The dynamics of risk-sensitive allocations

This paper describes Pareto optimal allocations when agents have risk-sensitive preferences as formulated by Hansen and Sargent (IEEE Trans. Automat. Control 40(5) (1995) 968-971). Necessary and sufficient conditions are given for the existence and stability of steady states at which Pareto weights are time-invariant. When all agents are risk-sensitive with the same power reward function there is a unique interior steady state which is stable when the power is positive and unstable when the power is negative. When there is at least one agent with time-additive preferences eventually all risk-sensitive agents have zero Pareto weights.