Governments, Large Corporations and Labour: A Differential Game Model of Class Conflict

This paper attempts to analyse the problem of how a government allocates resources to different social classes. We combine and extend two existing lines of research in game theoretical studies of political economy, building on Buenrostro et al. [3] who analysed how protests affect governments’ decisions, but not including class conflict, and Acemouglu [1] who does include class conflict but does not take into account protests. We develop a continuous time framework and obtain a stochastic differential game, where the government as well as the upper and lower social classes represent the players involved in the game. The stationary feedback Nash-equilibrium strategies are derived. Furthermore, we compare the results with another two cases where the government and the upper social class maximize their joint utility and the government transfers some resources to the lower social class. We find that under some specific conditions, the government which transfers some resources to the lower social class is more successful in creating a more harmonious society.