DIFFERENTIAL GAME MODEL OF THE DYNASTIC CYCLE - 3D-CANONICAL SYSTEM WITH A STABLE LIMIT-CYCLE

Ancient Chinese history reveals many examples of a cyclical pattern of social development connected with the rise and the decline of dynasti es. In this paper, a possible explanation of the periodic alternation between despotism and anarchy by a dynamic game between the rulers and the bandits is offered. The third part of the society, the farmers, a re dealt with as a renewable resource which is exploited by both playe rs in a different manner. It is shown that the Nash solution of this o ne-state differential game may be a persistent cycle. Although we rest rict the analysis to open-loop solutions, this result is of interest f or at least two reasons. First, it provides one of the few existing dy namic economic games with periodic solutions. Second, and more importa nt, the model is an example of a three-dimensional canonical system (o ne state, two costates) with a stable limit cycle as solution. As far as we see, our model provides up to now the simplest (i.e., lowest dim ensional) case of a persistent periodic solution of an intertemporal d ecision problem.