Efficiency and equilibria in games of optimal derivative design

Abstract

In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal-agent models that are extended within, here the presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie-breaking rules. The main results of this paper are a proof of existence of (mixed-strategies) Nash equilibria in the case of profit-maximizing agencies, and of socially efficient allocations when the firms are risk minimizers. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix-mix" tie-breaking rule, in which case firms share the whole market over given proportions. Preliminary -Comments WelcomeJEL classification: C62, C72, D43, D82, G14.

The Effect of Market Power on Risk-Sharing

“…In the existed models of non-competitive risk-sharing, the agents' market power is asymmetric and stems mostly from asymmetric information or other types of imposed structural differences among players. For example, games on security design under adverse-selection problem (i.e., asymmetric information) have been recently studied (see among others Horst and Moreno-Bromberg [28,29] and Page and Monteiro [42,43]…”

“…In Section 6, we examine how the the main results of the paper are affected we withdraw the common-beliefs assumption. 15 The quadratic utility has be widely used in the risk-sharing literature in a variety of subjects, from adverse-selection problems (see e.g., Carlier et al [12], Horst and Moreno-Bromberg [28,29]) to games on financial innovation (as in Rahi and…”

“…(i) Each agent reports only a fraction of her true endowment and some exposure to the endowments of the rest of the agents. 29 It is a matter of simple calculations to get an equivalent inequality of condition λ −i λ −j /α < 1. Indeed, for n = 3, i = 1 and j = 2, the latter inequality is equivalent to…”

“…For this, we compare the coefficients λ i λ −i λ −j /α and λ i (recall again (2.5)) and observe that only in the special case of two agents, the size in Nash equilibrium is always less than the Pareto-optimal one (see also the indicative Table 1 below). For n ≥ 3, the inequality λ −i λ −j /α < 1 holds if λ i and λ j are sufficiently large 29 , meaning that agent i buys less of endowment E j if both agents i and j are sufficiently low risk averse. The latter implies that for relatively low risk averse agents, only a percentage of their true endowments is shared in Nash equilibrium.…”

Subgame-perfect equilibrium strategies in state-constrained recursive stochastic control problems

“…For a generalization, see [44] (CRRA preferences), so [36] and [9] (martingale methods). See also [24], [33] and [34].…”