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Impact of Geographical Separation on Spectrum Sharing Markets

Kangle Mu, Zongyun Xie, Igor Kadota, Randall Berry

TL;DR

The paper studies two service providers with partially overlapping coverage sharing a non-intermittent spectrum band, challenging prior work that assumed identical coverage. It formulates a Cournot competition model with three sub-markets $A\setminus B$, $AB$, $B\setminus A$, linear demand $p_d=1-x$, and latency costs that capture congestion on shared bandwidth $W$. The authors prove a unique Nash equilibrium exists for all $W$ and market sizes, show SPs avoid the overlap when bandwidth is limited and may enter it as $W$ grows, and demonstrate that cooperative abstention from the overlapping market can raise total welfare in many regimes. These results inform regulators on how to set $W$ to balance SP revenue, consumer surplus, and social welfare, while highlighting fairness concerns for overlapped areas.

Abstract

With the increasing demand for wireless services, spectrum management agencies and service providers (SPs) are seeking more flexible mechanisms for spectrum sharing to accommodate this growth. Such mechanisms impact the market dynamics of competitive SPs. Prior market models of spectrum sharing largely focus on scenarios where competing SPs had identical coverage areas. We depart from this and consider a scenario in which two competing SPs have overlapping but distinct coverage areas. We study the resulting competition using a Cournot model. Our findings reveal that with limited shared bandwidth, SPs might avoid overlapping areas to prevent potential losses due to interference. Sometimes SPs can strategically cooperate by agreeing not to provide service in the overlapping areas and, surprisingly, customers might also benefit from such cooperation under certain circumstances. Overall, market outcomes exhibit complex behaviors that are influenced by the sizes of coverage areas and the bandwidth of the shared spectrum.

Impact of Geographical Separation on Spectrum Sharing Markets

TL;DR

The paper studies two service providers with partially overlapping coverage sharing a non-intermittent spectrum band, challenging prior work that assumed identical coverage. It formulates a Cournot competition model with three sub-markets , , , linear demand , and latency costs that capture congestion on shared bandwidth . The authors prove a unique Nash equilibrium exists for all and market sizes, show SPs avoid the overlap when bandwidth is limited and may enter it as grows, and demonstrate that cooperative abstention from the overlapping market can raise total welfare in many regimes. These results inform regulators on how to set to balance SP revenue, consumer surplus, and social welfare, while highlighting fairness concerns for overlapped areas.

Abstract

With the increasing demand for wireless services, spectrum management agencies and service providers (SPs) are seeking more flexible mechanisms for spectrum sharing to accommodate this growth. Such mechanisms impact the market dynamics of competitive SPs. Prior market models of spectrum sharing largely focus on scenarios where competing SPs had identical coverage areas. We depart from this and consider a scenario in which two competing SPs have overlapping but distinct coverage areas. We study the resulting competition using a Cournot model. Our findings reveal that with limited shared bandwidth, SPs might avoid overlapping areas to prevent potential losses due to interference. Sometimes SPs can strategically cooperate by agreeing not to provide service in the overlapping areas and, surprisingly, customers might also benefit from such cooperation under certain circumstances. Overall, market outcomes exhibit complex behaviors that are influenced by the sizes of coverage areas and the bandwidth of the shared spectrum.
Paper Structure (10 sections, 4 theorems, 6 equations, 10 figures)

This paper contains 10 sections, 4 theorems, 6 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Market Model
  3. Main Results
  4. Equilibrium
  5. Numerical Results
  6. Equilibrium Quantities
  7. SP's Revenue
  8. Consumer Surplus
  9. Social Welfare
  10. Conclusions

Key Result

Theorem 1

There always exists a unique Nash equilibrium for any bandwidth $W$, and sub-market sizes $m^{A\backslash B}$, $m^{AB}$, and $m^{B\backslash A}$. For symmetric cases in which $m^{A\backslash B} = m^{B\backslash A}$, the quantities of users served by SP1 and SP2 at the equilibrium are given as follow where

Figures (10)

  • Figure 1: Venn diagram of three sub-markets and the sets of users served by different SPs.
  • Figure 2: User quantities at equilibrium versus bandwidth $W$ for two symmetric cases.
  • Figure 3: User quantities at equilibrium versus bandwidth $W$ for two asymmetric cases.
  • Figure 4: SP's revenue versus bandwidth $W$ for two symmetric cases.
  • Figure 5: SP's revenue versus bandwidth $W$ for two asymmetric cases.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Theorem 1: Uniqueness of Nash equilibrium
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof