A distributed coding-decoding-based Nash equilibrium seeking algorithm over directed communication network

This paper is concerned with the distributed Nash equilibrium (NE) computation problem for non-cooperative games subject to partial-decision information. For the purpose of congestion mitigation, coding-decoding-based schemes are constructed on the basis of logarithmic and uniform quantizers, respectively. To be specific, the data (decision variable) are first mapped to codewords by an encoder scheme, and then sent to the neighboring agents through a directed communication network (with non-doubly stochastic weighted matrix). By using a decoder scheme, a new distributed algorithm is established for seeking the NE. In order to eliminate the convergence error caused by quantization, a dynamic variable is introduced and a modified coding-decoding-based algorithm is constructed under the uniform quantization scheme, which ensures the asymptotic convergence to the NE. The proposed algorithm only requires that the weighted adjacency matrix is row stochastic instead of double stochastic. Finally, one numerical example is provided to validate the effectiveness of our algorithms.