통찰 - Mechanism Design - # Endogenous Perception in Screening Problems

Endogenous Perception and Optimal Mechanism Design

Q: How would the results change if the agent could dynamically adjust their cognitive state during the mechanism, rather than committing to it ex-ante?

If the agent could dynamically adjust their cognitive state during the mechanism, the results would likely shift significantly. The ability to switch between sophisticated and naive states in real-time would introduce a layer of strategic behavior that is currently absent in the model. Increased Flexibility: Agents would have the opportunity to respond to the unfolding dynamics of the mechanism, potentially leading to more accurate perceptions of their type as they gather information throughout the process. This could reduce the cognitive costs associated with maintaining a sophisticated state, as agents could choose to be naive when it is advantageous and switch to sophistication when the stakes are higher. Impact on Mechanism Design: Designers would need to account for this flexibility in cognitive states. Mechanisms would have to be structured to either incentivize or disincentivize switching behaviors. For instance, if agents can adjust their cognitive state based on the perceived benefits of sophistication, the designer might need to implement stronger incentives to maintain truthful reporting and discourage opportunistic behavior. Potential for Over-Sophistication: The risk of over-sophistication could also emerge, where agents might oscillate between states to exploit the mechanism's design, leading to inefficiencies. This could complicate the screening process, as the designer would need to ensure that the incentives for sophistication do not lead to excessive cognitive investment that detracts from overall welfare. Dynamic Value of Sophistication: The value of sophistication would become a dynamic function, potentially varying throughout the mechanism's execution. This could complicate the analysis of the value of sophistication, as it would no longer be a static measure but rather a fluid one that changes with the agent's decisions and the mechanism's outcomes.

Q: What are the implications if the agent can strategically manipulate their perception-generating process, rather than taking it as exogenous?

If the agent could strategically manipulate their perception-generating process (PGP), the implications for the model would be profound: Endogenous Perception Control: Agents would have the ability to influence how they perceive their type, potentially leading to more favorable outcomes for themselves. This could result in a form of strategic misrepresentation, where agents might choose to adopt a PGP that skews their perception in a way that maximizes their utility from the mechanism. Complexity in Mechanism Design: Designers would face increased complexity in crafting mechanisms that account for the potential manipulation of perceptions. The designer would need to anticipate the ways in which agents might distort their perceptions and incorporate safeguards to mitigate these effects. This could involve more sophisticated screening techniques or the introduction of penalties for perceived manipulation. Incentives for Truthful Reporting: The strategic manipulation of PGPs could undermine the incentives for truthful reporting. If agents can benefit from misperception, they may choose to report types that do not reflect their true valuations, complicating the designer's ability to screen effectively. This could lead to inefficiencies in resource allocation and a decrease in overall welfare. Variability in Outcomes: The variability in agents' perceptions could lead to a wider range of outcomes in the mechanism, as different agents might adopt different strategies for manipulating their perceptions. This could introduce additional uncertainty into the mechanism's performance, making it more challenging to predict outcomes and assess the effectiveness of the design.

핵심 개념

The agent's perception of their private information can be endogenously determined by the incentive structure of the mechanism, rather than being a fixed characteristic. The designer must account for how the mechanism shapes the agent's cognitive state and resulting perception when choosing an optimal mechanism.

초록

The paper presents a model of endogenous perception in single-agent screening problems. The agent's evaluation of their type is determined by their cognitive state - either sophisticated (correctly perceiving their type) or naive (potentially misperceiving their type). The cognitive state depends on the mechanism's incentive structure via costly investment in cognition.

The key insights are:

The value of sophistication, which determines the agent's cognitive state, can be represented as a linear functional of the mechanism's allocation rule. This makes it tractable to incorporate sophistication constraints into mechanism design.
Screening is necessary to create sophistication incentives. The set of allocation rules that maximize sophistication incentives all share the property of pooling sufficiently high and low types.
The paper defines a notion of accuracy of perception, where one perception-generating process (PGP) is more accurate than another if it implies a lower value of sophistication in every mechanism. This order is shown to be equivalent to informativeness (in the sense of mean-preserving spreads) for unbiased PGPs, and to natural notions of increasing bias for biased PGPs.
Applications showcase how perception both shapes and is shaped by the design of mechanisms, including in settings of efficient provision, revenue maximization, and product market hype.

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arxiv.org

통계

The agent's true type θ is distributed according to CDF F.
The agent's perception π when naive is distributed according to CDF ρ(·|θ), which depends on the true type θ.
The agent incurs cognitive cost κ ≥ 0 to become sophisticated and correctly perceive their type.

인용구

"We provide a model of endogenous perception of private information in single-agent screening problems."
"Whether the agent is sophisticated or naive when evaluating their type depends on how much cognitive effort they exert in this process."
"Screening is necessary to create sophistication incentives and we characterize the set of allocation rules that maximize these incentives."

핵심 통찰 요약

Mechanism Design with Endogenous Perception

by Benjamin Bal... 게시일 arxiv.org 10-01-2024

https://arxiv.org/pdf/2409.19853.pdf

Mechanism Design with Endogenous Perception

더 깊은 질문

How would the results change if the agent could dynamically adjust their cognitive state during the mechanism, rather than committing to it ex-ante?

If the agent could dynamically adjust their cognitive state during the mechanism, the results would likely shift significantly. The ability to switch between sophisticated and naive states in real-time would introduce a layer of strategic behavior that is currently absent in the model.

Increased Flexibility: Agents would have the opportunity to respond to the unfolding dynamics of the mechanism, potentially leading to more accurate perceptions of their type as they gather information throughout the process. This could reduce the cognitive costs associated with maintaining a sophisticated state, as agents could choose to be naive when it is advantageous and switch to sophistication when the stakes are higher.

Impact on Mechanism Design: Designers would need to account for this flexibility in cognitive states. Mechanisms would have to be structured to either incentivize or disincentivize switching behaviors. For instance, if agents can adjust their cognitive state based on the perceived benefits of sophistication, the designer might need to implement stronger incentives to maintain truthful reporting and discourage opportunistic behavior.

Potential for Over-Sophistication: The risk of over-sophistication could also emerge, where agents might oscillate between states to exploit the mechanism's design, leading to inefficiencies. This could complicate the screening process, as the designer would need to ensure that the incentives for sophistication do not lead to excessive cognitive investment that detracts from overall welfare.

Dynamic Value of Sophistication: The value of sophistication would become a dynamic function, potentially varying throughout the mechanism's execution. This could complicate the analysis of the value of sophistication, as it would no longer be a static measure but rather a fluid one that changes with the agent's decisions and the mechanism's outcomes.

What are the implications if the agent can strategically manipulate their perception-generating process, rather than taking it as exogenous?

If the agent could strategically manipulate their perception-generating process (PGP), the implications for the model would be profound:

Endogenous Perception Control: Agents would have the ability to influence how they perceive their type, potentially leading to more favorable outcomes for themselves. This could result in a form of strategic misrepresentation, where agents might choose to adopt a PGP that skews their perception in a way that maximizes their utility from the mechanism.

Complexity in Mechanism Design: Designers would face increased complexity in crafting mechanisms that account for the potential manipulation of perceptions. The designer would need to anticipate the ways in which agents might distort their perceptions and incorporate safeguards to mitigate these effects. This could involve more sophisticated screening techniques or the introduction of penalties for perceived manipulation.

Incentives for Truthful Reporting: The strategic manipulation of PGPs could undermine the incentives for truthful reporting. If agents can benefit from misperception, they may choose to report types that do not reflect their true valuations, complicating the designer's ability to screen effectively. This could lead to inefficiencies in resource allocation and a decrease in overall welfare.

Variability in Outcomes: The variability in agents' perceptions could lead to a wider range of outcomes in the mechanism, as different agents might adopt different strategies for manipulating their perceptions. This could introduce additional uncertainty into the mechanism's performance, making it more challenging to predict outcomes and assess the effectiveness of the design.

How could this framework be extended to settings with multiple agents, where the endogenous perceptions of each agent may interact?

Extending this framework to settings with multiple agents would introduce several complexities and opportunities for richer analysis:

Inter-Agent Perception Dynamics: In a multi-agent setting, the endogenous perceptions of each agent could interact, leading to a network of perceptions that influence one another. For instance, if one agent's perception is biased, it could affect the perceptions and decisions of others, creating a ripple effect throughout the mechanism. This would necessitate a model that captures these interactions and their implications for overall outcomes.

Strategic Interactions: Agents would need to consider not only their own perceptions but also how their perceptions might influence or be influenced by the perceptions of others. This could lead to strategic behavior where agents attempt to manipulate their perceptions in anticipation of others' actions, complicating the equilibrium analysis of the mechanism.

Collective Incentives: The designer would need to account for collective incentives in the mechanism design. The interactions among agents could lead to emergent behaviors that are not present in single-agent settings. For example, the designer might need to create mechanisms that encourage cooperation or competition among agents, depending on the desired outcomes.

Complexity in Screening: The screening process would become more complex, as the designer would need to consider the distribution of perceptions across multiple agents. This could involve developing mechanisms that are robust to various types of misperceptions and ensuring that the incentives for sophistication are aligned across agents.

Potential for Coordination: The framework could also explore the potential for coordination among agents. If agents can communicate or signal their perceptions, this could lead to more efficient outcomes, as they might collectively invest in sophistication or share information to improve their evaluations. This would add another layer of strategic interaction that could enhance or detract from the overall efficiency of the mechanism.