A Semidefinite Approach to Information Design in Non-atomic Routing Games
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We consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. All the agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signal respectively. The remaining non-receiving agents choose route according to Bayes Nash flow with respect to the prior. We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency cost over all public or obedient private signals. For a fixed flow induced by non-receiving agents, design of an optimal private signal is shown to be a generalized problem of moments for affine link latency functions, and to admit an atomic solution for the basic two link case. Motivated by this, a hierarchy of polynomial optimization is proposed to approximate, with increasing accuracy, information design over private and public signals, when the non-receiving agents choose route according to Bayes Nash flow. The first level of this hierarchy is shown to be exact for the basic two link case.
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