Transmission Power Control Game with SINR as Objective Function

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 HawkDove 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 big signal to transmit (called a stronger user) for both scenarious meanwhile his rival has small signal to transmit (weaker user) then behaviour of the stronger user drastically changes in cooperative plot compare to selfish one. Namely, in selfish one the stronger user squeezes the weaker one from the best channel meanwhile in cooperative he allows the weaker user employs the best channel and himself prefers to apply a mixed strategy.