How Much Would You Pay to Change a Game before Playing It?

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.