Case-Based Decision Theory: An Experimental Report

ABSTRACTThe subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry.The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.

Interpreting value creation model by case-based decision theory

Case-Based Decision Theory (CBDT) postulates that decision making under uncertainty is based on analogies to past cases. In its original version, it suggests that each of the available acts is ranked according to its own performance in similar decision problems encountered in the past. The purpose of this paper is to extend CBDT to deal with cases in which the evaluation of an act may also depend on past performance of different, but similar acts. To this end we provide a behavioral axiomatic definition of the similarity function over problem-act pairs (and not over problem pairs alone, as in the original model). We propose a model in which preferences are context-dependent. For each conceivable history of outcomes (to be thought of as the “context” of decision) there is a preference order over acts. If these context-dependent preference relations satisfy our consistency-across-contexts axioms, there is an essentially unique similarity function that represents these preferences via the (generalized) CBDT functional.

This paper starts out from the proposition that case-based decision theory (CBDT) is an appropriate tool to explain human decision behavior in situations of structural ignorance. Although the developers of CBDT suggest its reality adequacy, CBDT has not yet been tested empirically very often, especially not in repetitive decision situations. Therefore, our main objective is to analyse the decision behavior of subjects in a repeated-choice experiment by comparing the explanation power of CBDT to reinforcement learning and to classical decision criteria under uncertainty namely maximin, maximax, and pessimism-optimism. Our findings substantiate a predominant significantly higher validity of CBDT compared to the classical criteria and to reinforcement learning. For this reason, the experimental results confirm the suggested reality adequacy of CBDT in repetitive decision situations of structural ignorance.

In this paper, we show that Case-based decision theory, proposed by Gilboa and Schmeidler (Q J Econ 110(3):605–639, 1995), can explain the aggregate dynamics of cooperation in the repeated Prisoner’s Dilemma, as observed in the experiments performed by Camera and Casari (Am Econ Rev 99:979–1005, 2009). Moreover, we find CBDT provides a better fit to the dynamics of cooperation than does the existing Probit model, which is the first time such a result has been found. We also find that humans aspire to a payoff above the mutual defection outcome but below the mutual cooperation outcome, which suggests they hope, but are not confident, that cooperation can be achieved. Finally, our best-fitting parameters suggest that circumstances with more details are easier to recall. We make a prediction for future experiments: if the repeated PD were run for more periods, then we would be begin to see an increase in cooperation, most dramatically in the second treatment, where history is observed but identities are not. This is the first application of Case-based decision theory to a strategic context and the first empirical test of CBDT in such a context. It is also the first application of bootstrapped standard errors to an agent-based model.

Case-Based Decision Theory (CBDT) is a theory of decision making which postulates that people tend to choose acts which performed well in similar cases in the past. It was originally developed as a theory of decision making under uncertainty, for decision problems in which the states of the world are neither naturally given, nor can they be easily constructed. In such situations, where the expected utility paradigm seems hardly plausible either as a description of the way people make decisions, or as a prescription for “rational” decision making, CBDT is offered as an alternative.

Empirical research has revealed that people try to avoid ambiguity in the Ellsberg problem and make choices inconsistent with the predictions of Expected Utility Theory.We hypothesized that people might be forming implicit assumptions to deal with the ambiguity resulting from the incomplete information in the problem, and that some assumptions might lead them to deviate from normative predictions.We embedded the Ellsberg problem in various scenarios that made one source of ambiguity (i.e., the implied distribution of the unknown number of the colored balls) explicit.Results of an experiment showed that more people chose consistently (and hence rationally) when the scenario encouraged them to think that the probability distribution of the number of balls was normal.The results give insight into the implicit assumptions that might lead to choices congruent with normative models.

This chapter introduces the theories of decision-making under uncertainty and risk of socio-technical systems. Following the historic development of the main conceptions of rationality, we start with expected utility theories and explain the rational choice (or normative) perspective. We explain how decisions under risk can be optimized consistently within the framework of the theory, and under which conditions such analyses are particularly applicable and when they are reduced to an economic cost-benefit analysis. It is then discussed why the classic theories are sometimes misused and why the normative perspective is not suitable to describe or predict actual human behavior, perception or evaluation of decisions and their outcomes under uncertainty and risk. We then outline alternative theories of decision-making, including descriptive approaches from behavioral economics (e.g. cognitive biases) as well as ecological rationality and heuristic decision making. As is discussed in this article, the normative approach is suited for optimizing decisions in a consistent manner for relatively well defined (often technical) problems, whereas the alternative theories are more suitable to predict actual human and social evaluations and behavior and can provide improved decision making in complex situations where socio-technical system parameters as well as the decision maker’s preferences are not well defined.

We use an annual household panel to conduct a comparative analysis of which decision theory explains life satisfaction better. We consider expected utility theory and prospect theory. We consider the effects of three domains on life satisfaction: income, health, and (un)employment. Using a fixed effects estimator we find that life satisfaction contains features of both expected utility theory and prospect theory. However, the elements of expected utility theory are stronger predictors of life satisfaction. Life satisfaction depends positively on income, good health, and employment. It also depends positively on income and employment improvements, however the reverse is true for health improvements. Life satisfaction is concave in income gains and convex in income losses, and it exhibits loss aversion in income and employment status, but not in health. The results suggest that life satisfaction is best described by expected utility theory, but also contains some aspects of prospect theory.

Behavioral perspective of power systems’ decision makers

This article develops a decision-theoretic methodology for the risk-adjusted mission value (RAMV) for selecting between alternative missions in the presence of uncertainty in the outcomes of the missions. This methodology permits trading off mission risk for mission value, something that probabilistic risk analysis cannot do unless it explicitly incorporates both mission value and risk aversion of the project management. The methodology, in its complete implementation, is consistent with the decision theory known as expected utility theory, although it differs from conventional decision theory in that the probabilities and all but one of the utilities are not those of the decision maker. The article also introduces a new interpretation of risk aversion. The methodology is consistent with the elementary management concept concerning division of labor. An example is presented for selecting between discrete alternatives-four landing sites on Mars. A second example is presented for selecting among a set of continuous alternatives-a comet flyby distance. The methodology is developed within the context of scientific missions, but the methodology is equally applicable to any situation requiring outcome value judgments, probability judgments, and risk aversion judgments by different constituencies.

Decision theories give guidance about what to do when you face a particular decision. But they also give higher-level advice—depending on how likely you think it is that you’ll face various decision problems, decision theories give advice about the best strategy for picking what to do. For some ways of being uncertain over possible decisions, decision theories that accommodate risk undermine themselves. They simultaneously provide specific advice about what to pick whilst also deeming that very picking strategy to be impermissible. Savage-style expected utility theory does not have this flaw; it always deems its own picking strategies to be the rational ones. Popular decision rules for imprecise probabilities never straightforwardly undermine themselves but they often require adopting strategies that pick in accordance with expected utility theory, thereby coordinating how to pick across different potential decision problems. Some strategies that always pick an option that the decision theory does not reject are deemed impermissible. In particular, randomising amongst non-rejected options is often impermissible. This raises questions about how to use the guidance of an imprecise decision theory when it leaves different options non-rejected.

On the demand for information

Unlike many of the papers at this Conference, this paper concerns games against nature rather than games against strategically-motivated human (or computer) opponents. Nevertheless, games against nature are relevant to games against opponents - as the literature makes clear. Indeed, one of the seminal pieces of that literature, John von Neuman/Oskar Morgenstern, The Theory of Games and Economic Behaviour (1947)1, whilst ostensibly addressed to the theory of strategic games, derived one of the key elements of the theory of rational decision making against nature — namely Expected Utility theory — as a key component of the theory of strategic games. Moreover, many of the interesting new developments in Game Theory are pursuing the implications of non-Expected-Utility behaviour in games Contrariwise, some recent developments in individual decision-making, such as those related to intertemporal decision-making, are using results from the theory of games. Clearly, developments in each branch of the literature are relevant to the other branch.

Decision making investigates choices that have uncertain consequences and that cannot be completely predicted. Rational behavior may be described by the so-called expected utility theory (EUT), whose aim is to help choosing among several solutions to maximize the expectation of the consequences. However, Kahneman and Tversky developed an alternative model, called prospect theory (PT), showing that the basic axioms of EUT are violated in several instances. In respect of EUT, PT takes into account irrational behaviors and heuristic biases. It suggests an alternative approach, in which probabilities are replaced by decision weights, which are strictly related to the decision maker’s preferences and may change for different individuals. In particular, people underestimate the utility of uncertain scenarios compared to outcomes obtained with certainty, and show inconsistent preferences when the same choice is presented in different forms. The goal of this paper is precisely to analyze a real case study involving a decision problem regarding the Streicker Bridge, a pedestrian bridge on Princeton University campus. By modelling the manager of the bridge with the EUT first, and with PT later, we want to verify the differences between the two approaches and to investigate how the two models are sensitive to unpacking probabilities, which represent a common cognitive bias in irrational behaviors.