Transmission Power Control Game with SINR as Objective Function

Abstract

We consider the transmission power control problem with SINR as objective function in the two scenarii: selfish and cooperative. We show that in the selfish (non-cooperative) scenario several Nash equilibria can arise. In particular, the game can take the form of the Hawk-Dove game, where the users can choose either conciliation or conflict fighting for shared sub-carriers. We fully characterize different types of Nash equilibria. In the cooperative scenario, we show that the parameter area where users employ pure strategies is essentially narrower than the area where users employ mixed strategies. Moreover, we identify an area where Nash equilibrium and Pareto equilibrium coincide. If one of the users has a large power resource (called a stronger user) for both scenarii and his rival has small power resource (weaker user) then the behaviour of the stronger user drastically changes in cooperative scenario compared to the selfish one. Namely, in the selfish scenario the stronger user squeezes the weaker one from the best channel meanwhile in the cooperative scenario he allows the weaker user to employ the best channel and himself applies a mixed strategy.

The work was supported by EGIDE ECO-NET grant no.18933SL “Game Theory for Wireless Networks” and RFBR and NNSF Grant no.06-01-39005.