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Area of Science:

  • Game Theory
  • Behavioral Economics
  • Decision Analysis

Background:

  • Envelope theorems traditionally analyze rational decision-makers (DM) in strategic scenarios.
  • Existing frameworks lack methods for boundedly rational agents or general solution concepts.

Purpose of the Study:

  • To generalize envelope theorems for boundedly rational decision-makers and arbitrary solution concepts.
  • To analyze how information about willingness-to-pay (WTP) affects strategic parameter changes (public vs. private information).

Main Methods:

  • Decomposition of willingness to pay into three distinct effects: direct payoff impact, DM's strategic adaptation, and other players' strategic adaptation.
  • Application of the generalized framework to specific models like quantal response equilibrium and the matching pennies game.

Main Results:

  • Willingness to pay is decomposed into direct, self-strategic, and other-player-strategic effects.
  • The framework highlights differences in WTP when decisions are public versus private information.
  • Willingness to pay quantifies anticipation of future bounded rationality.

Conclusions:

  • The generalized envelope theorem provides a robust tool for analyzing boundedly rational decision-making in strategic environments.
  • Understanding the components of willingness to pay is crucial for designing interventions and predicting behavior under bounded rationality.