Nonbinding recommendations: the relative effects of focal points versus uncertainty reduction on bargaining outcomes

This article focuses on the effects of nonbinding recommendations on bargaining outcomes. Recommendations are theorized to have two effects: they can create a focal point for final bargaining positions, and they can decrease outcome uncertainty should dispute persist. While the focal point effect may lower dispute rates, the uncertainty reduction effect is predicted to do the opposite for risk-averse bargainers. Which of these effects dominates is of critical importance in the design of alternative dispute resolution (ADR) procedures, which are increasingly utilized in a variety of settings. We theoretically examine the effects of recommendations on the contract zone using a framework which allows bargainers’ final positions to influence a binding outcome should negotiations fail. This provides a more stringent test of focal points than previously considered. We also present data from controlled laboratory experiments consistent with our model. Recommendations are empirically shown to influence final bargaining positions and negotiated settlement values. In fact, recommendations significantly reduce dispute rates, even where they are completely ignored in final-stage arbitration. This highlights a potentially significant role for the use of nonbinding procedures, such as mediation, as a preliminary stage in more efficient ADR procedures.     

Risk aversion and the relationship between Nash's solution and subgame perfect equilibrium of sequential bargaining

This article presents some new, intuitive derivations of several results in the bargaining literature. These new derivations clarify the relationships among these results and allow them to be understood in a unified way. These results concern the way in which the risk posture of the bargainers affects the outcome of bargaining as predicted by Nash's (axiomatic) solution of a static bargaining model (Nash, 1950) and by the subgame perfect equilibrium of the infinite horizon sequential bargaining game analyzed by Rubinstein (1982). The analogous, experimentally testable predictions for finite horizon sequential bargaining games are also presented.     

Choices at various levels of uncertainty: An experimental test of the restated diversification theorem

Our “Restated diversification theorem” (Skogh and Wu, 2005) says that risk-averse agents may pool risks efficiently without assignment of subjective probabilities to outcomes, also at genuine uncertainty. It suffices that the agents presume that they face equal risks. Here, the theorem is tested in an experiment where the probability of loss, and the information about this probability, varies. The result supports our theorem. Moreover, it tentatively supports an evolutionary theory of the insurance industry—starting with mutual pooling at uncertainty, turning into insurance priced ex ante when actuarial information is available.     

Uncertainty,the bargaining problem,and the Nash-Zeuthen solution

The Zeuthen bargaining model occupies a prominent place among those theories of the bargaining process that have been formulated and expounded by economists. Its solution to the bargaining problem is essentially economic, since invariant utility functions based on economic factors alone determine the outcome. However, this paper shows that a necessary condition for reaching the Zeuthen solution (shown by Harsanyi to be mathematically equivalent to the game-theoretic solution of Nash's theory) is that bargainers initially take up positions on opposite sides of the outcome that maximizes their utility product. Whether utility functions are mutually known or unknown, inherent in the bargaining situation itself is the requirement that bargainers be at least initially uncertain as to each other's subsequent concession behaviour. With uncertainty, von Neumann-Morgenstern rationality implies that each bargainer would make an initial demand that maximizes the expected gain from holding fast. Therefore, even if Zeuthen's concession criterion should subsequently dictate concession behaviour, expected utility maximization within the context of subjective uncertainty may well yield initial demands that are inconsistent with reaching the Nash-Zeuthen solution. Finally, a general methodological conclusion that emerges from the analysis is that, since the bargaining process necessarily proceeds from a context of subjective uncertainty, greater emphasis needs to be placed on its role as a device for affecting expectations.     

Risk aversion in n-person bargaining

Relations between risk properties of Pareto optimal n-person bargaining solutions are studied. The (weak) worse alternative property, risk sensitivity property, and risk profit opportunity property are considered, in particular relations between these properties, and between these properties and other properties such as independence of irrelevant alternatives and individual monotonicity. A distinction is made between bargaining games where all Pareto optimal outcomes are riskless, and bargaining games where Pareto optimal outcomes may represent the utilities of lotteries between riskless alternatives. In the first mentioned case, more general results can be obtained.     

The effect of the background risk in a simple chance improving decision model

We experimentally investigate the effect of an independent and exogenous background risk to initial wealth on subjects’ risk attitudes and explore an appropriate incentive mechanism when identical or similar tasks are repeated in an experiment. Taking a simple chance improving decision model under risk where the winning probabilities are negatively related to the potential gain, we find that such a background risk tends to make risk-averse subjects behave more risk aversely. Furthermore, we find that risk-averse subjects tend to show decreasing absolute risk aversion (DARA), and that a random round payoff mechanism (RRPM) would control the possible wealth effect. This suggests that RRPM would be a better incentive mechanism for an experiment where repetition of a task is used.

Aversion to one risk in the presence of others

The more risk-averse of two individuals need not have the smaller certainty equivalent for a risk \~x if another risk or combination of risks w is present. It is shown that he must, however, if either individual's conditional certainty equivalent for x is increasing in w. For independent risks, this condition follows immediately if either individual is decreasingly risk-averse, giving a natural proof of a known result. Another short proof of this result and necessary and sufficient conditions in the independent case are give. For multivariate utilities, the corresponding results do not hold, but it is proved simply that any mixture of decreasingly risk-averse utilities is decreasingly risk-averse. Also touched upon are risk aversion's relation to generalized means, concave composition, risk sharing, and interest rates, the application of the results to discounting under uncertainty and selection of investment level, and their connection to singly crossing distributions, noise, and dominance.     

The effect of computer intervention and task structure on bargaining outcome

This paper reports on a study that examined the impact of computer presentation of suggested solutions during negotiation, in bargaining situations that can be characterized as integrative or distributive. It was found that in the integrative task, the bargainers achieved higher joint outcomes when presented with suggestions. They had a more negative perception of the negotiation atmosphere, however. In the distributive task, the suggestions did not help achieve joint gains, but it lessened negative attitudes of the bargainers. Bargainers who received suggestions felt both they and their partner had been somewhat more flexible, cooperative, considerate, and less suspicious. Thus, regardless of negotiation situation, the suggestions resulted in some benefit to the negotiators.     

Interpersonal comparisons of utility in bargaining: evidence from a transcontinental ultimatum game

This article presents the experimental results of a “Transcontinental Ultimatum Game” implemented between India and France. We use a standard ultimatum game, but in one treatment, Indian subjects made offers to French subjects (ItoF treatment) and, in another treatment, French subjects made offers to Indian subjects (FtoI treatment). We observed that FtoI treatment bargaining mostly ended up with unequal splits of money in favor of French, while nearly equal splits were the most frequent outcome in ItoF treatment interactions. The experimental results are organized through a standard social reference model, modified for taking into account the different marginal value of money for bargainers. In our model, bargaining is driven by relative standing comparisons between players, occurring in terms of real earnings (that is monetary earnings corrected for a purchasing power factor) obtained in the game. The norm of equity behind the equalization of real earnings is called local equity norm, and contrasted to a global equity norm which would encompass the wealth of players beyond the game. According to what we observed, no beyond-game concern seems to be relevantly endorsed by subjects.     

The strength of sensitivity to ambiguity

We report an experiment where each subject’s ambiguity sensitivity is measured by an ambiguity premium, a concept analogous to and comparable with a risk premium. In our design, some tasks feature known objective risks and others uncertainty about which subjects have imperfect, heterogeneous, information (“ambiguous tasks”). We show how the smooth ambiguity model can be used to calculate ambiguity premia. A distinctive feature of our approach is estimation of each subject’s subjective beliefs about the uncertainty in ambiguous tasks. We find considerable heterogeneity among subjects in beliefs and ambiguity premia; and that, on average, ambiguity sensitivity is about as strong as risk sensitivity.     

The role of risk preferences in bargaining when acceptance of a proposal requires less than unanimous approval

The role of risk preferences in determining the outcome to bargaining is examined for the case in which acceptance of a proposal requires less than unanimous approval. Using an n-agent extension of the Ståhl-Rubinstein alternating offer model, we find that risk preferences play a fundamentally different role when bargaining is settled using a nonunanimity voting rule. Risk preferences determine not only an agent's reservation price but also the likelihood that he is made part of the winning coalition. An implication of this analysis is that when the preferences of the agents are not too diverse, it is advantageous for an agent to be relatively risk-averse.The helpful comments and suggestions of Rich McLean and an anonymous referee are gratefully acknowledged. This article was presented as a paper at the 1988 Winter Econometric Society Meetings.     

Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study

We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and are mildly ambiguity seeking over losses. Further analysis shows that on an individual level, and with respect to both risky and ambiguous prospects, there is limited incidence of a reflection effect where subjects are risk/ambiguity averse (seeking) in gains and seeking (averse) in losses, though this incidence is higher for ambiguous prospects. A very high proportion of such cases of reflection exhibit risk (ambiguity) aversion in gains and risk (ambiguity) seeking in losses, with the reverse effect being significantly present in the case of risk but almost absent in case of ambiguity. Our results suggest that reflection across gains and losses is not a stable individual characteristic, but depends upon whether the form of uncertainty is precise or ambiguous, since we rarely find an individual who exhibits reflection in both risky and ambiguous prospects. We also find that correlations between attitudes towards risk and ambiguity were domain dependent.      

Sociotropes, Systematic Bias, and Political Failure: Reflections on the Survey of Americans and Economists on the Economy

Objectives . Economic models of politics typically make two assumptions about voters: first, their motives are egocentric, not sociotropic; second, their beliefs are rational, not subject to systematic bias. Political scientists have presented strong evidence against the first assumption (Mansbridge, 1990), but have become increasingly willing to accept the second (Page and Shapiro, 1992; Marcus and Hanson, 1993). This article tests these two assumptions, then explores the tests' broader implications. Methods . I use the Survey of Americans and Economists on the Economy to test for egocentricity of motivation and rationality of belief. Results . Both standard assumptions fail for the case where the economic approach would seemingly be most relevant: economic beliefs. Conclusions . This is not necessarily cause for greater optimism about the efficiency of democracy: sociotropic voters with biased economic beliefs are more likely to produce severe political failures than are selfish voters with rational expectations.     

Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.     

Paying to improve your chances: Gambling or insurance?

Will a more risk-averse individual spend more or less to improve probabilities, say on marketing efforts that enhance the chance of a sale? For any two payoffs and starting probabilities, the answer is unfortunately indeterminate. However, interpreting gambling as increasing small chances of good outcomes and insurance as reducing small chances of bad outcomes, the more risk-averse individual will pay less (more) to gamble (insure). We find a critical switching probability that depends on the individuals and outcomes involved. If the good outcome is less (more) likely than this critical value, the expenditures represent gambling (insurance).     

Sampling experience reverses preferences for ambiguity

People often need to choose between alternatives with known probabilities (risk) and alternatives with unknown probabilities (ambiguity). Such decisions are characterized by attitudes towards ambiguity, which are distinct from risk attitudes. Most studies of ambiguity attitudes have focused on the static case of single choice, where decision makers typically prefer risky over ambiguous prospects. However, in many situations, decision makers may be able to sample outcomes of an ambiguous alternative, allowing for inferences about its probabilities. The current paper finds that such sampling experience reverses the pattern of ambiguity attitude observed in the static case. This effect can only partly be explained by the updating of probabilistic beliefs, suggesting a direct effect of sampling on attitudes toward ambiguity.     

Rethinking Risk Attitude: Aspiration as Pure Risk

There exists no completely satisfactory theory of risk attitude in current normative decision theories. Existing notions confound attitudes to pure risk with unrelated psychological factors such as strength of preference for certain outcomes, and probability weighting. In addition traditional measures of risk attitude frequently cannot be applied to non-numerical consequences, and are not psychologically intuitive. I develop Pure Risk theory which resolves these problems – it is consistent with existing normative theories, and both internalises and generalises the intuitive notion of risk being related to the probability of not achieving one’s aspirations. Existing models which ignore pure risk attitudes may be misspecified, and effects hitherto modelled as loss aversion or utility curvature may be due instead to Pure Risk attitudes.     

Hope: An empirical study of attitude toward the timing of uncertainty resolution

Hope is experienced when there is enjoyment in delaying the resolution of uncertainty. The main objective of this article is to identify the phenomenon of hope. In addition, we empirically test several axiomatic theories of temporal preferences which have implications for attitudes toward the timing of uncertainty resolution. Overall, the data support the extension of recursive expected utility specification to incorporate a weighted utility model of attitude toward future uncertainty. We find that the instances where hopefulness are more prevalent tend to be associated with a small probability of occurrence of a large gain. Interestingly, the degree of hopefulness is not correlated with risk attitude.     

Risk-adjusted martingales and the design of “indifference” gambles

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function.     

Physician behavior and conditional altruism: the effects of payment system and uncertain health benefit

This paper experimentally investigates the altruistic behavior of physicians and whether this behavior is affected by payment system and uncertainty in health outcome. Subjects in the experiment take on the role of physicians and decide on the provision of medical care for different types of patients, who are identical in all respects other than the degree to which a given level of medical treatment affects their health. We investigate physician altruism from the perspective of ethical principles, by categorizing physicians according to how well their treatment decisions align with different principles for priority setting. The experiment shows that many physicians are altruistic toward their patients but also that the degree of altruism varies across patients with different medical needs. We find a strong effect of payment system that is overall unaffected by the introduction of risk and ambiguity in patients’ health outcomes. There is, however, substantial heterogeneity across individuals, in particular under the capitation payment system where physicians’ responses to the introduction of uncertainty in patient health are modulated by their own generic risk and ambiguity preferences.