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Strategy-proof Market Segmentation against Price Discrimination

Zhonghong Kuang, Sanxi Li, Yi Liu, Yang Yu

Abstract

In light of prevailing data regulations, consumer mobility across diverse markets inherently endogenizes market segmentation. Considering such strategic interactions, we define a market segmentation as strategy-proof when no consumer (with positive measure) has an incentive to deviate to another market. We show that in every strategy-proof market segmentation, the producer surplus remains at the uniform monopoly level, and the consumer surplus is bounded between the buyer-optimal level and the uniform monopoly level. Remarkably, no consumer is worse off than in the case of a uniform monopoly. We also construct a family of strategy-proof segmentations to realize every possible welfare outcome.

Strategy-proof Market Segmentation against Price Discrimination

Abstract

In light of prevailing data regulations, consumer mobility across diverse markets inherently endogenizes market segmentation. Considering such strategic interactions, we define a market segmentation as strategy-proof when no consumer (with positive measure) has an incentive to deviate to another market. We show that in every strategy-proof market segmentation, the producer surplus remains at the uniform monopoly level, and the consumer surplus is bounded between the buyer-optimal level and the uniform monopoly level. Remarkably, no consumer is worse off than in the case of a uniform monopoly. We also construct a family of strategy-proof segmentations to realize every possible welfare outcome.
Paper Structure (12 sections, 6 theorems, 6 equations, 3 figures)

This paper contains 12 sections, 6 theorems, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Timeline.
  4. Producer's Strategies.
  5. Consumer's Strategies.
  6. Payoffs.
  7. Solution Concept.
  8. The Main Result and the Proof
  9. Indifference Condition.
  10. Deviation Costs
  11. Comparison with Subgame Perfect Equilibrium
  12. Concluding Remarks

Key Result

Theorem 1

There exists a strategy profile $(\phi,\sigma)$ that induces strategy-proof segmentation if and only if producer surplus $\pi = \pi^{*}$ and consumer surplus $u\in[u^{*},\overline{w}-\pi^{*}]$. No positive measure of consumers is worse off compared with the uniform monopoly outcome.

Figures (3)

  • Figure 1: Surplus Triangle
  • Figure 2: Why $\max\left\{\phi(X_i)\right\}_{i=1}^n=v^*$?
  • Figure 3: Welfare Consequences with Different Deviation Costs

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Lemma 1
  • proof : Proof of \ref{['lemma:SPprice']}
  • Lemma 2
  • proof : Proof of \ref{['lemma:maxprice']}
  • Remark 1
  • Lemma 3
  • ...and 7 more