Mechanisms for Risk Averse Agents, Without Loss

Auctions in which agents' payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in response to limitations on deterministic mechanisms imposed by computational complexity. For many of these mechanisms, which are often referred to as truthful-in-expectation, incentive compatibility is contingent on the assumption that agents are risk-neutral. These mechanisms have been criticized on the grounds that this assumption is too strong, because "real" agents are typically risk averse, and moreover their precise attitude towards risk is typically unknown a-priori. In response, researchers in algorithmic mechanism design have sought the design of universally-truthful mechanisms --- mechanisms for which incentive-compatibility makes no assumptions regarding agents' attitudes towards risk. We show that any truthful-in-expectation mechanism can be generically transformed into a mechanism that is incentive compatible even when agents are risk averse, without modifying the mechanism's allocation rule. The transformed mechanism does not require reporting of agents' risk profiles. Equivalently, our result can be stated as follows: Every (randomized) allocation rule that is implementable in dominant strategies when players are risk neutral is also implementable when players are endowed with an arbitrary and unknown concave utility function for money.Comment: Presented at the workshop on risk aversion in algorithmic game theory and mechanism design, held in conjunction with EC 201

Dynamic Managerial Compensation: a Mechanism Design Approach

We characterize the optimal incentive scheme for a manager who faces costly effort decisions and whose ability to generate profits for the firm varies stochastically over time. The optimal contract is obtained as the solution to a dynamic mechanism design problem with hidden actions and persistent shocks to the agent's productivity. When the agent is risk-neutral, the optimal contract can often be implemented with a simple pay package that is linear in the firm's profits. Furthermore, the power of the incentive scheme typically increases over time, thus providing a possible justification for the frequent practice of putting more stocks and options in the package of managers with a longer tenure in the firm. In contrast to other explanations proposed in the literature (e.g., declining disutility of effort or career concerns), the optimality of seniority-based reward schemes is not driven by variations in the agent's preferences or in his outside option. It results from an optimal allocation of the manager's informational rents over time. Building on the insights from the risk-neutral case, we then explore the properties of optimal incentive schemes for risk-averse managers. We find that, other things equal, risk-aversion reduces the benefit of inducing higher effort over time. Whether (risk-averse) managers with a longer tenure receive more or less high-powered incentives than younger ones then depends on the interaction between the degree of risk aversion and the dynamics of the impulse responses for the shocks to the manager's type.dynamic mechanism design; adverse selection; moral hazard; incentives; optimal pay scheme; risk-aversion; stochastic process

MUTUAL INSURANCE WITH ASYMMETRIC INFORMATION: THE CASE OF ADVERSE SELECTION

This paper examines the impact of risk heterogeneity and asymmetric information on mutual risk-sharing agreements. It displays the optimal incentive compatible sharing rule in a simple two-agent model with two levels of risk. When individual risk is public information, equal sharing of wealth is not achievable when risk heterogeneity is too large or when risk aversion is too low. However the mutualization principle still holds as agents only bear aggregate risk. This result no longer holds when risk is private information. Moreover, the asymmetry of information (i) makes equal sharing unsustainable when both individuals are low risk types (ii) induces some exchanges when agents have the same level of initial wealth and (iii) induces changes in the direction of transfer with respect to the complete information benchmark in some states of nature when risk types are independent and absolute risk aversion is decreasing and convex.Mutual agreements; Asymmetric information; Mechanism Design

Moral hazard and risk-sharing: risk-taking as an incentive tool

We examine how moral hazard impacts risk-sharing when risk-taking can be part of the mechanism design. In a two-agent model with binary effort, we show that moral hazard always increases risk-taking (that is the amount of wealth invested in a risky project) whereas the effect on risk-sharing (the amount of wealth transferred between agents) is ambiguous. Risk-taking therefore appears as a useful incentive tool. In particular, in the case of preferences exhibiting Constant Absolute Risk Aversion (CARA), moral hazard has no impact on risk-sharing and risk-taking is the unique mechanism used to solve moral hazard. Thus, risk-taking appears to be the prevailing incentive tool.Risk-Taking, Informal Insurance, Moral Hazard

Dynamic Managerial Compensation: A Variational Approach

We study the optimal dynamics of incentives for a manager whose ability to generate cash flows changes stochastically with time and is his private information. We show that distortions (aka, wedges) under optimal contracts may either increase or decrease over time. In particular, when the manager's risk aversion and ability persistence are small, distortions decrease, on average, over time. For sufficiently high degrees of risk aversion and ability persistence, instead, distortions increase, on average, with tenure. Our results follow from a novel variational approach that permits us to tackle directly the "full program," thus bypassing some of the difficulties of the "first-order approach" encountered in the dynamic mechanism design literature

Moral hazard and risk-sharing: risk-taking as an incentive tool

We examine how moral hazard impacts risk-sharing when risk-taking can be part of the mechanism design. In a two-agent model with binary effort, we show that moral hazard always increases risk-taking (that is the amount of wealth invested in a risky project) whereas the effect on risk-sharing (the amount of wealth transferred between agents) is ambiguous. Risk-taking therefore appears as a useful incentive tool. In particular, in the case of preferences exhibiting Constant Absolute Risk Aversion (CARA), moral hazard has no impact on risk-sharing and risk-taking is the unique mechanism used to solve moral hazard. Thus, risk-taking appears to be the prevailing incentive tool

Optimal auctions with ambiguity

A crucial assumption in the optimal auction literature has been that each bidder's valuation is known to be drawn from a single unique distribution. In this paper we relax this assumption and study the optimal auction problem when there is ambiguity about the distribution from which these valuations are drawn and where the seller or the bidder may display ambiguity aversion. We model ambiguity aversion using the maxmin expected utility model where an agent evaluates an action on the basis of the minimum expected utility over the set of priors, and then chooses the best action amongst them. We first consider the case where the bidders are ambiguity averse (and the seller is ambiguity neutral). Our first result shows that the optimal incentive compatible and individually rational mechanism must be such that for each type of bidder the minimum expected utility is attained by using the seller's prior. Using this result we show that an auction that provides full insurance to all types of bidders is always in the set of optimal auctions. In particular, when the bidders' set of priors is the ε- contamination of the seller's prior the unique optimal auction provides full insurance to bidders of all types. We also show that in general, many classical auctions, including first and second price are not the optimal mechanism (even with suitably chosen reserve prices). We next consider the case when the seller is ambiguity averse (and the bidders are ambiguity neutral). Now, the optimal auction involves the seller being perfectly insured. Hence, as long as bidders are risk and ambiguity neutral, ambiguity aversion on the part of the seller seems to play a similar role to that of risk aversion.Optimal auction, mechanism design, ambiguity, uncertainty

On the Role of Risk Aversion and Market Design in Capacity Expansion Planning

Investment decisions in competitive power markets are based upon thorough profitability assessments. Thereby, investors typically show a high degree of risk aversion, which is the main argument for capacity mechanisms being implemented around the world. In order to investigate the interdependencies between investors\u27 risk aversion and market design, we extend the agent-based electricity market model PowerACE to account for long-term uncertainties. This allows us to model capacity expansion planning from an agent perspective and with different risk preferences. The enhanced model is then applied in a multi-country case study of the European electricity market. Our results show that assuming risk-averse rather than risk-neutral investors leads to slightly reduced investments in dispatchable capacity, higher wholesale electricity prices, and reduced levels of resource adequacy. These effects are more pronounced in an energy-only market than under a capacity mechanism. Moreover, uncoordinated changes in market design may also lead to negative crossborder effects