Subjective Equilibria under Beliefs of Exogenous Uncertainty

We present a subjective equilibrium notion (called "subjective equilibrium under beliefs of exogenous uncertainty (SEBEU)" for stochastic dynamic games in which each player chooses its decisions under the (incorrect) belief that a stochastic environment process driving the system is exogenous whereas in actuality this process is a solution of closed-loop dynamics affected by each individual player. Players observe past realizations of the environment variables and their local information. At equilibrium, if players are given the full distribution of the stochastic environment process as if it were an exogenous process, they would have no incentive to unilaterally deviate from their strategies. This notion thus generalizes what is known as the price-taking equilibrium in prior literature to a stochastic and dynamic setup. We establish existence of SEBEU, study various properties and present explicit solutions. We obtain the $\epsilon$-Nash equilibrium property of SEBEU when there are many players

Classes of decision analysis

The ultimate task of an engineer consists of developing a consistent decision procedure for the planning, design, construction and use and management of a project. Moreover, the utility over the entire lifetime of the project should be maximized, considering requirements with respect to safety of individuals and the environment as specified in regulations. Due to the fact that the information with respect to design parameters is usually incomplete or uncertain, decisions are made under uncertainty. In order to cope with this, Bayesian statistical decision theory can be used to incorporate objective as well as subjective information (e.g. engineering judgement). In this factsheet, the decision tree is presented and answers are given for questions on how new data can be combined with prior probabilities that have been assigned, and whether it is beneficial or not to collect more information before the final decision is made. Decision making based on prior analysis and posterior analysis is briefly explained. Pre-posterior analysis is considered in more detail and the Value of Information (VoI) is defined

Sensitivity and Bias in Decision-Making under Risk: Evaluating the Perception of Reward, Its Probability and Value

BACKGROUND: There are few clinical tools that assess decision-making under risk. Tests that characterize sensitivity and bias in decisions between prospects varying in magnitude and probability of gain may provide insights in conditions with anomalous reward-related behaviour. OBJECTIVE: We designed a simple test of how subjects integrate information about the magnitude and the probability of reward, which can determine discriminative thresholds and choice bias in decisions under risk. DESIGN/METHODS: Twenty subjects were required to choose between two explicitly described prospects, one with higher probability but lower magnitude of reward than the other, with the difference in expected value between the two prospects varying from 3 to 23%. RESULTS: Subjects showed a mean threshold sensitivity of 43% difference in expected value. Regarding choice bias, there was a 'risk premium' of 38%, indicating a tendency to choose higher probability over higher reward. An analysis using prospect theory showed that this risk premium is the predicted outcome of hypothesized non-linearities in the subjective perception of reward value and probability. CONCLUSIONS: This simple test provides a robust measure of discriminative value thresholds and biases in decisions under risk. Prospect theory can also make predictions about decisions when subjective perception of reward or probability is anomalous, as may occur in populations with dopaminergic or striatal dysfunction, such as Parkinson's disease and schizophrenia

Directed search with real options

While search is normally modelled by economists purely in terms of decisions over making observations, this paper models it as a process in which information is gained through feedback from innovatory product launches. The information gained can then be used to decide whether to exercise real options. In the model the initial decisions involve a product design and the scale of production capacity. There are then real options to change these factors based on what is learned. The case of launching product variants in parallel is also considered. Under ‘true’ uncertainty, the model can be seen in terms of heuristic decision-making based on subjective beliefs with limited foresight. Search costs, the values of the real options, beliefs, and the cost of capital are all shown to be significant in determining the search path

Group Decision Making with Uncertain Outcomes: Unpacking Child-Parent Choices of High School Tracks

Predicting group decisions with uncertain outcomes involves the empirically difficult task of disentangling individual decision makers' beliefs and preferences over outcomes' states from the group's decision rule. This paper addresses the problem within the context of a consequential family decision concerning the high school track of adolescent children in presence of curricular strati cation. The paper combines novel data on children's and parents' probabilistic beliefs, their stated choice preferences, and families' decision rules with standard data on actual choices to estimate a simple model of curriculum choice featuring both uncertainty and heterogeneous cooperative-type decisions. The model's estimates are used to quantify the impact on curriculum enrollment of policies affecting family members' expectations via awareness campaigns, publication of education statistics, and changes in curricular specialization and standards. The latter exercise reveals that identity of policy recipients--whether children, parents, or both--matters for enrollment response, and underlines the importance of incorporating information on decision makers' beliefs and decision rules when evaluating policies.Choice under Uncertainty, Multilateral Choice, Heterogeneous Decision Rules, Curricular Tracking, Curriculum Choice, Child-Parent Decision Making, Subjective Probabilities, Stated and Revealed Preferences, Choice-Based Sampling

Harnessing BIM data in the management of project risks: the Bayesian risk-bearing capacity approach

With the increasing proliferation of Building Information Modelling (BIM) worldwide, an emerging issue is how to better leverage the BIM data in decision making. This research demonstrates formally that the cost information attached to BIM can be utilised to inform risk management decisions by incorporating the newly developed risk-bearing capacity (RBC) approach into the Bayesian statistics framework. Under BIM, the deviations of outturn costs from planned costs can be systematically recorded and used to update the old ‘beliefs’ that are normally formed by resorting to subjective probabilities. With the potential to integrate the data held by insurers, cost estimators and credit raters, this framework can greatly facilitate the effective use of enormous new data in improving risk management practices

Children perform extensive information gathering when it is not costly

Humans often face decisions where little is known about the choice options. Gathering information prior to making a choice is an important strategy to improve decision making under uncertainty. This is of particular importance during childhood and adolescence, when knowledge about the world is still limited. To examine how much information youths gather, we asked 107 children (8-9 years, N = 30), early (12-13 years, N = 41) and late adolescents (16-17 years, N = 36) to perform an information sampling task. We find that children gather significantly more information before making a decision compared to adolescents, but only if it does not come with explicit costs. Using computational modelling, we find that this is because children have reduced subjective costs for gathering information. Our findings thus demonstrate how children overcome their limited knowledge and neurocognitive constraints by deploying excessive information gathering, a developmental feature that could inform aberrant information gathering in psychiatric disorders

Rationality versus reality: the challenges of evidence-based decision making for health policy makers

<p>Abstract</p> <p>Background</p> <p>Current healthcare systems have extended the evidence-based medicine (EBM) approach to health policy and delivery decisions, such as access-to-care, healthcare funding and health program continuance, through attempts to integrate valid and reliable evidence into the decision making process. These policy decisions have major impacts on society and have high personal and financial costs associated with those decisions. Decision models such as these function under a shared assumption of rational choice and utility maximization in the decision-making process.</p> <p>Discussion</p> <p>We contend that health policy decision makers are generally unable to attain the basic goals of evidence-based decision making (EBDM) and evidence-based policy making (EBPM) because humans make decisions with their naturally limited, faulty, and biased decision-making processes. A cognitive information processing framework is presented to support this argument, and subtle cognitive processing mechanisms are introduced to support the focal thesis: health policy makers' decisions are influenced by the subjective manner in which they individually process decision-relevant information rather than on the objective merits of the evidence alone. As such, subsequent health policy decisions do not necessarily achieve the goals of evidence-based policy making, such as maximizing health outcomes for society based on valid and reliable research evidence.</p> <p>Summary</p> <p>In this era of increasing adoption of evidence-based healthcare models, the rational choice, utility maximizing assumptions in EBDM and EBPM, must be critically evaluated to ensure effective and high-quality health policy decisions. The cognitive information processing framework presented here will aid health policy decision makers by identifying how their decisions might be subtly influenced by non-rational factors. In this paper, we identify some of the biases and potential intervention points and provide some initial suggestions about how the EBDM/EBPM process can be improved.</p

Bayesian Theory of Games: A Statistical Decision Theoretic Based Analysis of Strategic Interactions

Bayesian rational prior equilibrium requires agent to make rational statistical predictions and decisions, starting with first order non informative prior and keeps updating with statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. The main difference between the Bayesian theory of games and the current games theory are: I. It analyzes a larger set of games, including noisy games, games with unstable equilibrium and games with double or multiple sided incomplete information games which are not analyzed or hardly analyzed under the current games theory. II. For the set of games analyzed by the current games theory, it generates far fewer equilibria and normally generates only a unique equilibrium and therefore functions as an equilibrium selection and deletion criterion and, selects the most common sensible and statistically sound equilibrium among equilibria and eliminates insensible and statistically unsound equilibria. III. It differentiates between simultaneous move and imperfect information. The Bayesian theory of games treats sequential move with imperfect information as a special case of sequential move with observational noise term. When the variance of the noise term approaches its maximum such that the observation contains no informational value, there is imperfect information (with sequential move). IV. It treats games with complete and perfect information as special cases of games with incomplete information and noisy observation whereby the variance of the prior distribution function on type and the variance of the observation noise term tend to zero. Consequently, there is the issue of indeterminacy in statistical inference and decision making in these games as the equilibrium solution depends on which variances tends to zero first. It therefore identifies equilibriums in these games that have so far eluded the classical theory of games.Games Theory, Bayesian Statistical Decision Theory, Prior Distribution Function, Conjectures, Subjective Probabilities