Loss-averse Agents Research Articles

Bilateral trade with loss-averse agents

AbstractWe introduce expectations-based loss aversion, which can explain the empirically well-documented endowment and attachment effect, into the classical bilateral-trade setting (Myerson and Satterthwaite in J. Econ. Theory 29:265–281, 1983). We derive optimal mechanisms for different objectives and find that relative to no loss aversion, the platform designer optimally provides agents with partial insurance in the ownership dimension and with full insurance in the money dimension. Notably, the former is achieved either by increasing or decreasing the trade frequency, depending on the distribution of types. Finally, we show that the impossibility of inducing materially efficient trade persists with loss aversion.

Loss aversion in asymmetric anti‐coordination games

AbstractThis paper studies theoretically and experimentally how the possibility of a negative payoff to one player in 2‐by‐2 hawk‐dove games affects the strategic behavior of both players. Exposing column players to a possibility of negative payoff allows us to examine if row players can anticipate the column players' loss aversion. A level‐k model with loss averse agents predicts treatment effects across two versions of hawk‐dove games with and without losses. Our data support a direct effect of loss aversion and fail to support the anticipation of loss aversion. Specifically, the column players in the treatment group are more likely to play Dove when they face losses; while, only few untreated participants acting as row players seem to anticipate such increased propensity of choosing Dove by their opponents. Further, a time effect is documented and found to be explained by increases in participants' depths of strategic reasoning over time.

Loss aversion and lying behavior

We theoretically show that loss-averse agents are more likely to lie to avoid receiving a low payoff after a random draw the lower the ex-ante probability of this bad outcome. The ex-ante expected payoff increases as the bad outcome becomes less likely, and hence the greater is the loss avoided by lying. We demonstrate robust support for this theory by reanalyzing the results from the extant literature and with a new experiment that varies the outcome probabilities and is run double-anonymous.

Intertemporal incentives under loss aversion

This paper studies the intertemporal allocation of incentives in a repeated moral hazard model where the loss averse agent experiences today utility from changes in their expectations about present and future wages and effort. In contrast to the standard prediction, under mild restrictions over the utility function, uncertainty is fully deferred into future payments allowing the principal to pay fixed wages. Although the intertemporal allocation of incentives is nonstandard, the optimal contract is well behaved as essential features of the contract with classical preferences—no rents to the agent, conditions to achieve first-best cost and non-optimality of ex-post random contracts—still hold.

Prospect dynamics and loss dominance

This paper investigates the role of loss-aversion in affecting the long-run equilibria of stochastic evolutionary dynamics. We consider a finite population of loss-averse agents who are repeatedly and randomly matched to play a symmetric two-player normal form game. When an agent revises her strategy, she compares the payoff from each strategy to a reference point. Under the resulting dynamics, called prospect dynamics, risk-dominance is no longer sufficient to guarantee stochastic stability in 2 × 2 coordination games. We propose a stronger concept, loss-dominance: a strategy is loss-dominant if it is risk-dominant and a maximin strategy. In 2 × 2 coordination games, the state where all agents play the loss-dominant strategy is uniquely stochastically stable under prospect dynamics for any degree of loss-aversion and all types of reference points. For symmetric two-player normal form games, a generalized concept, generalized loss-dominance, gives a sufficient condition for stochastic stability under prospect dynamics.

Goal bracketing and self-control

This paper studies the role of goal bracketing to attenuate time inconsistency. When setting non-binding goals for a multi-stage project, an agent must decide how to group, or bracket, such goals for evaluation. He can bracket broadly by setting an aggregate goal for the entire project, or narrowly by setting incremental goals for individual stages. A loss averse agent brackets optimally by trading off motivation and risk pooling, which interacts non-trivially with time discounting. An aggregate goal becomes more attractive as early-stage uncertainty increases, while incremental goals become more attractive when later-stage uncertainty increases.

Endogenous reference points in bargaining

We allow the reference point in (cooperative) bargaining problems with a reference point to be endogenously determined. Two loss averse agents simultaneously and strategically choose their reference points, taking into consideration that with a certain probability they will not be able to reach an agreement and will receive their disagreement point outcomes, whereas with the remaining probability an arbitrator will distribute the resource by using (an extended) Gupta–Livne bargaining solution (Gupta and Livne in Manag Sci 34:1303–1314, 1988). The model delivers intuitive equilibrium comparative statics on the breakdown probability, the loss aversion coefficients, and the disagreement point outcomes.

Optimal task assignments with loss-averse agents

This paper studies optimal task assignments in a setting where agents are expectation-based loss averse according to Köszegi and Rabin (2006, 2007) and are compensated according to an aggregated performance measure in which tasks are technologically independent. We show that the optimal task assignment is determined by a trade-off between paying lower compensation costs and restricting the set of implementable effort profiles under multitasking. We show that loss aversion combined with how much the marginal cost of effort in one task increases with the effort chosen in other tasks determines when multitasking saves on compensation costs, but results in an implementation problem.

The Effect of Loss Aversion on the Multiperiod Principal-Agent Problem

This paper studies how compensation and incentives are provided in a multiperiod setting to a loss averse agent with reference-dependent preferences. The two-period contract is different contingent on whether or not the agent has committed to remain both periods. The two-period analysis shows that, if the agent is a poor performer (in a sense to be made precise), it is to his advantage to not commit whereas if he is a superior performer, commitment is to his advantage. Whether or not the agent has committed to remain, the two-period moral hazard contract compensates the agent in the second period based on his performance in the first period, providing incentives both immediate and intertemporal. When the agent is committed, a natural measure of the agent's first-period performance emerges. The analysis of the general T-period contract shows that the two-period results hold in all but the last period.

Optimal Task Assignments with Loss-Averse Agents

This paper studies optimal task assignments in a setting where agents are expectation-based loss averse according to KoszegiRabin (2006) and KoszegiRabin (2007) and are compensated according to an aggregated performance measure in which tasks are technologically independent. We show that the optimal task assignment is determined by a trade-off between paying lower compensation costs and restricting the set of implementable effort profiles under multitasking. We show that loss aversion combined with how much the marginal cost of effort in one task increases with the effort chosen in other tasks determines when multitasking saves on compensation costs, but results in an implementation problem.

Your Loss Is My Gain: A Recruitment Experiment with Framed Incentives

Empirically, labor contracts that financially penalize failure induce higher effort provision than economically identical contracts presented as paying a bonus for success, an effect attributed to loss aversion. This is puzzling, as penalties are infrequently used in practice. The most obvious explanation is selection: loss averse agents are unwilling to accept such contracts. I formalize this intuition, then run an experiment to test it. Surprisingly, I find that workers were 25 percent more likely to accept penalty contracts, with no evidence of adverse or advantageous selection. Consistent with the existing literature, penalty contracts also increased performance on the job by 0.2 standard deviations. I outline extensions to the basic theory that are consistent with the main results, but argue that more research is needed on the long-term effects of penalty contracts if we want to understand why firms seem unwilling to use them.

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.

Your Loss is My Gain: A Recruitment Experiment with Framed Incentives

Empirically, labor contracts that financially penalize failure induce higher effort provision than economically identical contracts presented as paying a bonus for success, an effect attributed to loss aversion. This is puzzling, as penalties are infrequently used in practice. The most obvious explanation is selection: loss averse agents are unwilling to accept such contracts. I formalize this intuition, then run an experiment to test it. Surprisingly, I find that workers were 25 percent more likely to accept penalty contracts, with no evidence of adverse or advantageous selection. Consistent with the existing literature, penalty contracts also increased performance on the job by 0.2 standard deviations. I outline extensions to the basic theory that are consistent with the main results, but argue that more research is needed on the long-term effects of penalty contracts if we want to understand why firms seem unwilling to use them.

Loss Aversion and Lying Behavior: Theory, Estimation and Empirical Evidence

We theoretically show that loss-averse agents are more likely to lie to avoid receiving a low payoff after a random draw, the lower the ex-ante probability of this bad outcome. The ex-ante expected payoff increases as the bad outcome becomes less likely, and hence the greater is the loss avoided by lying. We demonstrate robust support for this theory by reanalyzing the results from the extant literature and with two new experiments that vary the outcome probabilities and are run doubleanonymous to remove reputation effects. To measure lying, we develop an empirical method that estimates the full distribution of dishonesty

Strongly Loss Averse CEO Compensation: Long Calls or Short Puts?

This paper studies how compensation and incentives are provided to a loss averse agent with reference-dependent preferences, first in a single-period and then in a multiperiod setting. In the single-period contract, when the agent's actions are not observable by the principal (moral hazard), the paper shows how the presence of loss aversion can lead to simple contracts in contrast with the more complex contracts of classical principal-agent theory. Further, under these circumstances, the principal should offer the agent a base plus malus contract rather than base plus bonus as is current practice. Regarding multiperiod contracts, the two-period contract is different contingent on whether or not the agent has committed to remain both periods or not. Whether or not the agent has committed to remain, the two-period moral hazard contract compensates the agent in the second period based on his performance in the first period, providing incentives both immediate and intertemporal. The analysis of the general T-period contract shows that the single-period results hold in every period and the two-period results hold in all but the last period.

Loss Aversion on the Links

Prospect theory predicts that loss averse agents who fear they will not reach their reference utility level are more apt to adopt risky strategies to avoid that painful possibility compared to agents who are more sure of their relative standing. This paper tests this theory with data from professional golf events and finds evidence of economically inefficient loss aversion amongst tournament competitors. While playing par five holes, golfers who have been penalized because of a poor first shot are more likely to adopt an aggressive strategy for finishing the hole compared to their non-penalized rivals who are not feeling the burden of not meeting a preconceived reference score. The risks the penalized golfers take are economically inefficient, as their average performances are worse than their non-penalized rivals' average performances for the balance of the hole.

Loss averse agents and lenient supervisors in performance appraisal

A consistent empirical literature shows that in many organizations supervisors systematically overrate their employees’ performance. Such leniency bias is at odds with the standard principal-agent model and has been explained with causes that range from social interactions to fairness concerns and to collusive behavior between the supervisor and the agent. We show that the principal-agent model, extended to consider loss-aversion and reference-dependent preferences, predicts that the leniency bias is comparatively less detrimental to effort provision than the severity bias. We test this prediction with a laboratory experiment where we demonstrate that failing to reward deserving agents is significantly more detrimental than rewarding undeserving agents. This offers a novel explanation as to why supervisors tend to be lenient in their appraisals.

Prospect Dynamic and Loss Dominance

This paper investigates the role of loss-aversion in affecting the long run equilibria of stochastic evolutionary dynamics. We consider a finite population of loss-averse agents who are repeatedly and randomly matched to play a 2 x 2 coordination game. When an agent revises her strategy, she compares the payoff from each strategy to a reference point which is endogenously formed. Based on the comparison, she makes a (possibly stochastic) choice. We call the resulting dynamics prospect dynamics. Three types of endogenous reference points are examined: social average, expectations and status-quos. We find that risk-dominance is no longer sufficient to guarantee stochastic stability under prospect dynamics with any type of reference points. Therefore, we propose a stronger concept, loss-dominance: a strategy is loss-dominant if it is both risk-dominant strategy and the maximin strategy. This concept captures people's psychological needs to avoid not only risks but also losses. We show that it serves as a natural selection refinement for games with loss-averse agents. The state in which all agents play the loss-dominant strategy (if exists) is uniquely stochastically stable under prospect dynamics for any degree of loss-aversion and all types of reference points. We also characterize the precise conditions for stochastic stability in games with no loss-dominant strategy.

Lossed in translation: an off-the-shelf method to recover probabilistic beliefs from loss-averse agents.

Strictly proper scoring rules are designed to truthfully elicit subjective probabilistic beliefs from risk neutral agents. Previous experimental studies have identified two problems with this method: (i) risk aversion causes agents to bias their reports toward the probability of 1/2, and (ii) for moderate beliefs agents simply report 1/2. Applying a prospect theory model of risk preferences, we show that loss aversion can explain both of these behavioral phenomena. Using the insights of this model, we develop a simple off-the-shelf probability assessment mechanism that encourages loss-averse agents to report true beliefs. In an experiment, we demonstrate the effectiveness of this modification in both eliminating uninformative reports and eliciting true probabilistic beliefs.Electronic supplementary materialThe online version of this article (doi:10.1007/s10683-015-9429-0) contains supplementary material, which is available to authorized users.

Bilateral Trade with Loss-Averse Agents

We study the bilateral trade problem put forward by Myerson and Satterthwaite (1983) under the assumption that agents are loss-averse, using the model developed by Kőszegi and Rabin (2006, 2007). We show that the endowment effect increases the sellers information rent, and that the attachment effect reduces the buyer’s information rent. Further, depending on the distribution of types, loss-aversion can reduce the severity of the impossibility problem. However, the result cannot be reversed. Turning to the design of optimal mechanisms, we show that in both revenue and welfare maximizing mechanisms the designer optimally provides the agents with full insurance in the money dimension and with partial insurance in the trade dimension. In fact, when the stakes are large, loss-aversion can eliminate trade altogether. We show that all results display robustness to the exact specification of the reference point and provide some results on general mechanism design problems.