Ambiguity and price competition

Theory and Decision - There are few models of price competition in a homogeneous-good market which permit general asymmetries of information amongst the sellers. This work studies a price game with...     

Ambiguity aversion under maximum-likelihood updating

Maximum-likelihood updating (MLU) is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility (MEU) decision-maker to (1) prefer a bet on an ambiguous over a risky urn and (2) be more willing to bet on the ambiguous urn compared to an (ambiguity neutral) subjective expected utility (SEU) decision-maker. This is challenging, since prior to observing (symmetric) draws from the urns, the MEU decision-maker (in line with the usual notion of ambiguity aversion) actually preferred the risky over the ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process.     

Ambiguity aversion in multi-armed bandit problems

In multi-armed bandit problems, information acquired from experimentation is valuable because it tells the agent whether to select a particular option again in the future. This article tests whether people undervalue this information because they are ambiguity averse, or have a distaste for uncertainty about the average quality of each alternative. It is shown that ambiguity averse agents have lower than optimal Gittins indexes, appearing to undervalue information from experimentation, but are willing to pay more than ambiguity neutral agents to learn the true mean of the payoff distribution, appearing to overvalue objectively given information. This prediction is tested with a laboratory experiment that elicits a Gittins index and a willingness to pay on six two-armed bandits. Consistent with the predictions of ambiguity aversion, the Gittins indexes are significantly lower than optimal and willingnesses to pay are significantly higher than optimal.     

Ambiguity and risk taking in organizations

Kunreuther, Meszaros, and Hogarth (1993) argue that insurers are risk averse and ambiguity averse, and that they use cognitive reference points and constraints in making pricing decisions. They further claim that insurer ambiguity may be a factor that has a role in market failure at the industry level. Arguably, ambiguity may be an important aspect of decision behavior. In this article, research on managerial risk taking is reviewed with a focus on the relationship between ambiguity and risk taking. In particular, the effects of the organizational and institutional context are highlighted. It is argued that the political aspects of insurer decision behavior should be considered as well. Implications for further study and understanding of decision making are discussed.     

Ambiguity and the value of information

The value of information is studied in a non-expected utility model of ambiguity with second-order probabilities. Information that reduces ambiguity has a positive value for ambiguity-averse decision makers, and the value of information that resolves ambiguity increases with greater ambiguity and with greater ambiguity aversion. Since information that resolves risk is valuable, and must also resolve ambiguity, the value of such information for ambiguity averters increases with greater ambiguity and with greater ambiguity aversion.     

Ambiguity aversion in first-price sealed-bid auctions

Experiments on first-price sealed-bid auctions with independent private values have shown that submitted bids typically exceed Nash-equilibrium predictions for risk-neutral bidders. Existing bidding models explain this phenomenon by assuming that the bidders are risk-averse and capable of drawing complete and correct inferences about their winning probabilities. In this article, we use the Choquet expected utility (CEU) theory to demonstrate that the observed bidding behavior can also be attributed to ambiguity aversion which causes the bidders to underestimate their chances of winning the auction. Empirical support for CEU bidding models is given through an analysis of recent bidding data.     

Ambiguity when playing coordination games across cultures

Cultural differences can be a source of ambiguity in coordination games. As players are likely to experience more ambiguity when playing a different culture, we expect players to choose safer strategies. We run experiments with a stag hunt and bargaining coordination game. Using a between-subjects design, we vary the identity of the opponent between someone of the same culture or a different culture. We compare the responses of British and East Asian students at the University of Exeter and show the cultural identity of the opponent by physical appearance. While we find no significant differences between treatments for East Asians, the British choose the safer option in the stag hunt and demand more of the pie in the bargaining game when faced with an opponent from a different culture.

     

Ambiguity and decision modeling: A preference-based approach

In this article, we develop a model that permits a decision maker's preferences to depend on the decision maker's ambiguity about the probability of an event that is relevant for decision-making purposes. We deal with ambiguity through preference modeling, with ambiguity leading to modifications in the utilities of outcomes. The behavior of ambiguity premiums and probability premiums as the payoffs are varied depends on the nature of the modifications in utilities. Particular forms of the model that arise under different sets of assumptions about preferences include additive, bilinear, and ratio forms. We conclude with a brief example and some thoughts about potential generalizations and implications of the model.     

Choices Under Ambiguity With Familiar And Unfamiliar Outcomes

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet Integral is formalized when the decision maker holds capacities and probabilities. A characterization of the decision-maker’s behavior is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones.     

Ellsberg paradox: Ambiguity and complexity aversions compared

We present a simple model where preferences with complexity aversion, rather than ambiguity aversion, resolve the Ellsberg paradox. We test our theory using laboratory experiments where subjects choose among lotteries that “range” from a simple risky lottery, through risky but more complex lotteries, to one similar to Ellsberg’s ambiguity urn. Our model ranks lotteries according to their complexity and makes different—at times contrasting—predictions than most models of ambiguity in response to manipulations of prizes. The results support that complexity aversion preferences play an important and separate role from beliefs with ambiguity aversion in explaining behavior under uncertainty.     

Ambiguity,pessimism, and rational religious choice

Using a subclass of the α-maximin expected-utility preference model, in which the decision maker’s degree of ambiguity and degree of pessimism are each parameterized, we present a theory of religious choice in the Pascalian decision theory tradition, one that can resolve dilemmas, address the “many Gods objection,” and address the ambiguity inherent in religious choice. Parameterizing both the degree of ambiguity and the degree of pessimism allows one to examine how the two interact to impact choice, which is useful regardless of the application. Applying this model to religious choice is a move beyond subjective expected-utility theory, allowing us to show that a change in either the degree of ambiguity or the degree of pessimism can lead a decision maker to “convert” from one religion to another.     

Effects of Outcome and Probabilistic Ambiguity on Managerial Choices

Information ambiguity is prevalent in organizations and likely influences management decisions. This study examines, given imprecise probabilities and outcomes, how managers make choices when they are provided with single-figure benchmarks. Seventy-nine MBA students completed two experiments. We found that, in a decision framed as a decision under certainty involving an ambiguous outcome, the majority of the subjects were ambiguity prone in the loss condition and switched to ambiguity aversion in the gain condition. However, in the presence of probabilistic ambiguity in a decision under risk, this expected switching pattern was shown only when the difference in riskiness between the two choice options (in the loss condition) was perceived to be relatively small. In a companion study, we used a written protocol approach to identify factors that affect decision makers' investment choices when faced with ambiguous outcomes. Protocols frequently mentioned that the ambiguous outcome option was risky, even in the case which was framed as a decision under certainty in the problem statement. In a decision under risk with ambiguous outcomes, the combination of probabilistic risk and outcome ambiguity was seen as even more risky.     

Ambiguity attitudes and social interactions: An experimental investigation

This paper reports the results of experiments testing prevalence of non-neutral ambiguity attitudes and how these attitudes change as a result of interpersonal interactions. To address the first question we conducted experiments involving individual choice between betting on ambiguous and unambiguous events of the subject’s choice. We found that a large majority of subjects display ambiguity neutral attitudes, many others display ambiguity incoherent attitudes, and few subjects display either ambiguity-averse attitudes or ambiguity-seeking attitudes. To address the second question we designed a new experiment with a built-in incentive to persuade. We found that interpersonal interactions without incentives to persuade have no effect on behavior. However, when incentives were introduced, the ambiguity neutral subjects were better able to persuade ambiguity seeking and ambiguity incoherent subjects to adopt ambiguity neutral choice behavior and, to a lesser extent, also ambiguity averse subjects.     

Ambiguity aversion and the propensities for self-insurance and self-protection

Two models of ambiguity preferences that permit comparative statics analysis of greater ambiguity aversion yield definite predictions concerning propensities for self-insurance and self-protection: The levels of both activities that are optimal for an ambiguity-averse decision maker are higher in the presence of ambiguity than in its absence, and demands for both activities increase with greater ambiguity aversion. The reason is that, at levels optimal for one decision maker, an increase in either activity results in a mean-preserving contraction in the distribution of expected utility in the presence of ambiguity, which is valuable to anyone with the same risk preferences who is more ambiguity averse.     

Granny Versus Game Theorist: Ambiguity in Experimental Games

We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions.      

Hopes and Fears: the Conflicting Effects of Risk Ambiguity

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit fear effects of ambiguity for small probabilities of suffering a loss and hope effects for large probabilities. Estimates of the crossover point from ambiguity aversion (fear) to ambiguity seeking (hope) place this value between 0.3 and 0.7 for the risk per decade lotteries considered, with empirical estimates indicating a crossover mean risk of about 0.5. Attitudes toward the degree of ambiguity also reverse at the crossover point.     

Ambiguity and Cooperation in the Implementation of Adult Protection Policy

Using a classification of public policy developed by Matland, we examine implementation of policy on adult protection as outlined in ‘No Secrets’, the government's guidance to local agencies. This policy appears to exemplify a ‘high‐ambiguity/low‐conflict’ model. Detailed interviews with staff charged with developing multi‐agency procedures, in local authority departments, health authorities, the police and the voluntary sector, confirmed the ambiguity of the policy and the uncertainty experienced by staff as a consequence. However, the interviews also revealed a number of areas of conflict, particularly as people gave precedence to their own professional norms and organizational priorities over partnership working.     

Commonalities in Time and Ambiguity Aversion for Long-Term Risks*

Optimal protective responses to long-term risks depend on rational perceptions of ambiguous risks and uncertain time horizons. Our study examined the joint influence of uncertain delay and risk in an original sample of business owners and managers. We found that many subjects disliked uncertainty in the timing of an outcome, a reaction we term ``lottery timing risk aversion.' Such aversion to uncertain timing was positively related to aversion to ambiguous probabilities for lotteries involving storm damage risks. This association suggests that uncertainty may be processed similarly in both the risk and time dimensions.