We formulate and solve the problem of optimizing the structure of an information propagation network between multiple agents. In a given space of interests (e.g., information on certain targets), each agent is defined by a vector of their desirable information, called filter, and a vector of available information, called source. The agents seek to build a directed network that maximizes the value of the desirable source-information that reaches each agent having been filtered en route, less the expense that each agent incurs in filtering any information of no interest to them. We frame this optimization problem as a game of common interest, where the Nash equilibria can be attained as limit points of Sampled Fictitious Play (SFP), offering a method that turns out computationally effective in traversing the huge space of feasible networks on a given node set. Our key idea lies in the creative use of history in SFP, leading to the new History Value-Weighted SFP method. To our knowledge, this is the first successful application of FP for network structure optimization. The appeal of our work is supported by the outcomes of the computational experiments that compare the performance of several algorithms in two settings: centralized (full information) and decentralized (local information).
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