  In multiagent environments, the capability of learning is important for an
agent to behave appropriately in face of unknown opponents and dynamic
environment. From the system designer's perspective, it is desirable if the
agents can learn to coordinate towards socially optimal outcomes, while also
avoiding being exploited by selfish opponents. To this end, we propose a novel
gradient ascent based algorithm (SA-IGA) which augments the basic
gradient-ascent algorithm by incorporating social awareness into the policy
update process. We theoretically analyze the learning dynamics of SA-IGA using
dynamical system theory and SA-IGA is shown to have linear dynamics for a wide
range of games including symmetric games. The learning dynamics of two
representative games (the prisoner's dilemma game and the coordination game)
are analyzed in details. Based on the idea of SA-IGA, we further propose a
practical multiagent learning algorithm, called SA-PGA, based on Q-learning
update rule. Simulation results show that SA-PGA agent can achieve higher
social welfare than previous social-optimality oriented Conditional Joint
Action Learner (CJAL) and also is robust against individually rational
opponents by reaching Nash equilibrium solutions.
