9.2 Access Control Games for Multiple Access Collision Channels 253 9.2.2 Aloha-Based Protocol Medium Access Control Games with Pricing As mentioned in Chapters 2 and 3, pricing is way of improving the efficiency of the outcome of a game. In this case, there is usually an additional player (e.g., the network owner or base station) who wants to maximize a certain global performance metric. But pricing can also be used to model the cost of transmission, in which case the cost is evaluated by the transmitter himself. The one-shot access control game of Sec. 9.2 becomes a new game: G c = K, P, u c K,m i with: u c : i P K [0, 1] (a 1 , . . . , a K ) 1 {a i >max j=i a j } - c(a i ) l (9.18) iK (9.17) and c : R + R + is the cost or pricing function of transmitter i (assumed to be identical for all transmitters), which only depends on the action of transmitter i and not on the other played actions. The cost function is assumed to be strictly increasing, that is: