Equilibrium in risk-sharing games

TL;DR

This paper models risk-sharing as a strategic game where agents choose securities and pricing kernels, revealing unique equilibria with endogenous bounds and efficiency losses, especially impacting highly risk-tolerant agents.

Contribution

It introduces a novel game-theoretic framework for risk-sharing, characterizing equilibrium securities and beliefs, and analyzing the effects of strategic behavior on efficiency and agent profits.

Findings

Existence of risk-sharing Nash equilibrium for any number of agents.

Equilibrium securities are endogenously bounded, leading to efficiency loss.

Highly risk-tolerant agents benefit more from Nash equilibrium than from Arrow-Debreu equilibrium.

Abstract

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents' best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to exist for arbitrary number of agents and be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different than their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.