Modifications of the Omega ratio for decision making under uncertainty

The Omega ratio (Ω-ratio) was proposed by Shadwick and Keating in 2002 as a performance measure applied to rankings of assets, portfolios or funds. It involves partitioning returns into loss and gain below and above a given threshold. The original version was designed for decision making under risk (probabilities completely known), but recent research has shown that this measure can be adapted to decision making under partial information (likelihood known incompletely). Our contribution will be to use the concept of the Omega ratio in decision making under uncertainty (DMUU) which occurs when the decision maker (DM) chooses the appropriate alternative on the basis of certain scenarios for which probabilities are not known at all. The goal of this article is to adjust the Ω-ratio to DMUU so that it takes into consideration the DM’s attitude towards risk and the distribution of all payoffs connected with particular decisions. The Ω-ratio is combined with a hybrid of Hurwicz and Bayes rules proposed by the author in another paper. The significant advantage of the new measure, Ω(H+B)ratio, is the possibility to compare alternatives (strategies, projects) when the likelihood of particular scenarios is not known or when the DM does not intend to use the available data

Implementation in Minimax Regret Equilibrium

This note studies the problem of implementing social choice correspondences in environments where individuals have doubts about the rationality of their opponents. We postulate the concept of "-minimax regret as our solution concept and show that social choice correspondences that are Maskin monotonic and satisfy the no-veto power condition are implementable in "-minimax regret equilibrium for all " ? [0, 1).Implementation; minimax regret; Maskin monotonicity.

Maximin Safety: When Failing to Lose is Preferable to Trying to Win

We present a new decision rule, \emph{maximin safety}, that seeks to maintain a large margin from the worst outcome, in much the same way minimax regret seeks to minimize distance from the best. We argue that maximin safety is valuable both descriptively and normatively. Descriptively, maximin safety explains the well-known \emph{decoy effect}, in which the introduction of a dominated option changes preferences among the other options. Normatively, we provide an axiomatization that characterizes preferences induced by maximin safety, and show that maximin safety shares much of the same behavioral basis with minimax regret.Comment: 14 page

Transitive regret

Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. We ask whether regret-based behavior is consistent with non-expected utility theories of transitive choice and show that the answer is no. If choices are governed by ex ante regret and rejoicing then non-expected utility preferences must be intransitive.Regret, transitivity, non-expected utility

Statistical Treatment Choice Based on Asymmetric Minimax Regret Criteria

This paper studies the problem of treatment choice between a status quo treatment with a known outcome distribution and an innovation whose outcomes are observed only in a representative finite sample. I evaluate statistical decision rules, which are functions that map sample outcomes into the planner’s treatment choice for the population, based on regret, which is the expected welfare loss due to assigning inferior treatments. I extend previous work that applied the minimax regret criterion to treatment choice problems by considering decision criteria that asymmetrically treat Type I regret (due to mistakenly choosing an inferior new treatment) and Type II regret (due to mistakenly rejecting a superior innovation). I derive exact finite sample solutions to these problems for experiments with normal, Bernoulli and bounded distributions of individual outcomes. In conclusion, I discuss approaches to the problem for other classes of distributions. Along the way, the paper compares asymmetric minimax regret criteria with statistical decision rules based on classical hypothesis tests.treatment effects, loss aversion, statistical decisions, hypothesis testing.

Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret

We examine if and to what extent choice dispositions can allow dependence on contexts and maintain consistency over time, in a dynamic environment under uncertainty. We focus on a 'minimal' case of context dependence, opportunity dependence due to being affected by anticipated regret. There are two sources of potential inconsistency, one is arrival of information and the other is changing opportunities. First, we go over the general method of resolution of potential inconsistency, by taking any kinds of inconsistency as given constraints. Second, we characterize a class of choice dispositions that are consistent to information arrival but may be inconsistent to changing opportunities. Finally, we consider the full requirement of dynamic consistency and show that it necessarily implies independence of choice opportunities.

Robust Monopoly Pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. Distinct implications of how a monopolist responds to an increase in uncertainty emerge under the two criteria.Monopoly, Optimal pricing, Robustness, Multiple priors, Regret

Robust Monopoly Pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version of the problem the seller only knows that demand will be in a neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. The resulting optimal pricing policy under either criterion is robust to the model uncertainty. Finally we derive distinct implications of how a monopolist responds to an increase in ambiguity under each criterion.Monopoly, Optimal pricing, Robustness, Multiple priors, Regret