• Radio Spectrum - the radio frequency (RF) portion of the electromagnetic spectrum. Spectrum is divided by the bands, which is allocated to the companies. In the literature it is conventional to call them primary users (PU's) of radio spectrum;

• Recent legislative attempts to liberalize spectrum market and award complete property rights to the licensed primary users of the spectrum highlight the demand to establish foundation of instruments and techniques to analyze the secondary spectrum sharing market (FCC 04-167, FCC 03-113, IA DCMS070);

• Increasing amount of network devices pose an issue of the frequency scarcity. Current dominating approach - static network allocation, has a problem of under-utilization of the bandwidth. Dynamic Spectrum Sharing (DSS) allow devices to opportunistically transmit on available radio spectrum. Some IEEE standards (IEEE 802.16, 802.22) and framework of cognitive radio supports this technology;

• Aside from technical difficulties of implementing DSS, it is as important to address economic part of such market interactions.

• Our model is another representation of the buyer-seller network. Similar analysis can be found for: efficiency for static networks Kranton and Minehart (2001), stability in dynamic networks Jackson and Watts (2002), private negotiations Manea (2011), Abreau and Manea (2012), Watts (2015a);

• There are various research that considers market of secondary spectrum sharing. Zhang and Zhou (2014) uses evolutionary game theory in location-oriented games, Watts (2015b) considers auction of uncertain good, Zhou and Zheng (2009) consider information asymmetry in double auctions;

• We use two types auction - ascending bid and clock auction. Detailed comparison of the two can be found in Cramton (1998) and Ausubel and Cramton (2004).

• Participants are randomly assigned over metric space \( \Omega \);

• During first stage, auction takes place in the coverage areas simultaneously. The result of the auction is price vector \( \mathcal{P}_t \);

• During second stage, if SU won the auction, he will remain in place for the next period. If buyer was misplaced, he get the chance to reallocate to the any point of the space while incurring the transaction cost. We assume SU will move if minimal price exceed his valuation;

• Next period, two-stage game will repeat with new positions. Equilibrium is achieved if no buyers has any incentive to reallocate.

We propose two type of auctions:

• Simultaneous Ascending Auction (SAA) - open ascending bid auction take place simultaneously in all coverage areas.

• Ascending Clock Auction (ACA) - ascending auction, where buyers compete for quantities given the price.

At first, we consider only static context, restricting SU's to their initial positions. What market mechanism will be superior in terms of welfare?

• If coverage areas do not intersect - both ACA and SAA auctions are price efficient. Price efficiency reached by maximizing total welfare with respect to the price, given allocation;

• Intersection can potentially create inefficient outcome under SAA auction due to absence of clearing mechanism;

• In general case, ACA auction is price efficient.

• Suppose now we allow buyers to reallocate to any point of the space;

• Cost of reallocating - fixed payment incurred at the start of next period (transportation cost, cost of doing business, etc.);

• Misplaced buyers are naive and myopic - they will always move the area with minimum price as long as it exceed their valuation minus transaction cost. No strategic behavior;

• What transaction cost do we need to impose on the buyers to stop moving after certain point of time?

• We introduce two notions - truncated neighbor gap and closest intercoverage gap;

• Consider the case of two sellers with non-intersecting coverage areas. Transaction cost equal to maximum of truncated neighbor gap will be sufficient to ensure stability;

• What about general case?

• If transaction cost exceed both closest intercoverage gap and truncated neighbor gap, general model will achieve equilibrium.

• So far intersection between coverage areas did not affect any of our dynamic results.

• Consider two models that only difference between them is presence of intersection. If stability conditions are satisfied, which one will take more time to converge to an equilibrium?

• As we have shown, intersection will never reduce speed of convergence.

• Can the welfare be improved if we change allocation of the buyers at the equilibrium?

• The answer is no, equilibrium is allocation efficient. No reposition of the buyers can improve the equilibrium.

• Other constrains impact;
• Experimental trials;
• Necessity conditions for stability;
• Interference analysis.

• Pianov Dmitrii |
  dapyanov@siu.edu
• Paper URL |
  https://bit.ly/21Sg9ER
• Presentation URL |
  https://rpubs.com/PDmiriy/rspectrummea
• Program simulation |
  https://radiospectrum.shinyapps.io/Spectrum

• Thank you!

• Similarly to radio spectrum example, we can formulate school voucher problem* - market that allocates good (education) among set of buyers (families), pertaining to certain location (school);

• Another example - emission trading. Production companies can participate in auctions to purchase pollutant allowances at certain locations (countries). Prices difference provides the incentive in commit FDI in one country rather than another;

• In general, model represents location-oriented market with homogeneous good. As shown later on, results hold for any efficient market allocation.