Bayesian Reinforcement Learning for Coalition Formation under Uncertainty
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 3
Coalition formation under uncertainty: bargaining equilibria and the Bayesian core stability concept
Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems
Social and Economic Networks
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In this paper we study network games where agents with different skills come together to cooperate and yet competitively pursue individual goals. We propose a multi-agent based utilitarian approach to model the payoff allocation problem for a class of such games where the capabilities of the agents and the payoffs are not known with certainty. The primary objective is to maximize a linear sum of the expected utilities of risk-averse agents, and we consider constant risk-aversion with exponential utility functions. We pose the problem as a stochastic cooperative game which is solved in two phases. In the first phase we apply a learning mechanism on this 'social' network of fully connected agents to arrive at a consensus on the capability of every agent in the coalition thus resolving uncertainty in capabilities. Agents initially start with a social influence matrix reflecting the influence agents have on each other and prior subjective beliefs of the capabilities of the others and these beliefs evolve through a process of interaction. We use a variant of the DeGroot algorithm to show that over time learning results in a dynamic update of the beliefs and the social influence matrix leading to a consensus. We provide theoretical convergence proofs for the algorithm. The second phase involves optimizing a capability-weighted sum of the expected utilities of the agents to achieve a group Pareto optimal solution. In this paper we propose a new framework called the Capability Weighted Group Utility Maximizer developed around Borch's theorem borrowed from the actuarial world of insurance to obtain a fair distribution of the stochastic payoffs once a consensus is reached on the capabilities of the agents in the coalition.