A Note on Reference-Dependent Choice with Threshold Representation
-
Dan Qin
Abstract
This note considers reference-dependent choice procedures shaped by a utility function and a threshold function. Alternatives are considered only when the utility gain of moving from the reference is bigger than the threshold. We impose no requirement on the threshold functions whereas previous works characterize the special case of strictly positive threshold functions. We also examine the case when the threshold function depends on both compared alternatives.
Funding statement: This work was supported by Japan Society for the Promotion of Science, Funder Id: http://dx.doi.org/10.13039/501100001691, Grant Number: 16K17091, 18K12739.
A Axiom independence
In this appendix, we show that results are tight. Let X = {x, y, z}. Rows stand for reference alternatives and columns stand for opportunity sets.
| x,y,z | x,y | x,z | y,z | |
|---|---|---|---|---|
|
|
y,z | y | z | y,z |
| x | x,y,z | x,y | x,z | |
| y | y,z | y | y,z | |
| z | y,z | z | y,z |
This choice correspondence satisfies eqs. (3) and (5) while violates eq. (4).
| x,y,z | x,y | x,z | y,z | |
|---|---|---|---|---|
|
|
x,y,z | x,y | x,z | y,z |
| x | x | x | x | |
| y | x,y | y | y | |
| z | z | z | z |
This choice correspondence satisfies eqs. (4) and (3) while violates 5.
| x,y,z | x,y | x,z | y,z | |
|---|---|---|---|---|
|
|
x,y,z | x,y | x | y,z |
| x | x | x | x | |
| y | y | y | y | |
| z | z | z | z |
This choice correspondence satisfies eqs. (4) and (5) while violates eq. (3).
References
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Articles in the same Issue
- Research Articles
- Optimal Forestry Contract with Interdependent Costs
- Bi and Branching Strict Nash Networks in Two-way Flow Models: A Generalized Sufficient Condition
- Pay-What-You-Want in Competition
- Two Rationales for Insufficient Entry
- Students’ Social Origins and Targeted Grading
- Pricing, Signalling, and Sorting with Frictions
- On the Economic Value of Signals
- The Core in Bertrand Oligopoly TU-Games with Transferable Technologies
- Reasoning About ‘When’ Instead of ‘What’: Collusive Equilibria with Stochastic Timing in Repeated Oligopoly
- Timing Games with Irrational Types: Leverage-Driven Bubbles and Crash-Contingent Claims
- Costly Rewards and Punishments
- Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies
- Strategic Activism in an Uncertain World
- On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy
- Optimal Incentives Under Gift Exchange
- Public Good Indices for Games with Several Levels of Approval
- Vagueness of Language: Indeterminacy under Two-Dimensional State-Uncertainty
- Winners and Losers of Universal Health Insurance: A Macroeconomic Analysis
- Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy
- Flourishing as Productive Tension: Theory and Model
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- A Note on Reference-Dependent Choice with Threshold Representation
- Regular Equilibria and Negative Welfare Implications in Delegation Games
- Unbundling Production with Decreasing Average Costs
- A Simple and Procedurally Fair Game Form for Nash Implementation of the No-Envy Solution
- Decision Making and Games with Vector Outcomes
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