Abstract
This article examines the famous distributed algorithm: try-again-till-you're-satisfied in opinion formation game. It illustrates that a simple learning algorithm which consists to react only when unsatisfied through on/off observation can provide a satisfactory solution. Learning takes place during the interactions of the game, in which the agents have no direct knowledge of the payoff model. Each agent is allowed to observe their own satisfaction/dissatisfaction state and has only one-step memory. The existing results linking the outcomes to stationary satisfactory set do not apply to this situation because of continuous action space. We provide a direct proof of convergence of the scheme for arbitrary initial conditions and arbitrary number of agents. As the number of iterations grows, we show that there is an emergence of a consensus in terms of opinion distribution of satisfied agents. A similar result holds for the mean-field opinion formation game.
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