Learning in the real world occurs when an agent, which perceives its current state and takes actions, interacts with the environment, which in return provides a positive or negative feedback. The field of reinforcement learning studies such processes and attempts to find policies that map states of the world to the actions of agents in order to maximize cumulative reward over the long run. In multi-agent systems, agent learning becomes more challenging, since the optimal action of each agent generally depends on the actions of other agents. Most studies in multiagent learning research employ non-cooperative equilibrium as a learning objective. However, in many situations, the equilibrium gives worse payoffs to both players than their payoffs would be in the case of cooperation. Therefore the agents have strong desire to choose a cooperative solution instead of the non-cooperative equilibrium. In this work, we apply the Nash Bargaining Solution (NBS) to multi-agent systems with unknown parameters and design a multiagent learning algorithm based on bargaining, in which the agents can reach the NBS by learning through experience. We show that the solution is unique and is Pareto-optimal. We also prove theoretically that the algorithm converges. In addition, we extend the work to multi-agent systems with asymmetric agents having different powers in decision making and design a multiagent learning algorithm with asymmetric bargaining. To evaluate these learning algorithms and compare with the existing learning algorithms, the benchmark, grid world games, are adopted as the simulation test-bed. The simulation results demonstrate that our learning algorithms converge to the unique Pareto-optimal solution and the convergence is faster in comparison to the existing multiagent learning algorithms. Finally, we discuss an application of multiagent learning algorithms to a classic economic model, which is known as oligopoly.
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