Game-Theoretic Specificity of a Competitive Allocation of the Frequency Spectrum

Abstract

We consider the problem of developing and optimizing the rules of the spectrum auction. One-sided sealed-bid spectrum auctions are studied. Two types of pricing are compared theoretically: the first-price and the second-price. А game model of the auction with free riders is constructed. A free rider uses frequencies purchased by another such participant for free. All Nash equilibria of the obtained games are found and represented in an analytical form. The significant difference between games with all free riders and games with at least one ordinary player is shown. It is proved that when players eliminate their dominated strategies, the resulting auction price of the lot is determined by its value for ordinary players. In the case when all players are free riders, the price is equal to the minimal bid price. The influence of the information the participants have about their partners’ values of a lot on the outcome of the game is discussed. The theoretically obtained properties are in agreement with the results of the experiments presented for spectrum auctions in the scientific literature.