The late Professor Masanao Aoki of UCLA, who passed away at the end of July 2018, in his later years dedicated himself to the reconstruction of macroeconomics mainly in terms of statistical physics. Professor Aoki, who was already an IEEE fellow, was also named an Econometric Society Fellow in 1979. Until the early 1990s, however, his contributions were focused on the new developments of a novel algorithm for the time series model and their applications to economic data. Those contributions were undoubtedly equivalent to the Nobel Prize-winning work of Granger's "co-integration method". Afterthe publications of his and both published by Cambridge University Press, in 1996 and 2002, respectively, his contributions rapidly became known and spread throughout the field. In short, these new works challenged econophysicists to develop evolutionary shastic dynamics, multiple equilibria, and externalities as field effects and revolutionized the shastic views of interacting agents. In particular, the publication of , also by Cambridge University Press (2007), in cooperation with Hiroshi Yoshikawa, further sharpened the process of embodying “a perspective from statistical physics and combinatorial shastic processes” in economic modeling. Interestingly, almost concurrently with Prof. Aoki’s newest development, similar approaches were appearing. Thus, those who were working in the same context around the world at that time cametogether, exchanging their results during the past decade. In memory of Prof. Aoki, this book has been planned by authors who followed him to present the most advanced outcomes of his heritage.