This paper considers a topology formation problem for wireless ad hoc networks.
There are wireless nodes located on a plane. Each node can adjust its transmission power
in the dynamic mode. The global objective lies in assigning an optimal transmission power
to each node so that the resulting topology is connected and minimizes the total power cost.
The topology formation problem is studied as a noncooperative game. The author proposes
two algorithms of collective behavior and network formation based on the so-called “double
best response” decision rule. This decision rule originates from the reflexive game framework
and describes the behavior of an agent with reflexion rank 1. The efficiency of the suggested
algorithms is evaluated by simulation and compared with the standard best response algorithm.