  This paper handles a kind of strategic game called potential games and
develops a novel learning algorithm Payoff-based Inhomogeneous Partially
Irrational Play (PIPIP). The present algorithm is based on Distributed
Inhomogeneous Synchronous Learning (DISL) presented in an existing work but,
unlike DISL,PIPIP allows agents to make irrational decisions with a specified
probability, i.e. agents can choose an action with a low utility from the past
actions stored in the memory. Due to the irrational decisions, we can prove
convergence in probability of collective actions to potential function
maximizers. Finally, we demonstrate the effectiveness of the present algorithm
through experiments on a sensor coverage problem. It is revealed through the
demonstration that the present learning algorithm successfully leads agents to
around potential function maximizers even in the presence of undesirable Nash
equilibria. We also see through the experiment with a moving density function
that PIPIP has adaptability to environmental changes.
