Exploring Risk Sharing in Stochastic Exchange Networks

Abstract

This study examines the dynamics of bargaining in a social system that incorporates risk sharing through exchange network models and stochastic matching between agents. The analysis explores three scenarios: convergent expectations, divergent expectations, and social preferences among model players. The study introduces stochastic shocks through a Poisson process, which can disrupt coordination within the decentralized exchange mechanism. Despite these shocks, agents can employ a risk-sharing protocol utilizing Pareto weights to mitigate their effects. The model outcomes do not align with the generalized Nash bargaining solutions across all scenarios. However, over a sufficiently long time frame, the dynamics consistently converge to a fixed point that slightly deviates from the balanced outcome or Nash equilibrium. This minor deviation represents the risk premium necessary for hedging against mutual risk. The risk premium is at its minimum in the scenario with convergent expectations and remains unchanged in the case involving social preferences.