Double best response as a network stability concept

We introduce a novel concept of network formation with rational players. The concept is called double best response by analogy with conventional best response dynamics used in network formation games. We applied double best response to the game called minimal-cost connectivity game where every player wants to be connected to as many players as possible with minimal individual cost. We introduce a concept of equilibrium in double best responses (EDBR) and show that the set of EDBR profiles is a subset of Nash equilibria profiles and EDBR networks demonstrate some nice properties in comparison with conventional NE.