## Example 43 Application of the SCG algorithm

There are five students, A, B, C, D, and E, and five rooms, V, W, X, Y, and Z. Three of the rooms are presently occupied W by student B, X by student C, and Y by student D. All five students will participate in the allocation scheme because all three tenants are guaranteed rooms that are at least as attractive as the ones they currently occupy. Assume that the priority ordering is ABCDE. A partial list of the students's preferences is presented in Table 9.21. We have given only a partial...

## Relation to the Gibbard Satterthwaite Theorem

Truthful revelation is a dominant strategy for each individual when the pivotal mechanism is used to select a public project. Why does that not contradict the Gibbard-Satterthwaite Theorem of Chapter 7 (Section 2) That theorem establishes that there does not exist a nondictatorial incentive scheme for inducing truthful revelation when there are more than two possible outcomes. The pivotal mechanism is even invulnerable to manipulation when there is a continuum of possible outcomes. And the...

## Example 51 Extensive form twoperson game

The game is represented as Figure 1.5 . At the first stage player A has a choice of moving left or right. If A moves left the game is over, and A's payoff is 1 and B's payoff is 5. If player A moves right at the first stage then player B has the next move and can go up or down. If B chooses up then each gets a payoff of 3, but if B moves down then A's payoff is 0 and B's payoff is 2. Consider the normal form representation of the same game displayed as Table 1.13. R U represents the strategy B...

- .bidder1haslearned That Bidder 2 Plans To Bid 50.
- A A continuum of options
- Beggarthyneighbor policies
- Brief Tour Of Several Countries
- A computer network
- A continuum of effort supply levels
- A general model
- Riskaverse managers and binary effort supply
- The market opportunity line
- A twoperson partnership
- Acid Rain
- Adoption of a standard
- Allocating Dormitory Rooms
- An efficient procedure
- Applications Of The Revenue Equivalence Theorem
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- Auctions
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- Constrained maximization - 2
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- Contents
- Corporate Governance
- D 15 Average cost taxation
- D Constrained optimization
- D Example 24 Competitive equilibrium in a simple economy with productuion
- D Example 26 One private good and one public good
- D Example 51 Output is proportional to the square root of effort
- D V0 c
- Decision Making Under Uncertainty
- Defects of the pivotal mechanism
- Deliberate mismanagement
- DExample 41 Three individuals
- DExample 92 Calculating the efficient effort supply
- Disarmament
- Dissolving a partnership - 2 3 4
- Donald E Campbell
- Efficiency - 2
- Efficiency And Incentive Compatibility - 2
- Efficiency of competitive insurance markets with full information
- Equilibrium
- Equilibrium bids in a firstprice sealedbid auction
- Equilibrium Efficiency and Asymmetric Information
- Equilibrium payoffs
- Equilibrium theorem for infinitely repeated games
- Example 11 A bargaining breakdown
- Example 11 Two agents of each type
- Example 11 Two consumers with unequal marginal rates of substitution
- Example 11 Two individuals and constant marginal cost
- Example 11 Two individuals with straightline indifference curves
- Example 11 Two projects Fand G and three individuals
- Example 110 Borda or rank order voting with four alternatives
- Example 12 A variable number of votes
- Example 12 An unstable matching
- Example 12 Competitive equilibrium with three agents
- Example 12 Indifference curves that are curved
- Example 13 A majority rule cycle with three feasible alternatives
- Example 13 An efficient matching that is not stable
- Example 13 Cleaning up the neighborhood
- Example 14 Deferred acceptance with five agents of each type
- Example 14 The status quo receives special treatment
- Example 14 Two individuals
- Example 15 Sharing the power
- Example 15 The benefit tax mechanism with three agents
- Example 15 The roles are switched
- Example 16 Compromise
- Example 16 Nash equilibrium of the benefit tax mechanism
- Example 17 Veto power
- Example 18 Plurality rule
- Example 19 Plurality rule with runoff
- Example 21 A community of three individuals
- Example 21 A specific case with two partners
- Example 21 Buying back some of your endowment
- Example 21 Finding the stable matchings
- Example 21 Four bidders
- Example 21 Maximizing the function fx 10x x2
- Example 21 The linear fare induces shirking
- Example 21 Three ways to hit the target
- Example 22 A simple consumer choice problem
- Example 22 Equal sharing of the surplus
- Example 22 Four bidders again
- Example 22 Infinitely repeated version of Example
- Example 22 Pollution and profit
- Example 22 The nonlinear fare motivates the agent to perform well
- Example 22 The profit calculation
- Example 22 The SODA outcome
- Example 23 Deriving a demand function
- Example 23 Feasibility in a simple economy
- Example 23 Participation can be harmful
- Example 23 Reporting a fraction of ones reservation value
- Example 23 The CODA outcome
- Example 23 Two firms each with quadratic profit functions
- Example 24 Consumer choice with nonnegative consumption
- Example 24 Four colleges and two tests
- Example 24 Twoperson manipulation of the pivotal mechanism
- Example 25 A lower test score can mean a better college
- Example 25 A twoperson exchange economy with externalities
- Example 25 Corner points need not apply
- Example 26 Fairness and efficiency cannot be satisfied simultaneously
- Example 26 Tangency and consumer choice
- Example 28 The chain rule and consumer choice
- Example 31 A large number of workers
- Example 31 F is the uniform distribution
- Example 31 Nonexistence of equilibrium with increasing MRS
- Example 31 Retardation of global warming
- Example 31 Ten utilities with different production processes
- Example 31 The car is worth 50 more to the buyer than to the seller
- Example 31 The Lagrangian approach to consumer choice
- Example 31 The Vickrey and English auctions
- Example 31 Three hospitals and three doctors
- Example 32 Linear functions
- Example 32 Preference misrepresentation by a doctor
- Example 32 The binary choice model
- Example 32 The Dutch and firstprice auctions
- Example 32 Two consumers each with increasing MRS
- Example 33 Example 31 with the revised algorithm
- Example 33 The probability that you have the higher bid
- Example 33 The public goods model of Section
- Example 33 Three identical consumers each with increasing MRS
- Example 34 Allocation of a single indivisible asset
- Example 34 An odd but large number of consumers
- Example 41 A twoperson twocommodity exchange economy
- Example 41 Inefficiency of the SCNG with three students and three rooms
- Example 41 The movie or the restaurant
- Example 41 Transplanting the legal system
- Example 41 Two bidders and two pairs of reservation values
- Example 41 Two borrowers
- Example 42 A generic version of Example
- Example 42 Efficiency of SCG1 for the utility functions of Example
- Example 42 Misrepresentation in the economy of Example
- Example 42 nv and ev for a firstprice auction with two bidders
- Example 42 Stock options and managerial incentive
- Example 42 Three individuals and five feasible alternatives
- Example 43 A very simple resource allocation problem
- Example 43 Dividing a cake
- Example 43 No owner has an incentive to monitor the manager
- Example 43 The winner has to pay four times the bid
- Example 43 Two individuals and two feasible outcomes
- Example 44 A firm with a large stakeholder
- Example 44 A simple mechanism with subgameperfect equilibria that are optimal
- Example 44 Misrepresentation with a firstprice auction with two bidders
- Example 45 A simple illustration
- Example 45 Many traders of each type
- Example 46 How good is the approximation
- Example 51 No bilateral exchanges are possible
- Example 51 The benefits of diversification
- Example 51 Two preference types
- Example 52 The effort supply function
- Example 52 Three individuals
- Example 53 Counterexample when one of the utility functions is not quasilinear
- Example 53 Deriving the optimal contract
- Example 54 Using the effort supply function to derive the optimal contract
- Example 55 Binary choice of effort level
- Example 55 Consumer choice with quasilinear utility
- Example 56 A nonlinear contract for Example
- Example 56 Consumer surplus with quasilinear utility
- Example 57 A less riskaverse manager
- Example 57 Total consumer surplus with quasilinear utility
- Example 58 A continuum of effort levels
- Example 61 A simple utility function
- Example 61 EMV when the bad outcome is a burglary
- Example 61 Interdependent values
- Example 62 EU when the bad outcome is a burglary
- Example 62 Three hats
- Example 62 Two simple cost functions
- Example 63 Correcting for the overestimate
- Example 63 Education is not productive
- Example 63 Individuals with different preferences make different choices
- Example 64 A chance to double your salary
- Example 65 An investment
- Example 65 The L types value of marginal product is nine
- Example 66 Insurance
- Example 67 Insurance with fair odds
- Example 71 A run of Cs and Ds
- Example 71 A specific utilityofwealth function
- Example 71 Full information equilibrium in a special case
- Example 72 Asymmetric equilibrium in the market of Example
- Example 72 Insurance without fair odds
- Example 72 The continuum dilemma
- Example 73 Nonexistence of equilibrium for a special case of Example
- Example 73 The same odds but a different utilityofwealth function
- Example 74 Existence of equilibrium for a special case of Example
- Example 74 The chosen coverage under fair odds
- Example 75 A simple case
- Example 75 Efficiency of equilibrium in the market of Example
- Example 76 A higher probability of an accident
- Example 77 A highly unlikely scenario
- Example 78 Expected premiums and expected claims for Example
- Example 91 An inefficient effort supply at equilibrium
- Example 93 The efficient effort supply when odds are not fair
- Examples of managerial shirking
- Expected revenue is equal for the Vickrey and firstprice auctions
- Franchises
- Full information equilibrium - 2 3
- General Competitive Equilibrium
- General Proof Of The Gibbardsatterthwaite Theorem
- Groves Mechanisms
- Hidden Action
- Hidden Characteristics
- Hospitals And Doctors
- Hostile takeovers
- Incentive Regulation Of The Telecommunications Industry
- Incentives
- Incentives efficiency and social cost pricing
- Incomplete insurance
- Inertiasins of omission
- Infinitely repeated prisoners dilemma
- Insurance
- Integral calculus proof of the revenue equivalence theorem
- Interdependent Values
- Introduction
- J A commonly used scheme
- The budget constraint and preferences
- Kidney Transplants
- Lagrangian Multipliers
- Lagrangian multipliers with more than one resource constraint
- LB A diagrammatic introduction
- LB Multistage auctions
- Links - 2 3 4 5 6
- LJ A continuum of public projects
- LJ Students apply to colleges
- Marketable Pollution Rights
- Matching
- Maximizing A Quadratic
- Minimization
- Moral Hazard And Insurance
- Nash equilibrium - 2 3
- Nonconvex Economies
- Onetoone matching
- Other probability distributions
- Other voting schemes
- Overview Of Calculus
- P - 2
- Partnerships
- Pay And Performance In Us Public Schools
- Performance bonuses
- Personal Bankruptcy
- Pi qdqpUp V 1p
- Pollution
- Pooling equilibria
- Preface to the Second Edition
- Preference Revelation In General
- Problem set - 2 3 4 5 6
- Procurement
- Product markets
- Proof - 2 3 4 5 6 7 8
- Proof for two individuals and three alternatives
- Proof for two individuals and three or more alternatives
- Proof for two or more individuals and three or more alternatives 9 10 11 12 13 14
- Proof of statement [10
- Proof of the revenue equivalence theorem 15 16 17 18 19 20 21 22 23
- Public Goods and Preference Revelation
- Public opinion
- Quasilinear preference and demand
- Quasilinear Preferences
- Remark on planning and Lagrangians
- Repeated prisoners dilemma with terminal date
- Repetition And Equilibrium
- Reputation and repeated interaction
- Resource Allocation
- Resource allocation
- Responsiveness of competitive markets
- Revenue Equivalence
- Revenue equivalence for the four basic auctions
- Risk aversion and a negative second derivative
- Riskaverse managers and a continuum of effort levels
- Riskneutral managers
- Selfdealing
- Separating equilibria
- Singletest placement
- Sketch of the proof of the complete insurance theorem
- Social cost pricing
- Source - 2 3
- Sources
- Strictly concave functions
- Student placement
- Students And Advisors
- Subgameperfect Nash Equilibrium
- Taxi
- Ten significant auctions
- Tenure And The Performance Of Professors
- Terminal date and unknown type
- The Arrowdebreu Economy
- The basic agency model
- The binary choice model of moral hazard
- The case of n bidders
- The centipede game
- The complete insurance theorem
- The composite commodity theorem
- The continuum case in general
- The converse of the Pythagorean theorem
- The Economic Model
- The Enron debacle
- The formal argument
- The formal model
- The Gibbard Satterthwaite Theorem
- The incentive to harbor terrorists
- The intertemporal budget constraint
- The invisible hand
- The legal system
- The lenders point of view
- The main results
- The mechanisms
- The model - 2
- The number of contracts in equilibrium
- The Owneremployee Relationship
- The Ownermanager Relationship In Practice
- The pivotal mechanism
- The Pivotal Mechanism
- The Prisoners Dilemma Game
- The Revelation Principle
- The Savings And Loan Debacle
- The tangency approach
- The total derivative and the chain rule
- The uniform probability distribution
- The Vickrey Auction
- The Vickrey auction
- The welfare theorem in the general model
- The winners curse
- Tort damages
- Two options
- U 2 lnq 1 2 3q
- Uhsh uhsl
- Unconstrained maximization - 2
- Valuerestricted preferences
- Vickrey English Dutch and firstprice auctions
- Voluntary contributions
- Voting and Preference Revelation
- Voting Schemes
- 1x 11 4y 11 x 4x 11 4y
- Welfare theorem for an exchange economy
- Why not China
- Why shareholders allow managerial shirking
- X3 Xi