Advances in Mobile Cloud Computing Systems

Mobile Cloud Computing with Telecom Operator Cloud 31

Theorem 1.1 The unique Nash equilibrium exists in the proposed

Stackelberg game.

Proof: In our Stackelberg game model, each stage has its flawless equi-

librium in a Nash equilibrium, respectively: the service price strate-

gies x

∗

in Equation 1.26 offered by the CMM SPs, the service allocation

strategy s

∗

m

, the interference price, and the service allocation strategy

s

∗

k

in Equation 1.10. Because we have proven that each stage exists a

perfect equilibrium in a Nash equilibrium, the Nash equilibrium of

the proposed Stackelberg game model exists. We also know that the

subgame perfect equilibrium in each stage is unique. Therefore, the

total Stackelberg Nash equilibrium is unique.

To get the Nash equilibrium ...