Shape factor (K) and the price elasticity of demand (PED) in stationary markets

Originality

The originality of our work relates to two aspects of market economics. The first aspect is studying the practical volume-based pricing strategy that is used by many providers around the world. In Chapter 1, we consider different access technologies to model the relation between spectrum assignment mechanisms and the profit of providers. We propose a method to relate the data usage pattern of subscribers to data rate and service availability. For the first time, to the best of our knowledge, we consider the available budget of subscribers as a random variable and introduce a mathematical framework for SLA-based volume-based data plans. We also model providers with multiple data packages and investigate the package renovation process for the subscribers during their monthly payment period. The second aspect is the comprehensive study of coalitions in wireless markets in which we consider technological and service-oriented HetNets. Our work in Chapter 2 studies the impact of providers’ cost functions on their strategy of coalition formation. We propose multi-provider utility functions for users to study their data usage behavior under cellular-cellular and cellular- WiFi cooperative providers.

Unlike many other studies in this field, we build our analysis based the markets with negative externalities. In this way, the convergence of an existing coalition formation process is proved for wireless market. We model the role of regulatory units in coalition formation and analyze their best strategy based on the status quo of the Wireless HetNet market. Considering the service-oriented HetNets, our work in Chapter 3 is the first work which considers a class of applications which can be offered free of charge to all users based on a cooperation mechanism between CP and cellular SP. To the best of our knowledge, this is the first work that considers an analysis of the payments’ directions to provide a completely free access for several types of mobile services such as mapping applications and intelligent personal assistants. Our work shows that the directions of payments in today’s cellular market can be altered to increase the satisfaction of end users at no profit-loss for both SP and CP. We also found the side-payment from CP to SP by using the concepts of the Nash bargaining solution as well as the Shapely value that also proves the possibility of our proposed method for selective free content delivery.

Cooperative game theory

A cooperative game, especially from an economic viewpoint, is using coalition among decision makers to increase their profit. In a competitive market, forming coalitions changes the state of the market from individual competition to coalition competitions. There are two general forms of coalitional games. First, the canonical cooperative games (Saad et al.) where players want to form a coalition that consists of all players i.e. grand coalition. In this form, the profit division mechanisms that make the grand coalition stable are the main subject of study. The main usage of canonical games’ concepts is in analyzing the profit division among the members of a coalition mechanisms such as the core, Shapley value, and nucleolus mechanisms. Since the grand coalition leads to a monopoly market, the regulatory entities do not allow formation of such coalitions. Therefore, it is not practical to investigate such cooperations for interprovider cooperations. Hence, we exclude discussing such games in this thesis. The second form of cooperative games is the coalition formation games where the structures and processes that force the players to a particular set of coalitions and the stability of these coalition structures are the research subjects. While in the canonical coalition games the payoff is the most important factor, in coalition formation games the network structure and cost of cooperation (Saad et al.) are the main factors. A coalition formation game has the following characteristics:

• The game in not necessarily supperadditive, which means that the cooperation does not always lead to higher overall profit for the coalition unit. Also, the utility function can be in the form of transferable (TU) or non-transferable utilities (NTU).

• While the coalition forming can provide an additional profit for players, there is also a cost of formation.

• The grand coalition is not always the coalition with the maximum profit.

• Environmental changes like players’ strength variation can change the best coalition (Saad et al.).

Coalition formation games can be divided into two major subcategories: static coalition formation games and dynamic coalition formation games. The former analyzes the effect of an external factor on the coalitional structure. The latter investigates the process of forming the coalitional structure (Saad et al.). The coalitional game considered in this research is, by its nature, a game with negative externalities, which means that players in the market with any coalitional structure (CS) try to reduce other members’ profit and maximize their revenue. In our model, the coalition formation process can be sequential or takes place in a parallel manner for all negotiators.

Results We achieved the following results in this thesis:

a. In Chapter 1, we modeled the markets with volume-based pricing and linked the data usage and price to the offered service data rate based on the utility of users and the available bandwidth to the provider. We found the optimal service parameters for providers with different access technologies such as OFDMA and CDMA. The relation between the available spectrum bandwidth of the provider and the offerable data rate to the users is investigated based on the data cap and price on a data plan. We considered the budget of subscribers as a key parameter and modeled their package renovation procedure. A model for service availability in the dynamic sub-carrier allocation method is proposed in which provider guarantees a data rate and service availability level to the users regardless of their distance from a base station. In this way, we built a mathematical framework that connects the cap of a data plan and its price to the optimal data rate and service availability. The markets with multiple packages are analyzed in which the provider adjust the cap of each package to address a particular group of users based on their monetary resources. We considered the case of bandwidth splitting in which the provider can assign separated spectrum bandwidths for its voice and data subscribers. We showed the efficiency of our model in giving the optimal market parameters with the help of several realistic numerical scenarios.

b. In Chapter 2, we analyzed technological HetNets. We modeled the markets with flat-rate pricing and found the optimal values of data usage for subscribers based on the data rate, data unit price and coverage of providers. We analyzed several market forms such as monopoly, duopoly, and oligopoly and investigated the effect of competition on the service parameters. We showed that the providers’ cost function affects their best strategy to enter a coalition formation process. In particular, we proved that in the case of linear cost functions, the providers are better off to expand their network without cooperating with their competitors. In special forms of exponential costs, providers need to form a coalition to increase their profit, otherwise, investing on network expansion is not profitable for them. We proved the form of a multi-provider utility function which is used to model the behavior of subscribers when they are under the coverage of a coalition of providers. We modeled the multi-provider utility functions for cellular-cellular and cellular-WiFi coalitional models. The profit of the providers is analyzed based on the usage patterns in the multi-provider model. We used an existing coalition formation process which has a mathematical base for the markets with negative externalities. We proved that in wireless markets in which users consistently churn to newer technologies, a coalition formation process is always convergent. We provided a model for the role of regulatory units in coalition formation processes and proposed a method that finds the best cooperation strategies for increasing the social efficiency. The regulatory entity uses this method to allow or ban a coalition formation action. Various scenarios for coalition formation are analyzed in which we showed that the cooperation of small providers is an efficient way to compete with a monopolist. The efficiency is measured based on a social efficiency function that balances the overall payoff of the users as well as the profit of the providers.

c. In Chapter 3, we analyzed service-oriented HetNets. We investigated the statistics of real mobile markets provided by (Ericsson, 2016) and defined three categories of mobile applications based on the usage patterns of mobile subscribers. We found applications with particular business models that can be offered free of charge to all subscribers without being concerned about their data usage in those applications. We call this model a selective free content (SFC) program. Three categories of such applications are investigated: the Mapping applications along with intelligent personal assistants, the cloud-based IoT services, and the smart city and e-governance applications. We showed the difference between these categories by analyzing the direction of payments in each category that cause different business models. We showed the possibility of an SFC program by modeling the interaction between users, service and content providers in a wireless market. A three-stage Stackelberg game is introduced and solved by backward induction. Each stage of the game shows the best response strategy of one network entity. The sidepayment from CP to SP is found based on the Nash bargaining solution as well as the concept of Shapely value. Our model showed that even with a linear profit model for the CP, an SFC program is possible. We found the profit threshold of SP in which an SFC program is possible. Several realistic numerical scenarios are analyzed, and the sidepayment from CP to SP is found based on different bargaining powers of SP over CP.

Table des matières

INTRODUCTION
CHAPTER 1 PRICING THE VOLUME-BASED DATA SERVICES IN CELLULAR WIRELESS MARKETS
1.1 Related Works
1.2 Notation and System model
1.2.1 Data rate models based on channel access method
1.2.1.1 Shared single carrier
1.2.1.2 Dynamic Bandwidth Allocation
1.3 Data package pricing
1.3.1 Single-package problem
1.3.1.1 Users’ decision criterion
1.3.1.2 Provider profit
1.3.2 User monetary resources and budget
1.3.2.1 Multi-package data network with wealth information
1.3.3 Package Renovation
1.4 Dynamic Bandwidth Allocation Model
1.4.1 Finding b( j)
1.4.2 Finding P( j)
1.4.3 Expected blocking with user utility applied
1.4.4 Optimization problem
1.4.5 Final profit
1.4.6 Multi-package market for dynamic allocation method
1.5 Numerical Results
1.6 Conclusion
CHAPTER 2 COALITIONS IN HETEROGENEOUS WIRELESS NETWORKS: USER BEHAVIOR AND PROVIDER PROFIT
2.1 Related Works
2.2 Basic Notation and Assumptions
2.3 Operator Selection
2.3.1 Payoff function for the users
2.3.2 Provider selection mechanism
2.4 Shape factor (K) and the price elasticity of demand (PED) in stationary markets
2.5 Provider profit in different market forms
2.5.1 Monopoly
2.6 Duopoly
2.6.1 Oligopoly
2.7 Coalition formation
2.7.1 Multi-provider payoff for single price networks
2.7.2 The multi-provider payoff function for dual price scheme networks
2.7.3 Coalition formation
2.7.3.1 Regulatory unit policies on coalition formation
2.8 Numerical Analysis
2.9 Conclusion and future work
CHAPTER 3 SELECTIVE FREE CONTENT IN CELLULAR NETWORKS
3.1 On the possibility of selective free access
3.1.1 Category 1: mapping and other business related applications
3.1.1.1 Other candidates in this category
3.1.2 Category 2: real-time cloud-based IoT services
3.1.3 Category 3: Smart cities and the social right to access the Internet
3.1.4 Characteristics of eligible applications for the SFC program
3.2 The Game for Category 1 applications
3.2.1 Stage III: user’s utility and best response
3.2.2 Stage II: The best strategy for SP
3.2.3 The profit of SP in non-cooperative strategy
3.2.3.1 Ultra-high price regime:
3.2.3.2 High price regime:
3.2.3.3 Moderate price regime:
3.2.3.4 low price regime: p
3.2.4 The profit of SP in cooperative strategy
3.2.4.1 Ultra high price regime:
3.2.5 Stage I: The strategies of CP
3.2.6 Nash bargaining solution (NBS)
3.2.7 Shapley value
3.3 numerical results
3.4 Conclusion
CONCLUSION AND RECOMMENDATIONS
APPENDIX I PROOFS OF THE PROPOSITIONS IN CHAPTER 1
APPENDIX II PROOFS OF THE PROPOSITIONS IN CHAPTER 2
APPENDIX III PROOFS OF THE PROPOSITIONS IN CHAPTER 3
BIBLIOGRAPHY

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