A timestamp-based log-linear algorithm for solving locally-informed multi-agent finite games

In this paper, the distributed Nash equilibrium seeking problem for multi-agent finite games is considered. Considering the locally-informed communication structure, previous centralized game-theoretic learning dynamic methods are not feasible. To this end, we propose a distributed log-linear algorithm by introducing a timestamp-based communication mechanism that enables agents to acquire estimates of the true action profile from their neighborhoods. It is shown that the proposed distributed log-linear algorithm significantly outperforms the existing best response dynamics regarding both effectiveness and reliability. For illustration, a locally-informed multi-player Sudoku puzzle is introduced, where each cell is taken as a player, and each player fills numbers only based on the local information of its neighboring players. The simulation results validate the effectiveness of our algorithm in solving the locally-informed multi-player Sudoku puzzle. Our methodology provides a viable and benchmark approach to address the fully distributed locally-informed multi-agent joint decision-making problem.