Game Theory in Wireless and Communication Networks Theory

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Game Theory in Wireless and Communication Networks: Theory, Models, and Applications Lecture 8 Contract

Game Theory in Wireless and Communication Networks: Theory, Models, and Applications Lecture 8 Contract Theory Zhu Han, Dusit Niyato, Walid Saad, and Tamer Basar,

Overview of Lecture Notes l Introduction to Game Theory: Lecture 1, book 1 l

Overview of Lecture Notes l Introduction to Game Theory: Lecture 1, book 1 l Non-cooperative Games: Lecture 1, Chapter 3, book 1 l Bayesian Games: Lecture 2, Chapter 4, book 1 l Differential Games: Lecture 3, Chapter 5, book 1 l Evolutionary Games: Lecture 4, Chapter 6, book 1 l Cooperative Games: Lecture 5, Chapter 7, book 1 l Auction Theory: Lecture 6, Chapter 8, book 1 l Matching Game: Lecture 7, Chapter 2, book 2 l Contract Theory, Lecture 8, Chapter 3, book 2 l Learning in Game, Lecture 9, Chapter 6, book 2 l Stochastic Game, Lecture 10, Chapter 4, book 2 l Game with Bounded Rationality, Lecture 11, Chapter 5, book 2 l Equilibrium Programming with Equilibrium Constraint, Lecture 12, Chapter 7, book 2 l Zero Determinant Strategy, Lecture 13, Chapter 8, book 2 l Mean Field Game, Lecture 14, book 2 l Network Economy, Lecture 15, book 2 [2]

OUTLINE • Motivation • Contract theory – Adverse Selection – Moral Hazard • Applications

OUTLINE • Motivation • Contract theory – Adverse Selection – Moral Hazard • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network 3

Motivation • Imminent wireless traffic boost • Wireless network capacity crunch – Facebook and

Motivation • Imminent wireless traffic boost • Wireless network capacity crunch – Facebook and You. Tube – Smartphones and tablets – Users (will) have anywhere, anytime wireless communications – Additional spectrum is a tool that can help relieve congestion on wireless networks – Spectrum crisis 4

Possible Solutions for Capacity Crunch • Current cellular capacity constraint – Upper bounded by

Possible Solutions for Capacity Crunch • Current cellular capacity constraint – Upper bounded by Shannon theory • Possible solutions – Introduce more access points (APs) by making the wireless networks heterogeneous • Device-to-device (D 2 D) communication • Cognitive radio network (CRN) • Software defined network (SDN) • Small cell • Wireless network virtualization Combine Cellular and Heterogeneous Cell Capacity Optimal rate Kumar Scaling Law network capacity relies on bandwidth and APs Sum rates • Need of cooperation – e. g. traffic offloading Number of UE 5

Observation • Dramatic growing market of location based service – Navigation, local search, mobile

Observation • Dramatic growing market of location based service – Navigation, local search, mobile advertisements, emergency notification • Role Changing of users – Various embedded sensors in smartphone – Users are not only data receivers, but also active data providers 6

Possible Solution for Location Based Data Crunch • Sophisticated location based service constrained by

Possible Solution for Location Based Data Crunch • Sophisticated location based service constrained by – Adequate and comprehensive location based data • Possible solution – Crowdsourcing • Large group of users regularly transmit data obtained by the embedded sensors to the principal – Popular apps • Navigation: Google Map • Social network: Yelp • Sport: Sports Tracker • Need of cooperation 7

Possible Solution to Ensure Cooperation • In both traffic offloading and data uploading processes

Possible Solution to Ensure Cooperation • In both traffic offloading and data uploading processes – Third parties/users are consuming resources (battery power and computing capacity), and threaten to privacy • Motivations are needed to ensure cooperation – To successfully increase wireless network capacity – To collect adequate location based data • Design incentive mechanisms – Considering third parties/users' consumptions during the offloading/uploading processes – Provide necessary rewards/compensations according to their contributions 8

Methodology Adopted • Contract Theory – How to regulate monopoly with asymmetric information by

Methodology Adopted • Contract Theory – How to regulate monopoly with asymmetric information by introducing cooperation among competitors • Regulators don’t know everything about how firms are operating – Employer and employee(s)/Buyer and seller(s) • A manager hiring a worker • A farmer hiring a sharecropper • Jean Tirole - Nobel Prize winner in economic science of 2014 – Most economic theory before consisted of price caps for monopolists and preventing cooperation among competitors • Ideal analysis and unpractical in real world economics – “A Nobel Prize for Real World Economics” • Says the Enlightened Economist blog, written by Diane Coyle • Great potential to ensure cooperation in wireless networks • Two general types of asymmetric information problems – Hidden-information problem---- Adverse Selection – Hidden-action problem---- Moral Hazard 9

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) •

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) • One-dimension • Static contracting • Multi-dimension • Repeated contracting • Multilateral (One-to-many) • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network 10

Adverse Selection of Ph. D Student • The plan you try to find the

Adverse Selection of Ph. D Student • The plan you try to find the advisor with financial aid • The real plan • The secret plan • “I am going to be a professor at a major research university after I graduate. ” • Look for career alternatives • Become a baker/rock star/writer 11

Adverse Selection • Asymmetric information: – Relevant characteristics of the employee are hidden from

Adverse Selection • Asymmetric information: – Relevant characteristics of the employee are hidden from the employer • Distaste for certain tasks, the level of competence – Preference/productivity are private information of employee, but unavailable to employer • All employee types would respond by "pretending to be skilled" to get the higher wage • Employers respond to adverse selection by revelation principle – Employer offers multiple employment contracts • Different contracts destined to different skill level employees • Employee selects contract to maximize its benefit but will reveal his skill level 12

Bilateral Contracting • 13

Bilateral Contracting • 13

Bilateral Contracting • Individual Rationality (IR): The contract that selected should guarantee a nonnegative

Bilateral Contracting • Individual Rationality (IR): The contract that selected should guarantee a nonnegative utility Incentive Compatible (IC): Each one sho prefer the contract designed specifically for its own type 14

Bilateral Trading Extension • 15

Bilateral Trading Extension • 15

Multi-dimension Bilateral Contracting • One-dimension type Employer Seller Money Output Goods Money Employee with

Multi-dimension Bilateral Contracting • One-dimension type Employer Seller Money Output Goods Money Employee with uncertain capability Buyer with uncertain reservation price • Multi-dimension types –Seller who sells multiple different goods –A large supermarket or department store sells several thousand different items • Sales –Offer quantity discounts on anyone of these items –Special deals on any bundle of them 16

Example with Two Goods Type Probability A 90 10 100 0. 25 B 80

Example with Two Goods Type Probability A 90 10 100 0. 25 B 80 40 120 0. 25 C 40 80 120 0. 25 D 10 90 100 0. 25 17

Multilateral Contracting One-to-many • One-to-many – Several contracting parties have private information • Key

Multilateral Contracting One-to-many • One-to-many – Several contracting parties have private information • Key conceptual difference with bilateral contracting – The principal's contract-design problem is not controlling a single agent's decision problem – Designing a game involving the strategic behavior of several agents interacting with each other, and predicting how the game will be played by the agents • Auction 18

Repeated Contracting • Fixed Types – The agent's type is drawn once and remains

Repeated Contracting • Fixed Types – The agent's type is drawn once and remains fixed over time – Information revealed through contract execution – E. x. Bargaining Seller High Price • The seller sets a price so high that cannot sell with probability 1 Buyer H – If the buyer did not buy, the seller opens up a • Accept new trading opportunity at a lower price – High-valuation buyers will anticipate that an initial unwillingness to trade will prompt the Buyer H seller to lower price • Will anticipate • Changing Types – Types are independent across periods, things change drastically – There is a new independent draw every period – E. x. oil company spending and show initial unwillingness Buyer L • Reject Seller Low Price Buyer L • Accept 19

OUTLINE • Contract theory • Bilateral (One-to-one) • One-dimension • Multi-dimension • Repeated contracting

OUTLINE • Contract theory • Bilateral (One-to-one) • One-dimension • Multi-dimension • Repeated contracting • Multilateral (One-to-many) – Adverse Selection • Static contracting – Moral Hazard • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network 20

Moral Hazard of Ph. D student • What my parents thinks I do •

Moral Hazard of Ph. D student • What my parents thinks I do • What I actually do – When advisor presents • What my advisor thinks I do – When advisor on travel 21

Moral Hazard • Asymmetric information: – Employee's actions that are hidden from the employer

Moral Hazard • Asymmetric information: – Employee's actions that are hidden from the employer • Whether it works or not, how hard it works, how careful it is • In contrast to Adverse Selection – Informational asymmetries arising after the signing of a contract – Employee is not asked to choose from a menu of contracts • But from a menu of action-reward pairs • Employers typically respond to moral hazard by – Rewarding good performance • Through bonus payments, piece rates, efficiency wages, stock options – And/or punishing bad performance • Through layoffs 22

Bilateral Contracting One-dimension Hires Employer designs optimal contract to maximizes utility Employee chooses optimal

Bilateral Contracting One-dimension Hires Employer designs optimal contract to maximizes utility Employee chooses optimal effort to maximize utility Employee prefers to work than not 23

One-Dimension VS Multi-Dimension • One-dimension model is too abstract to capture the main features

One-Dimension VS Multi-Dimension • One-dimension model is too abstract to capture the main features of the user's contributions – Employees are supposed to work on several different tasks – Employee's action set is richer than one-dimension • Reward users based on one aspect of the performance will affect the overall performance – Measures only a part of what users are encouraged to contribute – There is a risk in this mechanism • Induce users to overwhelmingly focus on the part that will be rewarded • Neglect the other components that can enrich the output • Example: exam-oriented education 24

Bilateral trading Multi-dimension • 25

Bilateral trading Multi-dimension • 25

Multilateral Contracting One-to-Many • In corporate finance and firm organization – Output is produced

Multilateral Contracting One-to-Many • In corporate finance and firm organization – Output is produced by a group of employees • Act and react among employees – Positive: Cooperation or Competition • Drive incentive – Negative: Collision among agent • Auditing • How to reward a group of employees? – Group’s aggregate effort • Problem of free riding on others’ efforts – Individual effort • Absolute performance – Hard to measure • Relative performance – Lose of incentive 26

Issues When Measure by Absolute Performance • Common shock when rewarding users based on

Issues When Measure by Absolute Performance • Common shock when rewarding users based on absolute performance – Negative mean measurement error at user's performance Typically seen in economics: • The principal has a strong incentive to cheat by claiming that users had poor Booming and depression that are unpredictable, and typically performances that deserve low rewards impact supply or demand throughout the markets • Principal can pay less, an increase in utility/decrease of all users' utilities – Positive mean measurement error at user's performance • Every user's performance results in an increase at the principal's observation • Users are rewarded more, utility increases/principal encounters a loss of utility • In general case, common shock is unobservable to either or both sides – Incentive mechanism based on absolute performance can be easily affected • Relative performance (tournament design) can filter out this common shock problem – Ordinal ranking is hard to manipulate – The principal has to offer the fixed amount of rewards no matter who wins 27

Repeated Bilateral Contracting • Interaction of two effects results in a considerably more complex

Repeated Bilateral Contracting • Interaction of two effects results in a considerably more complex than the static problem – Repetition can make the employee less averse to risk • Engage in "self-insurance" – Choose when to work and offset a bad performance in one period by working harder the next period – Repeated output observations can provide better information about the employee's choice of action 28

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) •

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) • One-dimension • Static contracting • Multi-dimension • Repeated contracting • Multilateral (One-to-many) • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network Yanru Zhang, Lingyang Song, Walid Saad, Zaher Dawy, and Zhu Han, “Contract-Based Incentive Mechanisms for Device-to-Device Communications in Cellular Networks, ” IEEE Journal on Selected Areas on Communications (JSAC), Special Issue on Recent Advances in Heterogeneous Cellular Networks, vol. 33, no. 10, pp. 2144 -2155, Oct. 2015. 29

D 2 D Communication • User equipments (UEs) transmit data signals to each other

D 2 D Communication • User equipments (UEs) transmit data signals to each other directly – Over the licensed band – Under the control of base station (BS) • Why traffic can be offloaded? – Popular contents are requested more – BSs serving different users • With the same contents • Using multiple duplicate transmissions • Main design challenge to offload cellular traffic – Incentivize content owners to participate and cooperate via D 2 D communication 30

Apply of Adverse Selection • Information asymmetry • BS prefers users with high preference/capability

Apply of Adverse Selection • Information asymmetry • BS prefers users with high preference/capability • User will attempt to harness more reward by claiming that it is a high preference/capability user • The actual preference/capability • Naturally known by the users • The BSs may not be aware of • Adverse selection model can overcome this information asymmetry • Offering different contracts designed for different type users • Specify multiple contracts: (performance, reward) 31

Utility Functions • • 32

Utility Functions • • 32

Simulation Results Utility of BS with different type of UEs Utility of UE when

Simulation Results Utility of BS with different type of UEs Utility of UE when selecting different type contracts 33

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) •

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) • One-dimension • Static contracting • Multi-dimension • Repeated contracting • Multilateral (One-to-many) • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network Yanru Zhang, Yunan Gu, Lanchao Liu, Miao Pan, Zaher Dawy, and Zhu Han, “Incentive Mechanism in Crowdsourcing with Moral Hazard, ” IEEE Wireless Communications and Networking Conference (WCNC), New Orleans, LA, Mar. 2015. Yanru Zhang, Yunan Gu, Lingyang Song, Miao Pan, Zaher Dawy, and Zhu Han, “Tournament Based Incentive Mechanism Designs for Mobile Crowdsourcing, ” IEEE Globe Communication Conference (GLOBECOM), San Diego, CA, Dec. 2015. 34

Multi-Dimention Moral Hazard in Crowdsourcing • Incentivize users continuously uploading data instead of shutting

Multi-Dimention Moral Hazard in Crowdsourcing • Incentivize users continuously uploading data instead of shutting down the location services – Moral hazard model • Principal “employs” the users to upload data • Reward users based on performance • The necessarity to adopt multidimension model – User are suppose to work on different tasks – User’s cost include time, power, experience 35

System Model • • 36

System Model • • 36

Utility Functions • • 37

Utility Functions • • 37

Simulation Results 38

Simulation Results 38

Crowdsourcing by Tournament • 39

Crowdsourcing by Tournament • 39

Simulation Results Measurement Error Covariance Approximation of optimal contract by tournament The utility of

Simulation Results Measurement Error Covariance Approximation of optimal contract by tournament The utility of the principal as the number of users varies

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) •

OUTLINE • Contract theory – Adverse Selection – Moral Hazard • Bilateral (One-to-one) • One-dimension • Static contracting • Multi-dimension • Repeated contracting • Multilateral (One-to-many) • Applications – Device-to-device communication – Mobile crowdsourcing – Cognitive radio network Yanru Zhang, Yunan Gu, Miao Pan, Zaher Dawy, Lingyang Song, and Zhu Han, “Financing Contract with Adverse Selection and Moral Hazard for Spectrum Trading in Cognitive Radio Networks, ” invited, IEEE China Summit and International Conference on Signal and Information Processing (China. SIP), Chengdu, China, Jul. 2015. 41

Cognitive Radio Networks • Cognitive radio networks (CRNs) – Dynamic spectrum sharing where CR

Cognitive Radio Networks • Cognitive radio networks (CRNs) – Dynamic spectrum sharing where CR users can opportunistically access the licensed spectrum • Primary user (PU) – The licensed user to utilize the frequency band • Secondary user (SU) – Can only utilize those spectrum resources when the PU is vacant • Spectrum trading in CRNs – SU can purchase/rent the available licensed spectrum if it is in need of radio resources to support its traffic demands – Achieves SU's dynamic spectrum accessing/sharing – Creates more economically benefits for the PU 42

Adverse Selection and Moral Hazard in CRN • When SU purchasing spectrum from PU

Adverse Selection and Moral Hazard in CRN • When SU purchasing spectrum from PU – Allows the SU to do a financing – As we buy a house or a car • Problem of adverse selection – The PU may not have the full knowledge of the SU's capability in utilizing the spectrum as a service provider • Problem of moral hazard – The PU neither knows how much effort the SU puts into • How much down payment and installment payment to request? 1) Down payment : Pay part of the total amount at the point of signing the contract SU 3) Utilize spectrum • Transmit package • Generate revenue 2) Release the spectrum to the SU PU 4) Installment payment: The SU pays the rest of the loan 43

System Model Revenue Realizations Type of Capability • • Operation Cost 44

System Model Revenue Realizations Type of Capability • • Operation Cost 44

Information Asymmetry Adverse Selection • Moral Hazard • 45

Information Asymmetry Adverse Selection • Moral Hazard • 45

Payoffs Payoff of SU • Payoff of PU • 46

Payoffs Payoff of SU • Payoff of PU • 46

Simulation Results 47

Simulation Results 47

CONCLUSION • Theory – Adverse selection and moral hazard – Static and repeated, one/multi-dimension,

CONCLUSION • Theory – Adverse selection and moral hazard – Static and repeated, one/multi-dimension, one/multi-agents • Application in wireless networks – D 2 D communications, mobile crowdsourcing, cognitive radio network • Future work – Extension of previous models – New models in hierarchies organization, incomplete contract, investment 48

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