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Overview of Lecture Notes

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. Introduction to Game Theory: Lecture 1, book 1 Non-cooperative Games: Lecture 1, Chapter 3, book 1

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Overview of Lecture Notes

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  1. Game Theory in Wireless and Communication Networks: Theory, Models, and ApplicationsLecture 8Contract TheoryZhu Han, Dusit Niyato, Walid Saad, and Tamer Basar,

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

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

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

  5. 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 (D2D) communication • Cognitive radio network (CRN) • Software defined network (SDN) • Small cell • Wireless network virtualization • Need of cooperation • e.g. traffic offloading Combine Cellular and Heterogeneous Cell Capacity Optimal rate Sum rates Kumar Scaling Law network capacity relies on bandwidth and APs Number of UE

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

  7. 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 Large group of users

  8. 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

  9. 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

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

  11. Adverse Selection of PhD 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

  12. 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

  13. Bilateral Contracting

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

  15. Bilateral Trading Extension

  16. Multi-dimensionBilateral Contracting • One-dimension type • 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 Money Employer Employee with uncertain capability Output Goods Seller Buyer with uncertain reservation price Money

  17. Example with Two Goods

  18. Multilateral ContractingOne-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

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

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

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

  22. 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

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

  24. 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

  25. Bilateral tradingMulti-dimension

  26. 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

  27. Issues When Measure by Absolute Performance • Common shock when rewarding users based on absolute performance • Negative mean measurement error at user's performance • The principal has a strong incentive to cheat by claiming that users had poor performances that deserve low rewards • 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 Typically seen in economics: Booming and depression that are unpredictable, and typically impact supply or demand throughout the markets

  28. 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

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

  30. D2D 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 D2D communication

  31. 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)

  32. Utility Functions

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

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

  35. 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 multi-dimension model • User are suppose to work on different tasks • User’s cost include time, power, experience

  36. System Model

  37. Utility Functions

  38. Simulation Results

  39. Crowdsourcing by Tournament

  40. Approximation of optimal contract by tournament Simulation Results Measurement Error Covariance

  41. OUTLINE • Contract theory • Adverse Selection • Moral Hazard • Applications • Device-to-device communication • Mobile crowdsourcing • Cognitive radio network • Bilateral (One-to-one) • One-dimension • Multi-dimension • Multilateral (One-to-many) • Static contracting • Repeated contracting 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 (ChinaSIP), Chengdu, China, Jul. 2015.

  42. 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

  43. Adverse Selection and Moral Hazard in CRN • Problem of moral hazard • The PU neither knows how much effort the SU puts into • How much down payment and installment payment to request? • 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 1) Down payment : Pay part of the total amount at the point of signing the contract SU PU 2) Release the spectrum to the SU • 3) Utilize spectrum • Transmit package • Generate revenue 4) Installment payment: The SU pays the rest of the loan

  44. System Model Revenue Realizations Type of Capability Operation Cost

  45. Information Asymmetry Adverse Selection Moral Hazard

  46. Payoffs Payoff of SU Payoff of PU

  47. Simulation Results

  48. CONCLUSION • Theory • Adverse selection and moral hazard • Static and repeated, one/multi-dimension, one/multi-agents • Application in wireless networks • D2D communications, mobile crowdsourcing, cognitive radio network • Future work • Extension of previous models • New models in hierarchies organization, incomplete contract, investment

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