Double best response dynamics in topology formation game for ad hoc networks

We consider a topology formation problem for wireless ad hoc networks. There are wireless nodes located on a plane. Every node can dynamically adjust its transmission power. The global objective is to assign optimal transmission power to every node such that the resulting topology is connected and minimizes total power cost. The topology formation problem is studied as a noncooperative game. We propose two algorithms of collective behavior based on the, so-called, “double best response” decision rule . This decision rule originates from a reflexive game framework and describes behavior of an agent with the first rank of reflection. Efficiency of proposed algorithms is evaluated by simulations and is compared with a conventional best response algorithm