The Evolution of Economic Inequality and Political Hierarchy on Social Networks

Abstract Bowles (2009) proposed that the emergence of political hierarchy and economic inequality during the early Holocene might be explained by a progression of three equilibrium network structures derived from the economic and social conditions of the time. Bowles (2009) and Kets et al. (2011) determined the maximal degree of inequality that can persist on a network where coalitions may withdraw from the network, and the set of feasible coalitions is determined by network structure. Here I illustrate their models by studying the maximum inequality sustainable under costs and network decay conditions that may have existed during the Pleistocene and the Holocene, as well as the associated network efficiency, welfare, and levels of inequality. Further, I extend their work by studying the evolution of 4-node network structures subject to 2 dynamics: individually motivated endogenous network evolution and between network competition. Each network evolves according to the pairwise stability rule. Nodes may be shortsighted or far-sighted; the latter anticipate the effect of their actions on bargaining power and the network and hence foresee their post bargaining payoffs while the former consider only the primary payoffs from the network structure. In addition to within network updating, conflicts take place between networks, in which the networks with higher total utility win and replace the losers with a replica of their network structures. The model results show that homogeneous networks converge to the efficient outcomes when the agents on the network are rewarded with anticipated payoffs while the heterogeneous population networks produces diverse distribution of network structure types. We find that within network transitions and between network competitions work in opposite directions because of the concavity of utility function. Finally, the evolution of economic and political hierarchy not only depends on economic and political structures, but also the accessibility of network structure among the possible network structure set