Dynamic Choice Problem Research Articles

Joint vs. Individual performance in a dynamic choice problem

This paper compares the relative ability of individuals and pairs to solve a finite, stochastic lifecycle problem that requires borrowing and saving to achieve the rational benchmark. We find that pairs significantly outperform individuals, especially when allowing subjects to account for past mistakes along conditionally-optimal consumption paths. Joint decision-makers out-earn individuals by about 23%. Though pairs and individuals both overreact to income and wealth balances, these distortions are twice as large for individuals. Analyzing chat data reveals that pairs bargain to balance idiosyncratic consumption preferences, which reduces consumption errors. We estimate consumption heuristics at the observation level and study their dynamics. We show that about half our subjects (or pairs of subjects) stick to heuristics for the majority of the experiment. These ‘stable’ subjects significantly outperform their ‘unstable’ counterparts in the dynamic optimization task. Finally, we provide suggestive evidence that subjects who have a nuanced view of debt outperform subjects who think of debt as always bad, even after controlling for cognitive ability.

Objective rationality and recursive multiple priors

We provide an axiomatic characterization of recursive MaxMin preferences that stem from a (possibly) incomplete relation representing preference judgements that are justified by objective probabilistic information. To ensure that her choice behavior be informed by objective information, dynamically consistent, and ambiguity averse, the decision-maker evaluates alternatives by their minimal expected value over the rectangular hull of the objective information set. The characterization builds upon two axioms that naturally combine the three requirements in a behavioral way. Our main result suggests a principled justification for the use of recursive MaxMin preferences in applications to dynamic choice problems.

Quasilinearization Methods for Nonlocal Fully-Nonlinear Parabolic Systems

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling the subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by the study of behavioral economics. Different types of nonlocal parabolic systems were studied but left behind the fully-nonlinear case and the connections among them. This paper shows the equivalence in solvability between nonlocal fully-nonlinear and the associated quasilinear systems, given their solutions are regular enough. Moreover, we establish the well-posedness results for the nonlocal quasilinear parabolic systems, so do that for the nonlocal fully-nonlinear parabolic systems. The quasilinear case alone is interesting in its own right from mathematical and modelling perspectives.

Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation

Time inconsistency is prevalent in dynamic choice problems: a plan of actions to be taken in the future that is optimal for an agent today may not be optimal for the same agent in the future. If the agent is aware of this intrapersonal conflict but unable to commit herself in the future to following the optimal plan today, the rational strategy for her today is to reconcile with her future selves, namely to correctly anticipate her actions in the future and then act today accordingly. Such a strategy is named intra-personal equilibrium and has been studied since as early as in the 1950s. A rigorous treatment in continuous-time settings, however, had not been available until a decade ago. Since then, the study on intra-personal equilibrium for time-inconsistent problems in continuous time has grown rapidly. In this chapter, we review the classical results and some recent development in this literature.

Dynamic consistency and ambiguity: A reappraisal

The famous conflict between dynamic consistency and ambiguity purportedly undermines these models' normative credibility, and challenges their use in economic applications. Dynamic consistency concerns preferences over contingent plans: so what counts are the contingencies the decision maker envisages – and plans for – rather than independently fixed contingencies, as implicitly assumed in standard formalisations. An appropriate formulation of dynamic consistency resolves the aforementioned conflict, hence undermining the criticisms of ambiguity models based on it. Moreover, it provides a principled justification for the restriction to certain families of beliefs in applications of these models in dynamic choice problems. Finally, it supports a new analysis of the value of information under ambiguity, showing that decision makers may only turn down information if it has an opportunity cost, in terms of the compromising of information they had otherwise expected to receive.

Coupled dynamics with an external system and application to international finance

The paper develops a generalized model of coupled dynamics for addressing the choice theoretic problems of economics and other behavioural sciences. The model extends the framework of coupled system to include an external sector that generates a richer dynamics. The model is applied to explain foreign capital inflow from the developed to the developing countries. Under certain regularity conditions, the existence of the solutions to the dynamic choice problem is proved and they are then obtained by numerical technique because of the non-linearity of the related functions. Robustness results are achieved via additional simulations by perturbation of the baseline parameter values.

Instrumental Rationality Without Separability

This paper argues that instrumental rationality is more permissive than expected utility theory. The most compelling instrumentalist argument in favour of separability, its core requirement, is that agents with non-separable preferences end up badly off by their own lights in some dynamic choice problems. I argue that once we focus on the question of whether agents’ attitudes to uncertain prospects help define their ends in their own right, or instead only assign instrumental value in virtue of the outcomes they may lead to, we see that the argument must fail. Either attitudes to prospects assign non-instrumental value in their own right, in which case we cannot establish the irrationality of the dynamic choice behaviour of agents with non-separable preferences. Or they don’t, in which case agents with non-separable preferences can avoid the problematic choice behaviour without adopting separable preferences.

Dynamic Consistency and Ambiguity : A Reappraisal

It is commonly argued that dynamic consistency, consequentialism and non-expected utility are incompatible. The first aim of this paper is to rebut such arguments, by targeting the implicit assumption that the relevant contingencies correspond to objective resolutions of uncertainty (that is, events in a state space). These are not necessarily the same as the contingencies that the decision maker envisages, and we argue that any reasonable notion of dynamic consistency involves the latter, rather than the former, sort of contingency. We formulate such a version of dynamic consistency and show it to be compatible with consequentialism and non-expected utility. We then analyze the economic consequences of this new perspective. On the one hand, it provides a principled justification for restrictions on non-expected utility models (such as that proposed by Epstein and Schneider (2003)) in applications to dynamic choice problems. On the other hand, it provides a new analysis of the issue of attitude to information; contra standard arguments, the value of information under non-expected utility is non-negative as long as the information offered does not compromise information that the decision maker had otherwise expected to receive. Finally, we give a representation theorem for the contingencies the decision maker envisages, in the case where he uses the maxmin expected utility rule.

Are bygones bygones?

This article reports an experiment which tests the principle of separability, i.e. that behaviour in a dynamic choice problem is independent of history and of unreachable eventualities. Although this is a well-known principle of orthodox decision theory and central to conventional economic modelling, it has been questioned on grounds suggested by non-expected utility models of choice under risk and by the psychology of affective influences on risk-taking. Our experimental design, which provides between-subjects tests of separability using three treatments in which the history preceding a decision is manipulated, is inspired by these concerns. We expose separability to a clean and harsh test, but find no evidence that it is violated.

Global Risk, Investment and Emotions

We investigate a novel dynamic choice problem in an experiment where emotions are measured through self‐reports. The choice problem concerns the investment of an amount of money in a safe option and a risky option when there is a ‘global risk’ of losing all earnings, from both options, including any return from the risky option. Our key finding is that global risk canreducethe amount invested in the risky option. This result cannot be explained by Expected Utility or by its main contenders, Rank‐Dependent Utility and Cumulative Prospect Theory. An explanation is offered by taking account of emotions, using the emotion data from the experiment and recent psychological findings.

Catastrophic Risk and Egalitarian Principles for Risk Transfer Mechanisms

Financial aid for the worst off victims of earthquakes and other catastrophes seems tobe a morally unquestioned principle for the allocation of public funds. This paper shows however, that this principle is ambiguous if the decision is viewed as a dynamic choice problem where such resources need to be allocated in two periods: before and after the event takes place (before and after uncertainty is resolved). The literature on social choice suggests that utilitarian principles fare better in such situations. This paper provides a uniform formal framework to relate one such result, namely a multi-profile version of Harsanyis 1955 theorem by Mongin (1994) to another one by Myerson (1981), stated in a somewhat unconventional social choice framework. It shows that the Linearity condition, that is met only by welfare functions of the utilitarian type, has a natural interpretation in terms of an equivalence of ex ante and ex post evaluation, a concept that is related to but not equivalent with dynamic consistency. <italic>JEL Classification: G22, H42, I3, Q54</italic>

Dynamic Choice, Independence and Emotions

From the viewpoint of the independence axiom of expected utility theory, an interesting empirical dynamic choice problem involves the presence of a “global risk,” that is, a chance of losing everything whichever safe or risky option is chosen. In this experimental study, participants have to allocate real money between a safe and a risky project. Treatment variable is the particular decision stage at which a global risk is resolved: (i) before the investment decision; (ii) after the investment decision, but before the resolution of the decision risk; (iii) after the resolution of the decision risk. The baseline treatment is without global risk. Our goal is to investigate the isolation effect and the principle of timing independence under the different timing options of the global risk. In addition, we examine the role played by anticipated and experienced emotions in the choice problem. Main findings are a violation of the isolation effect, and support for the principle of timing independence. Although behavior across the different global risk cases shows similarities, we observe clear differences in people’s affective responses. This may be responsible for the conflicting results observed in earlier experiments. Dependent on the timing of the global risk different combinations of anticipated and experienced emotions influence decision making.

Dynamic Choice, Independence and Emotions

From the viewpoint of the independence axiom of expected utility theory, an interesting empirical dynamic choice problem involves the presence of a global risk, that is, a chance of losing everything whichever safe or risky option is chosen. In this experimental study, participants have to allocate real money between a safe and a risky project. Treatment variable is the particular decision stage at which a global risk is resolved: (i) before the investment decision; (ii) after the investment decision but before the resolution of the investment risk; (iii) after the resolution of the investment risk. The baseline treatment is without global risk. Our goal is to investigate the isolation effect and the principle of timing independence under the different timing options of the global risk. In addition, we examine the role played by anticipated and experienced emotions in the choice problem. Main findings are a violation of the isolation effect, and support for the principle of timing independence. Although behavior across the different global risk cases shows similarities, we observe clear differences in people's affective responses. This may be responsible for the conflicting results observed in earlier experiments. Dependent on the timing of the global risk different combinations of anticipated and experienced emotions influence decision making.

On the Observability of Plans in Dynamic Choice Problems Involving Risk: Comment about J. Hey

We show that in dynamic choice problems, the observability of a decision maker's first move does reveal his plan for the dynamic choice problem, only under strong restrictions about the structure of his preferences. These restrictions imply consequentialism which in turn implies dynamic consistency, a condition which is not necessarily satisfied by experimental subjects.

Dynamic Choice and Risk Aversion

This paper solves explicitly a dynamic choice problem for a class of stochastic volatility models. The explicit solution is used to show that intuitions on static choice problems do not apply in a dynamic choice setting. For example, even though the risk premium of the risky asset in the problem is strictly positive, a more risk-averse agent may hold more risky assets, and a risk-averse agent may short (sometimes infinite amount of) a risky asset. I argue that these counter-intuitive results are due to rebalancing. The results suggest that it may be not appropriate to use stock holdings as a proxy for risk aversion.

Dynamic Decision-Making Under Uncertainty: An Experimental Investigation of Choices Between Accumulator Gambles

This paper presents an experiment that is designed to be more effective than previous studies at reproducing in the laboratory the affective experiences of risk-taking, such as hope, fear, thrill, pain of loss, regret, disappointment or elation. The use of dynamic choice problems involving accumulator gambles, and a particular randomisation device to resolve them, are central to the design. Our results both are inconsistent with orthodox dynamic choice theory and cast doubt on the generality of effects observed in previous designs. We discuss these findings, in terms of the relative impacts on behaviour of affective experience and judgement.

Conditional Decision Processes with Recursive Function

We consider stochastic optimization of not necessarily additive but recursive functions over multistage decision processes. Without assuming any monotonicity, we optimize a regular process by a direct dynamic programming approach. On the regular decision process, we propose two related conditional decision processes: an a posteriori conditional decision process and an a priori. When the Markov transition law degenerates into a deterministic dynamics, the two conditional processes reduce to the same deterministic decision process. The conditional processes with monotonicity are optimized by the usual backward dynamic programming. We show that under additional convexity the regular process dominates the a priori in maximum value function and the a priori does the a posteriori. We show that the a posteriori process illustrates Kreps and Porteus's dynamic choice problem. The numerical example also verifies the dominance relation in three optimal value functions.

Uncertain lifetime, risk aversion and intertemporal substitution

This paper describes a simple utility function for dynamic choice problems under uncertain lifetime. Preferences are time consistent and similar to Selden's ordinal certainty equivalent hypothesis. For Yaari's model of consumption/savings decisions, holding intertemporal substitution fixed, the consumption growth rate is increasing (decreasing) in the mortality rate if risk aversion is lower (higher) than under expected utility preferences.

Two Dynamic Discrete Choice Estimation Problems and Simulation Method Solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

Betweenness satisfying preferences and dynamic choice

We consider the dynamic choice problem where uncertainty is resolved gradually (i.e., decision trees). We impose consistency on the decision maker by requiring that his behavior in trees conform to preference maximization over lotteries. We formulate and defend three different requirements on dynamic behavior and show that for any decision maker whose behavior is consistent with maximizing a continuous, monotone preference relation over lotteries, each one of these conditions is equivalent to the betweenness property of the underlying preferences.