  Coordination is often critical to forming prosocial behaviors -- behaviors
that increase the overall sum of rewards received by all agents in a
multi-agent game. However, state of the art reinforcement learning algorithms
often suffer from converging to socially less desirable equilibria when
multiple equilibria exist. Previous works address this challenge with explicit
reward shaping, which requires the strong assumption that agents can be forced
to be prosocial. We propose using a less restrictive peer-rewarding mechanism,
gifting, that guides the agents toward more socially desirable equilibria while
allowing agents to remain selfish and decentralized. Gifting allows each agent
to give some of their reward to other agents. We employ a theoretical framework
that captures the benefit of gifting in converging to the prosocial equilibrium
by characterizing the equilibria's basins of attraction in a dynamical system.
With gifting, we demonstrate increased convergence of high risk, general-sum
coordination games to the prosocial equilibrium both via numerical analysis and
experiments.
