  We studied spatial Prisoner's Dilemma and Stag Hunt games where both the
strategy distribution and the players' individual noise level could evolve to
reach higher individual payoff. Players are located on the sites of different
two-dimensional lattices and gain their payoff from games with their neighbors
by choosing unconditional cooperation or defection. The way of strategy
adoption can be characterized by a single $K$ (temperature-like) parameter
describing how strongly adoptions depend on the payoff-difference. If we start
the system from a random strategy distribution with many different player
specific $K$ parameters, the simultaneous evolution of strategies and $K$
parameters drives the system to a final stationary state where only one $K$
value remains. In the coexistence phase of cooperator and defector strategies
the surviving $K$ parameter is in good agreement with the noise level that
ensures the highest cooperation level if uniform $K$ is supposed for all
players. In this paper we give a thorough overview about the properties of this
evolutionary process.
