Multi-Leader Stackelberg Games in Multi-Channel Spatial Aloha Networks

This paper uses a multi-channel spatial Aloha model to describe a distributed autonomous wireless network where a group of transmit-receive pairs (users) share multiple collision channels via slotted-Aloha-like random access. The design objective is to enable each autonomous user i to select a channel c(i) and decide a medium access probability (MAP) q(i) to improve its throughput, while providing a certain degree of fairness among the users. Game theoretic approaches are applied, where each user i is a player who chooses the strategy (c(i), q(i)) to improve its own throughput. To search for a Nash Equilibrium (NE), a Multi-Leader Stackelberg Game (MLSG) is formulated to iteratively obtain a solution on each dimension of the (c(i), q(i)) strategy. Initially, multiple Stackelberg leaders are elected to manage the MAPs of all players. Then under the resulting MAP profile, each player iteratively chooses its channel to improve its throughput. An Oscillation Resolving Mechanism (ORM) is further proposed to stabilize the design in some special cases where the operating points of some players in a local region would oscillate between the two dimensions of the myopic search. Compared to existing methods of pre-allocating MAPs, the MLSG game further improves the overall network throughput by iteratively tuning the MAPs toward max-min throughput in each subnet. Simulation results show that the MLSG game gradually improves the total throughput until reaching a NE, which also provides good throughput fairness for the players.