Maximum Power Game as a Physical and Social Extension of Classical Games

We consider an electric circuit in which the players participate as resistors and adjust their resistance in pursuit of individual maximum power. The maximum power game(MPG) becomes very complicated in a circuit which is indecomposable into serial/parallel components, yielding a nontrivial power distribution at equilibrium. Depending on the circuit topology, MPG covers a wide range of phenomena: from a social dilemma in which the whole group loses to a well-coordinated situation in which the individual pursuit of power promotes the collective outcomes. We also investigate a situation where each player in the circuit has an intrinsic heat waste. Interestingly, it is this individual inefficiency which can keep them from the collective failure in power generation. When coping with an efficient opponent with small intrinsic resistance, a rather inefficient player gets more power than efficient one. A circuit with multiple voltage inputs forms the network-based maximum power game. One of our major interests is to figure out, in what kind of the networks the pursuit for private power leads to greater total power. It turns out that the circuits with the scale-free structure is one of the good candidates which generates as much power as close to the possible maximum total.