differentiated services. Proceedings of the Seventh International Workshop on Quality of Service, London, England, , J. Hwang, H.J. Kim, and M.B.H. Weiss. Interprovider differentiated service interconnection management models in the internet bandwidth commodity markets. Telematics and Informatics, 19(4): , J. Jormakka, I. Grgic, and V. Siris. Methods for monitoring, controlling and charging QoS in IP networks. Telektronikk, 97(2/3): , However, they all consider a monopolistic provider. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

76 Overview Our model Formulates a competitive oligopoly market of Internet network providers, Offers differentiated network services, Creates contracts for their users according to the users desires and needs. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

77 Overview Our model Formulates a competitive oligopoly market of Internet network providers, Offers differentiated network services, Creates contracts for their users according to the users desires and needs. The users/demand markets select contracts based on three main criteria: The amount of usage contracted for per period of time (the usage rate) during the contract duration (d), The quality level of service (q), The contract duration (T ). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

78 The Bipartite Structure of the Competition Among the Network Providers Network Providers 1 i m 7 Demand Markets 1 j n Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

79 The Bipartite Structure of the Competition Among the Network Providers Network Providers 1 i m 7 Demand Markets 1 j n Due to technological limitations: d ij d ij d ij, i, j Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

80 The Bipartite Structure of the Competition Among the Network Providers Network Providers 1 i m 7 Demand Markets 1 j n Due to technological limitations: d ij d ij d ij, i, j 0 q ij q ij, i, j Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

81 The Bipartite Structure of the Competition Among the Network Providers Network Providers 1 i m 7 Demand Markets 1 j n Due to technological limitations: d ij d ij d ij, i, j 0 q ij q ij, i, j T ij T ij T ij, i, j. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

82 Network Providers Behavior The price of i s service provision to j, p ij is: p ij = p ij (d, q, T ), i, j. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

83 Network Providers Behavior The price of i s service provision to j, p ij is: p ij = p ij (d, q, T ), i, j. The cost c ij incurred by network provider i for serving j is: c ij = c ij (d, q, T ), i, j. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

84 Network Providers Behavior The price of i s service provision to j, p ij is: p ij = p ij (d, q, T ), i, j. The cost c ij incurred by network provider i for serving j is: c ij = c ij (d, q, T ), i, j. The utility or profit of network provider i is the difference between his revenue and his total cost: n n U i = p ij T ij d ij c ij, i. j=1 j=1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

85 Theorem 5.1 Assume that the profit function U i (d, q, T ) is concave with respect to the variables and is continuous and continuously differentiable for each network provider i; + + m i=1 m i=1 m i=1 n [ n j=1 l=1 n [ n j=1 l=1 c il (d, q, T ) d ij n l=1 c il (d, q, T ) q ij n [ n c il (d, q, T ) j=1 l=1 d il T ij T il ] p ij (d, q, T ) T ij p il (d, q, T ) d ij n l=1 d il p il (d, q, T ) q ij p ij (d, q, T ) d ij ] Til (d ij dij ) d il ] Til (q ij qij ) n l=1 (T ij T ij ) 0, (d, q, T ) K.) p il (d, q, T ) T ij Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

86 Numerical Examples We initialized the algorithm for all the examples by setting d 0 ij = d ij ; q 0 ij = q ij ; T 0 ij = T ij, i, j. The contract durations, T ij s, are in hours, The reserved service usage rates, d ij s, are in Megabits/second, The prices p ij are in cents/megabit multiplied by Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

87 Example 5.1 Network Provider 1 Network Provider Demand Market 1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

88 Example 5.1 Network Provider 1 Network Provider Demand Market 1 The price functions at Demand Market 1 are: p 11 = d d q q T T 21, p 21 = d d q q T T 21. The cost functions for Network Providers 1 and 2 are, respectively: c 11 = (.0049 q q d 11 )T 11, c 21 = (.0037 q d21)t Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

89 Example 5.1 The utility functions of the network providers are: U 1 = p 11 d 11 T 11 c 11, U 2 = p 21 d 21 T 21 c d , 0 q , 8 T 11 40, 15 d , 0 q , 11 T Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

90 Example 5.1 The utility functions of the network providers are: U 1 = p 11 d 11 T 11 c 11, U 2 = p 21 d 21 T 21 c d , 0 q , 8 T 11 40, 15 d , 0 q , 11 T Equilibrium solution d 11 = 28.28, d 21 = 20.97, T 11 = 17.83, T 21 = 17.39, q 11 = 92.17, q 21 = 90.63, p 11 = 4.75, p 21 = The contract period for Network Provider 1 at Demand Market 1 is hours. The revenue in cents for Network Provider 1 for the contract is p 11 d 11 T seconds/hour = cents. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

91 Example 5.1 The utility functions of the network providers are: U 1 = p 11 d 11 T 11 c 11, U 2 = p 21 d 21 T 21 c d , 0 q , 8 T 11 40, 15 d , 0 q , 11 T Equilibrium solution d 11 = 28.28, d 21 = 20.97, T 11 = 17.83, T 21 = 17.39, q 11 = 92.17, q 21 = 90.63, p 11 = 4.75, p 21 = The contract period for Network Provider 1 at Demand Market 1 is hours. The revenue in cents for Network Provider 1 for the contract is p 11 d 11 T seconds/hour = cents. If the contract duration was 1 month, the revenue of a network provider per user would be approximately $35. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

92 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

93 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

94 This section corresponds to Chapter 6 of the dissertation, and is based on the paper: Nagurney, A., Saberi, S., Shukla, S., Floden, J Supply chain network competition in price and quality with multiple manufacturers and freight service providers. Transportation Research Part E: Logistics and Transportation Review 77, The paper has been cited in: Urciuoli, L., What are the causes of transport insecurity? Results from a survey with transport operators. Transport Policy 47, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

95 Freight Service Providers Growth of intercontinental multi-channel distribution, containerization, and direct to business/ customer shipping. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

96 Freight Service Providers Growth of intercontinental multi-channel distribution, containerization, and direct to business/ customer shipping. Freight service providers are increasingly focused on positioning themselves as more than just a commodity business. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

97 Freight Service Providers Growth of intercontinental multi-channel distribution, containerization, and direct to business/ customer shipping. Freight service providers are increasingly focused on positioning themselves as more than just a commodity business. Quality of service is driving logistics performance in both developed and emerging economies. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

98 Freight Service Providers Growth of intercontinental multi-channel distribution, containerization, and direct to business/ customer shipping. Freight service providers are increasingly focused on positioning themselves as more than just a commodity business. Quality of service is driving logistics performance in both developed and emerging economies. Intermodal company CargoNet withdrew from the Swedish rail market. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

99 Background and Motivation Increasingly, tough customer demands are also putting the transport system under pressure. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

100 Background and Motivation Increasingly, tough customer demands are also putting the transport system under pressure. Amazon.com recently submitted a patent for anticipatory shipping and speculative shipping. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

101 Background and Motivation Congestion is also highly relevant in cities in terms of freight distribution and last mile deliveries. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

102 Background and Motivation Congestion is also highly relevant in cities in terms of freight distribution and last mile deliveries. According to the American Road & Transportation Builders Association, nearly 75% of US freight is carried in the US on highways, and bottlenecks are causing truckers 243 million hours of delay annually with an estimated associated cost of $8 billion. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

103 Background and Motivation Congestion is also highly relevant in cities in terms of freight distribution and last mile deliveries. According to the American Road & Transportation Builders Association, nearly 75% of US freight is carried in the US on highways, and bottlenecks are causing truckers 243 million hours of delay annually with an estimated associated cost of $8 billion. According to an article in New York Times Magazine, poor freight service quality can lead to damaged and perished goods in China s biggest electronic commerce shopping day known as Singles Day. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

104 Quality in Freight Shipment Quality and price have been identified empirically as critical factors in transport mode selection for product/goods delivery (cf. Floden, Barthel, and Sorkina (2010), Saxin, Lammgard, and Floden (2005)). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

105 Quality in Freight Shipment Quality and price have been identified empirically as critical factors in transport mode selection for product/goods delivery (cf. Floden, Barthel, and Sorkina (2010), Saxin, Lammgard, and Floden (2005)). Encompasses factors such as on-time deliveries, reliability, and frequency (Danielis, Marcucci, and Rotaris (2005) and Zamparini, Layaa, and Dullaert (2011)). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

106 Relevant Literature Akerlof, G.A., The market for lemons: Quality uncertainty and the market mechanism. Quarterly Journal of Economics, 84(3), Spence, M., Monopoly, quality, and regulation. The Bell Journal of Economics, 6(2), Sheshinski, E., Price quality and quantity regulation in monopoly situation. Economica, 43, Mussa, M., Rosen, S., Monopoly and product quality. Journal of Economic Theory, 18, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

107 Relevant Literature Dixit, A., Quality and quantity competition. Review of Economic Studies, 46(4), Gal-or, E., Quality and quantity competition. Bell Journal of Economics, 14, Brekke, K.R., Siciliani, L., Straume, O.R., Price and quality in spatial competition. Regional Science and Urban Economics, 40, Nagurney, A., Li, D., A dynamic network oligopoly model with transportation costs, product differentiation, and quality competition. Computational Economics, 44(2), Nagurney, A., Li, D., Nagurney, L.S., Spatial price equilibrium with information asymmetry in quality and minimum quality standards. International Journal of Production Economics, 158, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

108 The Supply Chain Network Model with Price and Quality Competition Freight Service Providers Transportation Modes Manufacturing Firms Price Quality F 1 F i F N p i q i p F q F C 1 C j C O pijk m qijk m p 1 M C q C O 1 M 1 1 M j 1 M O 1 M O 1 M j 1 M1 1 M j 1 k Q Demand Markets 1 M 1 Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

109 The Supply Chain Network Model with Price and Quality Competition Freight Service Providers Transportation Modes Manufacturing Firms Price Quality F 1 F i F N p i q i p F q F C 1 C j C O pijk m qijk m p 1 M C q C O 1 M 1 1 M j 1 M O 1 M O 1 M j 1 M1 1 M j 1 k Q Demand Markets 1 M 1 The consumers at demand market k reveal their preferences for firm F i s product transported by freight service provider C j via mode m: d m ijk = d m ijk(p F, q F, p C, q C ), i = 1,..., N; j = 1,..., O; k = 1,..., Q; m = 1,..., M j. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

110 The Firms Behavior Supply of Firm: s i (p F, q F, p C, q C ) = O M Q j dijk(p m F, q F, p C, q C ); i. j=1 k=1 m=1 The Production Cost: PC i = PC i (s F (p F, q F, p C, q C ), q F ), i The Utility of Firm: UF i (p F, q F, p C, q C ) = p i [s i (p F, q F, p C, q C )] PC i, i. Bounds on Quality: Bounds on Price: q i q i q i, i. q i = p i p i, i. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

111 The Freight Service Providers Behavior The Transportation Cost: The Utility of Freight Service Provider: TC m ijk = TC m ijk(d(p F, q F, p C, q C ), q C ), i, j, k, m. UC j = N M O j i=1 k=1 m=1 [p m ijkd m ijk TC m ijk], j. Bounds on Quality: Bounds on Price: Feasible set, K 2 j ; K 2 O j=1 K 2 j. q m ijk qm ijk q m ijk, i, j, k, m. 0 p m ijk p m ijk, 1, j, k, m. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

112 The Equilibrium Conditions Definition 6.1: Nash Equilibrium in Prices and Quality Levels A price and quality level pattern (pf, qf, pc, qc) K 3 N i=1 K i 1 O j=1 K j 2, is said to constitute a Nash equilibrium if for each firm F i ; i = 1,..., N: where U Fi (p i, ˆp i, q i, ˆ q i, p C, q C) U Fi (p i, ˆp i, q i, ˆ q i, p C, q C), (p i, q i ) K 1 i, ˆp i (p 1,..., p i 1, p i+1,..., p N) and ˆ q i (q 1,..., q i 1, q i+1,..., q N), and if for each freight service provider C j ; j = 1,..., O: where U Cj (p F, q F, p C j, ˆ p C j, q C j, ˆ q C j ) U Cj (p F, q F, p Cj, ˆ p C j, q Cj, ˆ q C j ), pˆ C j (pc 1,..., pc j 1, pc j+1,..., pc O )and qˆ C j (qc 1,..., qc j 1, qc j+1,..., qc O ). Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

113 Variational Inequality Formulation Theorem 6.1 (p F, q F, p C, q C) K 3 is a Nash equilibrium according to Definition 6.1 if and only if it satisfies the variational inequality: N i=1 O j=1 U Fi (p F, q F, p C, q C) p i N i=1 k=1 m=1 (p i p i ) M Q j U Cj (pf, qf, pc, qc) O j=1 N i=1 k=1 m=1 p m ijk N i=1 U Fi (p F, q F, p C, q C) q i (q i q i ) (p m ijk p m ijk ) M Q j U Cj (pf, qf, pc, qc) q m ijk (p F, q F, p C, q C ) K 3, (q m ijk q m ijk ) 0, Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

114 A dynamic adjustment process for Manufacturers Price and Quality We now propose dynamic adjustment processes for the evolution of the firms product prices and quality levels and those of the freight service providers (carriers). Rate of change of p i : U Fi (p F,q F,p C,q C ), if 0 < p p i < p i ṗ i = i max { 0, min{ U F (p i F,q F,p C,q C ), p p i } }, if p i = 0 or p i = p i. i Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

115 A dynamic adjustment process for Manufacturers Price and Quality We now propose dynamic adjustment processes for the evolution of the firms product prices and quality levels and those of the freight service providers (carriers). Rate of change of p i : U Fi (p F,q F,p C,q C ), if 0 < p p i < p i ṗ i = i max { 0, min{ U F (p i F,q F,p C,q C ), p p i } }, if p i = 0 or p i = p i. i Rate of change of q i : U Fi (p F,q F,p C,q C ), if q q q i = i i < q i < q i max { q i, min{ U F (p i F,q F,p C,q C ), q q i } }, if q i = q i i or q i = q i. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

116 A dynamic adjustment process for Freight Service Providers Price and Quality Rate of change of pijk: m U Cj (p F,q F,p C,q C ) ṗijk m p = m, if 0 < pijk m < p ijk m ijk max { 0, min{ U C (p j F,q F,p C,q C ) p ijk m, p ijk} } m, if pijk m = 0 or p ijk. m Rate of change of qijk: m U Cj (p F,q F,p C,q C ) q ijk m q = m, if q m < ijk ijk qm ijk < q ijk m max { q m, min{ U C (p j F,q F,p C,q C ) ijk q ijk m, q ijk} } m, if qijk m = q m or ijk qm ijk. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

117 Example 6.2 The supply chain network topology is depicted as here: Manufacturing Firm F 1 Freight Service Provider Demand Market C The demand functions are: d = p q p q p q 2 111, d = p q p q p q Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

118 Example 6.2 The supply of manufacturing firm F 1 is : s 1 = d d The transportation costs of the freight service provider C 1 for modes 1 and 2 are: TC =.5d (q 1 111) 2, TC =.45d (q 2 111) d 2 111q The utility of freight service provider C 1 is: U C1 = p 1 111d p 2 111d TC TC 2 111, 0 p , 9 q Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

119 Example 6.2: Result The equilibrium solution, after 166 iterations, is: p = 21.68, p = 24.16, p 1 = q = 14.58, q = 22.43, q 1 = Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

120 Example 6.3 Manufacturing Firm Freight Service Providers Demand Market F 1 C 1 C Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

121 Example 6.3 The demand functions are: d = p q p q p q p q1 121, d = p q p q p q p q1 121, d = p q p q p q p q The transportation costs of freight service provider C 1 are: TC =.5d (q111) d121, 1 TC =.45d (q111) d111q 2 111, 2 and that of freight service provider C 2 is: TC =.64d (q121) 1 2. The utility of C 2 is: U C2 = p 1 121d TC p , 12 q Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

122 Example 6.3: Result The equilibrium solution, computed after 218 iterations, is: p = 45.69, p = 45.32, p = 44.82, p 1 = 53.91, q = 31.69, q = 41.32, q = 41.24, q 1 = The utility of manufacturing firm F 1 is and that of freight service providers C 1 and C 2 are and , respectively. The inclusion of an additional freight service provider helps to increase the total demand. So that, manufacturing firm F 1 increases his quality level and, consequently, his price. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

123 Example 6.5 Manufacturing Firms F 1 F 2 Freight Service Providers C 1 C Demand Markets 1 2 I consider competition at the manufacturers level, the freight service providers level, and between modes of a particular service provider, wherein all these players are competing to satisfy the demands at two different demand markets. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

124 Example 6.5: Result The equilibrium solution, after 254 iterations, is: p = 56.79, p = 55.45, p = 72.96, p = 36.93, p = 55.19, p = 53.55, p = 62.77, p = 53.28, p = 72.94, p = 65.91, p = 76.15, p = 83.73, p 1 = 63.76, p 2 = 64.90, q 1 = , q 2 = , q = 39.53, q = 51.20, q = 74.61, q = 23.54, q = 50.93, q = 51.05, q = 46.25, q = 36.72, q = 76.89, q = 69.56, q = 61.18, q = The price and quality levels have gone up as well as utilities for both manufacturers and carriers as compared to Example 6.3 since there are two demand markets to be satisfied now as opposed to one. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

125 Summary and Conclusions A game theory supply chain network model in both static and dynamic versions with multiple manufacturers and freight service providers is developed. The model captures competition on price and quality for both manufacturers and freight service providers. Variational inequality theory was employed in the formulation to govern equilibrium. The computational procedure utilized was the Euler method. Solutions to a series of numerical examples - small to large scenarios and their variants are provided with different scenarios. As we increase the competition, the entities increase the quality level of their products and as the result the price of them unless the sensitivity of consumers are so high with respect to price. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

126 1 Introduction 2 Price and Quality Competition A Service-Oriented Internet Network Economic Model with Price and Quality Competition in Both Content and Network Provision A Dynamic Service-Oriented Internet Network Economic Model with Price and Quality Competition 3 Quality with Flexible Contracts A Differentiated Service-Oriented Internet Network Economic Model with Duration-Based Contracts 4 Supply Chain with Freight Services A Supply Chain Network Model with Competition in Price and Quality between Multiple Manufacturers and Freight Service Providers with Multiple Modes of Shipment 5 Conclusions and Directions for Future Research Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

127 Dissertation Conclusions Service-oriented network frameworks corresponding to two main applications including, next generation Internet and freight transport supply chain were developed. The models: captured price and quality competition in service-oriented networks in both static and dynamic settings. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

128 Dissertation Conclusions Service-oriented network frameworks corresponding to two main applications including, next generation Internet and freight transport supply chain were developed. The models: captured price and quality competition in service-oriented networks in both static and dynamic settings. addressed pricing strategies in the future Internet networks with dynamic contract duration. Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

129 Dissertation Conclusions Service-oriented network frameworks corresponding to two main applications including, next generation Internet and freight transport supply chain were developed. The models: captured price and quality competition in service-oriented networks in both static and dynamic settings. addressed pricing strategies in the future Internet networks with dynamic contract duration. assessed the price and quality competition among multiple manufacturers and freight service providers with multiple modes of shipment Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77

130 Directions for Future Research Distribution supply chain network challenges: huge cost of transportation globalization, trade growth, and worldwide deregulation of transportation consistently increasing of world maritime shipment Doctoral Dissertation Defense University of Massachusetts Amherst August 12, / 77