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Total Categories: 5
Mechanism design is primarily concerned with analyzing the performance of pre-existing economic mechanisms, rather than constructing new ones.
Answer: False
Mechanism design is often described as 'reverse game theory' because it focuses on constructing new rules or mechanisms to achieve desired outcomes, rather than merely analyzing existing ones.
Leonid Hurwicz, Eric Maskin, and Roger Myerson were jointly awarded the Nobel Memorial Prize for their foundational contributions to mechanism design theory in 2007.
Answer: True
The 2007 Nobel Memorial Prize in Economic Sciences was awarded to Leonid Hurwicz, Eric Maskin, and Roger Myerson for their foundational work in mechanism design theory.
In a mechanism design problem, the 'principal' is typically an agent who possesses private information they wish to keep hidden from others.
Answer: False
The principal is the individual who wishes to base their actions on information privately known to the agents, not the one possessing the private information. Agents are the ones with private information.
The revelation principle simplifies mechanism design by allowing the principal to only consider games where agents are incentivized to report their true types.
Answer: True
The revelation principle is extremely useful because it allows the principal to simplify the design problem by only considering games where agents are incentivized to report their true types.
In a typical mechanism design game, agents report their types before the principal commits to a mechanism.
Answer: False
The typical timing of a mechanism design game involves the principal committing to a mechanism first, followed by agents reporting their types, and then the mechanism being executed.
Which of the following terms is NOT used interchangeably with mechanism design?
Answer: Traditional economic analysis
Mechanism design is also known as implementation theory or institution design, and is sometimes described as 'reverse game theory.' Traditional economic analysis is distinct as it typically analyzes existing mechanisms rather than designing new ones.
Who among the following was NOT awarded the Nobel Memorial Prize for foundational work in mechanism design theory in 2007?
Answer: William Vickrey
Leonid Hurwicz, Eric Maskin, and Roger Myerson were awarded the 2007 Nobel Memorial Prize for their work in mechanism design. William Vickrey received the Nobel Prize in 1996 for his related work, which also contributed to the field.
In mechanism design, what is the primary reason a principal cannot simply ask agents for their private information?
Answer: It is typically in agents' self-interest to distort the truth.
It is difficult for a principal to obtain truthful information directly from agents because it is typically in the agents' self-interest to distort the truth or lie if doing so would lead to a more favorable outcome for them.
What does an agent's 'type' refer to in the context of mechanism design?
Answer: Private information, such as preferences or quality of a good.
In mechanism design, an agent's 'type' refers to private information, such as their preferences or the quality of a good for sale, which is secretly received from 'nature.'
Which of the following correctly describes the typical sequence of events in a mechanism design game?
Answer: Principal commits to mechanism, agents report types, mechanism executed.
The typical timing of a mechanism design game involves three steps: first, the principal commits to a mechanism; second, the agents report their types; and third, the mechanism is executed.
What does y() represent in the context of a mechanism design game's timing?
Answer: The mechanism itself, determining an outcome based on reported types.
In the context of a mechanism design game's timing, y() represents the mechanism itself, which is a function that determines and grants an outcome based on the types reported by the agents.
A social choice function directly maps reported type profiles to an outcome, including both goods allocation and money transfer.
Answer: False
A social choice function maps the *true* type profile directly to a goods allocation. A mechanism maps the *reported* type profile to an outcome, which includes both goods allocation and money transfer.
A mechanism is considered truthfully implementable if agents find it optimal to report their true type, which is the designer's goal.
Answer: True
A mechanism is considered truthfully implementable if agents find it optimal to report their true type, meaning their reported type matches their actual type. The goal for the designer is to solve for a transfer function that ensures this truthful reporting.
The incentive compatibility (IC) constraint ensures that an agent's utility from misreporting their type is always less than or equal to their utility from truthful reporting.
Answer: True
The incentive compatibility (IC) constraint ensures an agent's utility from truthfully reporting their type and receiving the corresponding outcome is greater than or equal to the utility they would receive from misreporting their type.
The participation, or individual rationality (IR), constraint is always a mandatory component of any mechanism design problem.
Answer: False
The participation, or individual rationality (IR), constraint is *sometimes* included in mechanism design, ensuring agents have the option to not participate if the outcome is not at least as good as their outside option.
A necessary condition for a goods allocation to be implementable is that higher agent types must generally be given more of the good to prevent them from misrepresenting as lower types.
Answer: True
Practically, this condition means that agents will only tell the truth if the mechanism offers higher agent types a better deal. Specifically, higher types must generally be given more of the good; otherwise, they would have an incentive to lie and declare themselves as lower types.
The single-crossing condition implies that agents with higher types have a weaker preference for more of the good relative to money.
Answer: False
The single-crossing condition implies that agents with higher types have a *stronger* preference for more of the good relative to money, or are willing to pay more for an additional unit of the good.
What is the primary difference between a social choice function and a mechanism?
Answer: A social choice function maps true types, while a mechanism maps reported types.
A social choice function maps the *true* type profile directly to a goods allocation, whereas a mechanism maps the *reported* type profile to an outcome, which includes both a goods allocation and a money transfer.
What does it mean for a mechanism to 'implement' a social choice function?
Answer: To find a transfer function that motivates agents to achieve the social choice function's goods allocation.
To implement a social choice function means to find a transfer function that motivates agents to behave in a way that the equilibrium strategy profile under the mechanism results in the same goods allocation as the social choice function would have produced if true types were known.
The incentive compatibility (IC) constraint is fundamental because it ensures:
Answer: Agents find it optimal to report their true type.
The incentive compatibility (IC) constraint is a fundamental condition that ensures an agent's utility from truthfully reporting their type and receiving the corresponding outcome is greater than or equal to the utility they would receive from misreporting their type, thus making it optimal to report truthfully.
What is the practical implication of the implementability necessity condition regarding agent types and goods allocation?
Answer: Higher types must generally be given more of the good to ensure truth-telling.
Practically, the implementability necessity condition means that agents will only tell the truth if the mechanism offers higher agent types a better deal, specifically by giving them more of the good; otherwise, they would misrepresent as lower types.
What does the single-crossing condition imply about an agent's marginal rate of substitution (MRS)?
Answer: MRS increases with an agent's type.
The single-crossing condition implies that an agent's utility function is shaped such that their marginal rate of substitution (MRS) increases with their type, meaning higher types have a stronger preference for more of the good relative to money.
In the outcome y(theta) = {x(theta), t(theta)}, what does t signify?
Answer: The monetary transfer.
In the outcome y(theta) = {x(theta), t(theta)}, t signifies the monetary transfer, which is determined as a function of the agent's reported type (theta).
Myerson ironing is a technique used to make non-monotonic allocation schedules monotonic, which is necessary for implementability under certain conditions.
Answer: True
Myerson ironing is a technique used when optimal price and allocation schedules are not monotonic. It is required to flatten any non-monotonic intervals in the schedule to ensure that the incentive compatibility condition is met, as monotonic schedules are necessary for implementability under certain conditions.
In Mirrlees's (1971) model for price discrimination, the agent is assumed to have a utility function where the monetary component is non-linear.
Answer: False
In Mirrlees's (1971) model for price discrimination, the agent is assumed to have quasilinear utility, meaning their utility can be expressed as a value derived from the goods minus a monetary transfer, where the monetary component is *linear*.
The principal's objective in Mirrlees's price discrimination setting is to maximize expected profit while knowing the customer's true type.
Answer: False
In Mirrlees's price discrimination setting, the principal aims to maximize expected profit while facing the challenge of *not knowing* the customer's true type.
The envelope theorem is used in Mirrlees's model to simplify the principal's problem by eliminating the transfer function from the profit maximization.
Answer: True
Mirrlees (1971) introduced a method using the envelope theorem to eliminate the transfer function from the principal's expected profit maximization problem, allowing the designer to focus on optimizing the allocation of goods directly.
Myerson ironing is applied in price discrimination when the allocation schedule is found to be monotonic, to further optimize it.
Answer: False
Myerson ironing is specifically applied in price discrimination when the allocation schedule that satisfies the first-order conditions is found to be *non-monotonic*, not monotonic.
The intuitive reason for 'bunching' types during Myerson ironing is to offer differentiated contracts to a wide range of types.
Answer: False
The intuitive reason for 'bunching' certain types together during Myerson ironing is that the designer finds it optimal to offer the *same* contract to a range of types when differentiation is not optimal.
The proof for Myerson ironing is based on the mathematical theory of optimal control.
Answer: True
The proof for Myerson ironing is based on the mathematical theory of optimal control, a framework used to optimize a system's behavior over time.
When applying Myerson ironing, the allocation schedule within non-monotonic intervals must be monotonic and the monotonicity constraint must be binding at the interval boundaries.
Answer: False
When applying Myerson ironing using optimal control theory, the allocation schedule within non-monotonic intervals must be monotonic, but the monotonicity constraint must *not* be binding at the boundaries of the interval.
When is 'Myerson ironing' typically required in mechanism design?
Answer: When the optimal price and allocation schedules are not monotonic.
Myerson ironing is a technique used when the optimal price and allocation schedules derived from first-order conditions are not monotonic, as monotonic schedules are necessary for implementability under certain conditions.
In Mirrlees's (1971) model for price discrimination, what is the assumed utility function for the agent?
Answer: Quasilinear utility
In Mirrlees's (1971) model for price discrimination, the agent is assumed to have quasilinear utility, meaning their utility can be expressed as a value derived from the goods minus a monetary transfer, where the monetary component is linear.
What is the principal's objective in Mirrlees's price discrimination setting?
Answer: To maximize the expected profit from transactions.
In Mirrlees's price discrimination setting, the principal, often a monopolist, aims to maximize the expected profit from transactions.
What real-world scenario is often used to illustrate Mirrlees's price discrimination model?
Answer: An airline setting different fares for various customer segments.
A common real-world scenario used to illustrate Mirrlees's price discrimination model is an airline attempting to set different fares for various customer segments without being able to directly identify each customer's type.
How does the envelope theorem assist in solving the principal's problem in Mirrlees's model?
Answer: It eliminates the transfer function from the principal's expected profit maximization problem.
The envelope theorem assists in solving the principal's problem in Mirrlees's model by eliminating the transfer function from the principal's expected profit maximization problem, allowing focus on optimizing goods allocation.
When is Myerson ironing specifically applied in the context of price discrimination?
Answer: When the allocation schedule that satisfies first-order conditions is non-monotonic.
Myerson ironing is specifically applied in price discrimination when the allocation schedule that satisfies the first-order conditions is found to be non-monotonic, often due to a non-monotone hazard ratio of the type distribution.
What is the intuitive reason for 'bunching' certain types together during Myerson ironing?
Answer: To offer the same contract to a range of types when differentiation is not optimal.
The intuitive reason for 'bunching' certain types together during Myerson ironing is that the designer finds it optimal to offer the same contract to a range of types when the marginal benefit of differentiating contracts is outweighed by the cost of granting 'information rent' to lower types.
What mathematical theory forms the basis for the proof of Myerson ironing?
Answer: Optimal control theory
The proof for Myerson ironing is based on the mathematical theory of optimal control, a framework used to optimize a system's behavior over time.
When applying Myerson ironing using optimal control theory, what must be true about the monotonicity constraint at the boundaries of a non-monotonic interval?
Answer: It must not be binding.
When applying Myerson ironing using optimal control theory, the allocation schedule within non-monotonic intervals must be monotonic, and the monotonicity constraint must *not* be binding at the boundaries of the interval.
William Vickrey is credited with establishing the revenue equivalence theorem, which states that a large class of auctions yield the same expected revenue under specific conditions.
Answer: True
The revenue equivalence theorem, established by William Vickrey, is a celebrated result stating that under specific conditions, a large class of auctions will yield the same expected revenue for the seller.
One of the conditions for the revenue equivalence theorem to hold is that buyers' types must be dependent on each other.
Answer: False
One of the key conditions for the revenue equivalence theorem to hold is that buyers' types must be *independently* distributed.
A significant implication of the revenue equivalence theorem is that sellers can always achieve higher revenue by strictly selling to the highest bidder.
Answer: False
A significant implication for a seller is that to achieve higher revenue, they must be willing to take a chance on allocating the item to an agent with a lower valuation, or even risk not selling the item at all, rather than strictly selling to the highest bidder.
VCG mechanisms were developed by Vickrey, Clarke, and Groves to address public choice problems and motivate socially efficient allocation of public goods.
Answer: True
VCG mechanisms, developed by Vickrey, Clarke, and Groves, are designed to address public choice problems and can motivate agents to choose the socially efficient allocation of public goods.
VCG mechanisms motivate truthful revelation by rewarding agents for any positive distortion their report causes to other agents.
Answer: False
VCG mechanisms motivate truthful revelation by *penalizing* any agent for the cost of the distortion their report causes to other agents, rather than rewarding them.
Which of the following is NOT a condition under which the revenue equivalence theorem holds?
Answer: The mechanism sells the good to the buyer with the lowest valuation.
One of the key conditions for the revenue equivalence theorem to hold is that the mechanism sells the good to the buyer with the *highest* valuation, not the lowest.
What is a significant implication of the revenue equivalence theorem for a seller aiming for higher revenue?
Answer: Be willing to risk allocating the item to a lower valuation agent or not selling at all.
A significant implication for a seller is that to achieve higher revenue, they must be willing to take a chance on allocating the item to an agent with a lower valuation, or even risk not selling the item at all, rather than strictly selling to the highest bidder.
VCG mechanisms are designed to address what type of problem?
Answer: Public choice problems, such as allocating public goods.
VCG mechanisms are designed to address public choice problems, such as deciding on public projects where costs are shared by all agents, and can motivate agents to choose the socially efficient allocation of public goods.
How do VCG mechanisms primarily motivate truthful revelation from agents?
Answer: By penalizing agents for the cost of distortion their report causes to others.
VCG mechanisms motivate truthful revelation by penalizing any agent for the cost of the distortion their report causes to other agents, charging a fee if their report is 'pivotal.'
The Gibbard–Satterthwaite theorem is an impossibility result stating that only dictatorial social choice functions can be truthfully implemented under general conditions.
Answer: True
The Gibbard–Satterthwaite theorem is an impossibility result stating that for a very general class of games, only 'dictatorial' social choice functions can be truthfully implemented.
A dictatorial social choice function ensures that all agents receive their most-favored goods allocation, regardless of others' preferences.
Answer: False
A social choice function is defined as dictatorial if there exists *one specific agent* who always receives their most-favored goods allocation, regardless of the preferences or reports of any other agent.
Myerson and Satterthwaite (1983) proved that efficient trade between two parties with private valuations is always possible without risk of loss.
Answer: False
Myerson and Satterthwaite (1983) demonstrated that efficient trade between two parties with private valuations is *impossible* without incurring the risk of forcing one party to trade at a loss.
Phillips and Marden (2018) found that the Shapley value cost-sharing rule optimizes both worst-case inefficiencies and best-case outcomes in cost-sharing games with concave cost functions.
Answer: True
Phillips and Marden (2018) proved that for cost-sharing games with concave cost functions, the optimal cost-sharing rule that first optimizes the worst-case inefficiencies (price of anarchy) and then the best-case outcomes (price of stability) is precisely the Shapley value cost-sharing rule.
The 'price of anarchy' measures the best-case outcomes achievable in a system compared to a socially optimal outcome.
Answer: False
The 'price of anarchy' in cost-sharing games refers to a measure of the *worst-case inefficiencies* that can arise in a system when individual agents act selfishly, compared to a perfectly coordinated, socially optimal outcome.
The 'price of stability' refers to the best-case outcomes achievable in a system, often through coordination, compared to a socially optimal outcome.
Answer: True
The 'price of stability' in cost-sharing games refers to a measure of the best-case outcomes that can be achieved in a system, often through some form of coordination or specific mechanism design, compared to a socially optimal outcome.
The Gibbard–Satterthwaite theorem is an impossibility result conceptually similar to which other theorem?
Answer: Arrow's Impossibility Theorem
The Gibbard–Satterthwaite theorem is an impossibility result in mechanism design, conceptually similar to Arrow's impossibility theorem.
According to the Gibbard–Satterthwaite theorem, what defines a 'dictatorial' social choice function?
Answer: One specific agent always receives their most-favored goods allocation.
A social choice function is defined as dictatorial if there exists one specific agent who always receives their most-favored goods allocation, regardless of the preferences or reports of any other agent.
What significant negative result did Myerson and Satterthwaite (1983) establish regarding trade between two parties with private valuations?
Answer: Efficient trade is impossible without incurring the risk of forcing one party to trade at a loss.
Myerson and Satterthwaite (1983) demonstrated that efficient trade between two parties with private valuations is impossible without incurring the risk of forcing one party to trade at a loss.
What does the 'price of anarchy' measure in cost-sharing games?
Answer: The worst-case inefficiencies when agents act selfishly.
The 'price of anarchy' in cost-sharing games quantifies the worst-case inefficiencies that can emerge in a system when individual agents act selfishly, relative to a perfectly coordinated, socially optimal outcome.