Hidden Chinese Restaurant Game: Grand Information Extraction for Stochastic Network Learning

Agents in networks often encounter circumstances requiring them to make decisions. Nevertheless, the effectiveness of the decisions may be uncertain due to the unknown system state and the uncontrollable externality. The uncertainty can be eliminated through learning from information sources, such as user-generated contents or revealed actions. Nevertheless, the user-generated contents could be untrustworthy since other agents may maliciously create misleading contents for their selfish interests. The passively revealed actions are potentially more trustworthy and also easier to be gathered through simple observations. In this paper, we propose a new stochastic game-theoretic framework, Hidden Chinese Restaurant Game (H-CRG), to utilize the passively revealed actions in stochastic social learning process. We propose grand information extraction, a novel Bayesian belief extraction process, to extract the belief on the hidden information directly from the observed actions. We utilize the coupling relation between belief and policy to transform the original continuous belief-state Markov decision process (MDP) into a discrete-state MDP. The optimal policy is then analyzed in both centralized and game-theoretic approaches. We demonstrate how the proposed H-CRG can be applied to the channel access problem in cognitive radio networks. We then conduct data-driven simulations using the CRAWDAD Dartmouth campus wireless local area network (WLAN) trace. The simulation results show that the equilibrium strategy derived in H-CRG provides higher expected utilities for new users and maintains a reasonable high social welfare comparing with other candidate strategies.