Nash Equilibria in Optimal Reinsurance Bargaining

TL;DR

This paper models strategic behavior in reinsurance negotiations, showing that agents tend to appear homogeneous in risk preferences at equilibrium, which affects premium allocation but not total welfare.

Contribution

It introduces a game-theoretic framework for reinsurance bargaining, revealing how strategic choice of risk preferences influences equilibrium outcomes.

Findings

Agents appear homogeneous in risk preferences at Nash equilibrium.

Reinsurance premiums are affected by strategic behavior, while indemnities remain unchanged.

The bargaining power advantage determines which agent gains more welfare.

Abstract

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.