Effect of Geometric Complexity on Intuitive Model Selection

Occam’s razor is the principle stating that, all else being equal, simpler explanations for a set of observations are to be preferred to more complex ones. This idea can be made precise in the context of statistical inference, where the same quantitative notion of complexity of a statistical model emerges naturally from different approaches based on Bayesian model selection and information theory. The broad applicability of this mathematical formulation suggests a normative model of decision-making under uncertainty: complex explanations should be penalized according to this common measure of complexity. However, little is known about if and how humans intuitively quantify the relative complexity of competing interpretations of noisy data. Here we measure the sensitivity of naive human subjects to statistical model complexity. Our data show that human subjects bias their decisions in favor of simple explanations based not only on the dimensionality of the alternatives (number of model parameters), but also on finer-grained aspects of their geometry. In particular, as predicted by the theory, models intuitively judged as more complex are not only those with more parameters, but also those with larger volume and prominent curvature or boundaries. Our results imply that principled notions of statistical model complexity have direct quantitative relevance to human decision-making

A primal-dual decomposition based interior point approach to two-stage stochastic linear programming

Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties that has found applications in, e.g. finance, such as asset-liability and bond-portfolio management. Computationally however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. For a model to be well solvable, its special structure must be explored. Most of the solution methods are based on decomposing the data. In this paper we propose a new decomposition approach for two-stage stochastic programming, based on a direct application of the path-following method combined with the homogeneous self-dual technique. Numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs. In particular, we apply our deompostition method to a two-period portfolio selection problem using options on a stock index. In this model the investor can invest in a money-market account, a stock index, and European options on this index with different maturities. We experiment our model with market prices of options on the S&P500

Robust Optimization for Sequential Field Development Planning

To achieve high profitability from an oil field, optimizing the field development strategy (e.g., well type, well placement, drilling schedule) before committing to a decision is critically important. The profitability at a given control setting is predicted by running a reservoir simulation model, while determining a robust optimal strategy generally requires many expensive simulations. In this work, we focus on developing practical and efficient methodologies to solving reservoir optimization problems for which the actions that can be controlled are discrete and sequential (e.g., drilling sequence of wells). The type of optimization problems I address must take into account both geological uncertainty and the reduction in uncertainty resulting from observations. As the actions are discrete and sequential, the process can be characterized as sequential decision- making under uncertainty, where past decisions may affect both the possibility of the future choices of actions and the possibility of future uncertainty reduction. This thesis tackles the challenges in sequential optimization by considering three main issues: 1) optimizing discrete-control variables, 2) dealing with geological uncertainty in robust optimization, and 3) accounting for future learning when making optimal decisions. As the first contribution of this work, we develop a practical online-learning method- ology derived from A* search for solving reservoir optimization problems with discrete sets of actions. Sequential decision making can be formulated as finding the path with the maximum reward in a decision tree. To efficiently compute an optimal or near- optimal path, heuristics from relaxed problems are first used to estimate the maximum value constrained to past decisions, and then online-learning techniques are applied to improve the estimation accuracy by learning the errors of the initial approximations ob- tained from previous decision steps. In this way, an accurate estimate of the maximized value can be inexpensively obtained, thereby guiding the search toward the optimal so- lution efficiently. This approach allows for optimization of either a complete strategy with all available actions taken sequentially or only the first few actions at a reduced cost by limiting the search depth. The second contribution is related to robust optimization when an ensemble of reservoir models is used to characterize geological uncertainty. Instead of computing the expectation of an objective function using ensemble-based average value, we develop various bias-correction methods applied to the reservoir mean model to estimate the expected value efficiently without sacrificing accuracy. The key point of this approach is that the bias between the objective-function value obtained from the mean model and the average objective-function value over an ensemble can be corrected by only using information from distinct controls and model realizations. During the optimization process, we only require simulations of the mean model to estimate the expected value using the bias-corrected mean model. This methodology can significantly improve the efficiency of robust optimization and allows for fairly general optimization methods. In the last contribution of this thesis, we address the problem of making optimal decisions while considering the possibility of learning through future actions, i.e., op- portunities to improve the optimal strategy resulting from future uncertainty reduction. To efficiently account for the impact of future information on optimal decisions, we sim- plify the value of information analysis through key information that would help make better future decisions and the key actions that would result in obtaining that informa- tion. In other words, we focus on the use of key observations to reduce the uncertainty in key reservoir features for optimization problems, rather than using all observations to reduce all uncertainties. Moreover, by using supervised-learning algorithms, we can identify the optimal observation subset for key uncertainty reduction automatically and evaluate the information’s reliability simultaneously. This allows direct computation of the posterior probability distribution of key uncertainty based on Bayes’ rule, avoiding the necessity of expensive data assimilation algorithms to update the entire reservoir modeDoktorgradsavhandlin

Top-down and bottom-up decision-making for climate change adaptation. An application to flooding

There is strong scientific consensus on the evidence of anthropogenic climate change which will increasingly present social, economic and institutional challenges. The Fifth Assessment report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) established that ‘human influence on the climate system is clear’ and that ‘changes in many extreme weather and climate events have been observed since about 1950’ (IPCC 2014a). Associated impacts include sea level rise and increased likelihood of extreme weather worldwide such extreme rainfall, heat waves, hurricanes and tornados (IPCC 2014a; Klijn et al. 2015). Climate change adaptation is the adjustment in natural or human systems in response to actual or expected climatic stimuli or their effects in order to minimise the impacts and to take advantage of new opportunities (IPCC 2007). Many vulnerable countries, regions and cities have accepted that some form of adaptation is inevitable (Swart et al. 2014). This thesis contributes to the research on decision-making for climate change adaptation in order to reduce vulnerability. Both bottom-up and top-down analyses are applied to complement one another with an application to flooding. Flood risk is expected to increase in the UK under climate change (Alfieri et al. 2016; Scottish Government 2016) associated significant economic damage (CEA 2007). From a top-down perspective, the thesis explores how to enhance economic decision-making under climate change uncertainty. In a situation of uncertainty the costs may be clear and immediate whereas the benefits are uncertain and often only realised in the distant future. This impedes the use of standard decision-making tools such as cost-benefit analysis that rely on the quantification of (expected) costs and benefits. The thesis begins on the macro scale with a taxonomy of economic decision-making tools for climate change adaptation, discusses the sector level and subsequently proceeds to the case study micro-scale with applications of adaptation decision-making. First, the potential of alternative decision-making tools, so-called robust decision-making approaches, is examined. The strengths and weaknesses of these tools relative to traditional decision-making processes such as CBA are explored and their future potential in the adaptation process evaluated. It is found that robust decision-making tools under uncertainty provide performance across a range of climate change scenarios, but they may yield lower overall performance if compared with the alternative strategy under the actual climate outturn. Furthermore, they are resource intense and decision makers need to balance the resources required for employing the methods with the added value they can offer. A flow-chart is developed to provide guidance on which decision-making tool should be applied depending on the scale and type of adaptation project. On the sector level, the economic appraisal of adaptation options for agriculture is explored. Agriculture is particularly vulnerable to climate change due to the direct impacts of weather and climate on agricultural output and the sector plays an indispensable role in providing (and improving) food security as well as creating employment. Many of the adaptation options in agriculture involve short-term managerial changes and can be appraised with standard economic decision-making and the options can be carried out after the climate signal has been observed. For those adaptations that do require a longer time to take effect or are long-lived and are (partly) irreversible in nature, robust approaches have a valuable role to play in decision-making. Suggestions are made regarding how robust decisionmaking tools under uncertainty can be practically applied to adaptations in agriculture, outlining the data needs and the steps of the data analysis for three different applications. On the micro level, for a case study in the Eddleston Water catchment in the Scottish borders, UK, two different economic appraisal tools are applied. These include a cost-benefit analysis of afforestation as a flood management measure under different climate change scenarios which can provide important insights for adaptation decisions when robust decision-making tools under uncertainty are not feasible due to resource constraints. It is found that the flood risk under climate change increases substantially in the case study area which needs to be taken into consideration for economic appraisal. The results of the CBA reveal that all modelled scenarios of afforestation have positive NPVs which are driven by further eco-system services (including climate regulation, water quality and recreation) rather than flood regulation benefits. It is concluded that eco-system services beyond flood regulation should be considered for the appraisal of NFM to enable policy-makers to make informed decisions. Second, the Expected values can be used in situations of quantifiable uncertainty, i.e risk. But for climate change we do not have a strong methodology to assess these subjective probabilities. They cannot be fully based on the past, because climate change is a new process for which we have no historical equivalent. Models share common flaws in their assumptions and their dispersion in results cannot be used to assess the real uncertainty (Hallegatte, 2012). The term deep uncertainty (Lempert et al., 2003) or severe uncertainty is used (Ben-Haim, 2006) in these contexts. Such uncertainty is characterised as a condition where decision makers do not know or cannot agree upon a model that adequately describes cause and effect or its key parameters (Walker et al., 2012). This leads to a situation where it is not possible to say with confidence whether one future state of the world is more plausible than another. The robust decision-making tool under uncertainty real option analysis is applied to the same case study to allow for adjusting adaptation options over time by integrating lessons learned about climate change in the appraisal process. A simplified ROA is presented to minimise the life cycle cost of a system that aims to prevent flooding of a return period of 1/20 using tools which should be available to most public authorities. This includes the use of UKCP09 climate data, analysis of changes of peak flow under the measure implemented, cost structures for the measure and damage cost under different outcomes. The analysis can be carried out in an excel spread sheet with the aforementioned types of input. The results of the analysis demonstrate that the obtained strategy is significantly cheaper than planting for the worst case scenario and presents the potential for learning under climate change uncertainty as a way to allocate resources in a more efficient way. The complementing bottom up approach investigates behavioural barriers to decisionmaking for adaptation. Standard economic theory tells us that self-interest will motivate most actors to engage in efficient private adaptation as long as the costs do not exceed the benefits. Thus, we would expect households at flood risk to invest in flood adaptation measures. However, it has been observed that households do not necessarily take action to protect themselves and their assets from flooding. In a study carried out in co-operation with 36 communities around Scotland, protection motivation theory is used to explain the uptake of household flood protection and whether community led flood action groups can increase uptake. It is found that flood action groups directly and indirectly influence the uptake of some flood protection measures positively in particular if tailored information is provided. Overall, it is concluded that both top-down and bottom-up approaches play an important role to move towards an economically efficient adaptation in the context of flooding. From a top-down perspective, uncertainty should be explicitly acknowledged and included in economic decision-making for adaptation (to flooding) to make an informed decision. The type of analysis will depend on the adaptation project and resources at hand. Developing and fostering bottom-up tools such as flood action groups to increase the uptake of the type of household flood protection with a benefit-cost ratio above 1 may also contribute towards the more efficient allocation of resources

A Metaheuristic-Based Simulation Optimization Framework For Supply Chain Inventory Management Under Uncertainty

The need for inventory control models for practical real-world applications is growing with the global expansion of supply chains. The widely used traditional optimization procedures usually require an explicit mathematical model formulated based on some assumptions. The validity of such models and approaches for real world applications depend greatly upon whether the assumptions made match closely with the reality. The use of meta-heuristics, as opposed to a traditional method, does not require such assumptions and has allowed more realistic modeling of the inventory control system and its solution. In this dissertation, a metaheuristic-based simulation optimization framework is developed for supply chain inventory management under uncertainty. In the proposed framework, any effective metaheuristic can be employed to serve as the optimizer to intelligently search the solution space, using an appropriate simulation inventory model as the evaluation module. To be realistic and practical, the proposed framework supports inventory decision-making under supply-side and demand-side uncertainty in a supply chain. The supply-side uncertainty specifically considered includes quality imperfection. As far as demand-side uncertainty is concerned, the new framework does not make any assumption on demand distribution and can process any demand time series. This salient feature enables users to have the flexibility to evaluate data of practical relevance. In addition, other realistic factors, such as capacity constraints, limited shelf life of products and type-compatible substitutions are also considered and studied by the new framework. The proposed framework has been applied to single-vendor multi-buyer supply chains with the single vendor facing the direct impact of quality deviation and capacity constraint from its supplier and the buyers facing demand uncertainty. In addition, it has been extended to the supply chain inventory management of highly perishable products. Blood products with limited shelf life and ABO compatibility have been examined in detail. It is expected that the proposed framework can be easily adapted to different supply chain systems, including healthcare organizations. Computational results have shown that the proposed framework can effectively assess the impacts of different realistic factors on the performance of a supply chain from different angles, and to determine the optimal inventory policies accordingly

Validation of retrofit analysis simulation tool: Lessons learned

It is well known that residential and commercial buildings account for about 40% of the overall energy consumed in the United States, and about the same percentage of CO2 emissions. Retrofitting existing old buildings, which account for 99% of the building stock, represents the best opportunity of achieving challenging energy and emission targets. United Technologies Research Center (UTC) has developed a methodology and tool that provides computational support for analysis and decision-making for building retrofits. The tool is based on simplified physics-based models and incorporates intelligent defaulting capability, automatic model calibration and package selection as well as uncertainty and sensitivity analysis on both predicted energy consumption and potential savings. The latter is used to better inform decision makers on the quality of the data used for analysis and direct them in the overall process to achieve the required accuracies in the analysis. This paper addresses the validation of the simplified physics-based models. The validation is performed using three-tier approach: a) validation against ASHRAE 140 BESTEST Cases; b) inter-model comparison of results obtained by other more complex tools using more detailed models than in those required by ASHRAE 140 Standard and c) comparison to real building measured utility data. Findings and conclusions from each one of the three validation approaches are presented, as well as a discussion on model complexity vs. results accuracy based on lessons learned during the reported study. This material is based upon work supported by the Energy Efficient Buildings Hub (EEB Hub), an energy innovation hub sponsored by the U.S. Department of Energy under Award Number DE-EE0004261 and by the U.S Department of Defense ESTCP Program ESTCP Program # 201257, contract number W912HQ-12-C-0051

The Foreign Direct Investment Location Decision: A Contingency Model of the Foreign Direct Investment Location Decision-Making Process

Despite considerable prior research into foreign direct investment (FDI) location decisions, our understanding of the processes underlying such decisions is still limited. Findings from work based in the economics and behavioral theories of the multinational enterprise (MNE) both acknowledge that FDI is not a point-of-time decision but a gradual process that yields important changes over its duration. However, these competing traditions both fall short when attempting to portray the actual process by which FDI location decisions are made by managers in MNEs. This gap has been recently attributed to two interrelated limitations. Firstly, level of analysis concerns have artificially separated managerial decision-making processes from the organizational and environmental structures within which they are made. Secondly, because of the complexity inherent in the FDI location decision environment, the study of these decisions has not taken contextual factors into consideration. This study addresses three important questions in order to build our understanding of the FDI location decision-making processes: (1) What are the decision-making processes that lead to FDI location choice? (2) What is the impact of contextual variables on FDI location decision-making processes at different levels of analysis, and are there any patterns of variation in decision processes under different decision conditions? (3) What factors drive final FDI location choice, and can a useful framework or theory be developed that links FDI location decision-making processes and context to drivers of FDI location choice? In order to address level of analysis concerns, the study places the manager at the center of the FDI location decision in modeling and in research, a strategy recommended by an emerging stream of behavioral-focused international business research (Aharoni, 2010; Buckley et al., 2007; Devinney, 2011). By examining FDI location decisions from the perspective of the managers who implement them, it is possible to clarify the nature of processes that lead to FDI location choice, and identify the impact of different elements of decision maker, firm and environmental context on such processes. The conceptual framework builds on Aharoni’s (1966) pivotal research while incorporating findings from broader behavioral managerial decision models and international business research. The framework is based on the assumption that FDI location decision-making processes and final choice are contingent upon interactions between the environmental, firm and decision maker context under which the decision is made. The research was undertaken in three phases. Phase 1 included a literature review that covered research on the MNE, internationalization, and decision making. The findings of the review identified key aspects of FDI location decision context and led to the development of an initial contingency framework of strategic decision making. Phase 2 consisted of an exploratory case study of twenty four FDI location decisions. The initial contingency framework developed during the literature review was used during this stage to identify the relationship between decision-making processes and contextual variables at the case decisions. By drawing on results from the exploratory research, an initial conceptual model and a set of propositions were developed. In Phase 3, twenty case studies were theoretically sampled from a pool of MNEs of varying size and parent-country nationality within the knowledge-based industries. The data collection and analysis followed a process, event-driven approach to case study research involving the mapping of key sequences of events as well as within- and cross-case analysis. The results identify the key elements of the decision process that explain FDI location behavior and develop a framework that links them together and makes them sensible. The four key elements of the FDI location decision that comprise the framework include: (i) the process, (ii) the context, (iii) patterns, and (iv) location. Research findings show the FDI location decision process as comprising of five broad stages, the content of each driven by a dynamic and evolving interpretation of maximum subjective expected utility. Utility preferences are identified as the consequence of shifting and opaque goals, founded upon imperfect information, operating in an environment marked by uncertainty. Five variations in the overall orientation of utility at case decisions, classified in the study as ‘decision rules,’ proved to be more useful predictors of decision-making behavior than traditional notions of bounded rationality seeking rent extraction and profitability. Decision processes were found to vary in five prototypical patterns, according to clusters of contextual variables that together moderated the level of decision-maker autonomy, hierarchical centralization, rule formalization, commitment to strategy, and politicization of the decision. Patterns are described as FDI location decision-making models, and proposed as an initial step towards the development of a taxonomy of FDI location decision-making processes. Because of the dynamic and staged nature of the process, findings showed that factors that were important at one stage of the decision were not as important at the next. As such, the task of identifying universal drivers of FDI location was deemed an unfeasible one. In place of universal drivers, the initiating force of the investment, the purpose of investment and information sources and networks are identified as the key context-specific determinants of location in FDI decisions. Bounded by uncertainty, chance, the dynamics of the process and decision-maker effects, each of these aspects of the decision served to limit the possible consideration set for investment, and formed the value basis and measures from which to select the most attractive location choice. Despite the contextual differences in these drivers, however, the study revealed a strong pattern that showed that the importance of specific location considerations differed in much the same way across case decisions. During the first stage of case decisions primarily strategic aspects of locations were considered; during the second, considerations relating to the system; operational concerns in the third; implementation concerns in the fourth; and added value factors in the final choice. How each of these concerns was interpreted to reach final location choice differed according to the drivers mentioned previously, although the patterns were the same. This study develops a contingency framework for examining the FDI location decision-making processes of MNEs under different operating conditions. By identifying the four key components of the FDI location decision, their interrelationships and many sources of variance, this thesis shows that despite its complexity, the FDI location decision is amenable to useful conceptual structuring. From an academic standpoint, the framework answers Aharoni’s most recent call to action in ‘Behavioral Elements in Foreign Direct Investment’ (2010) by developing a replicable structure within which to think about incorporating managerial decision models and context into the theory of the MNE. These findings enhance understandings of decision making at MNEs, reconcile a number of inconsistencies between opposing perspectives of MNE theory, and thereby update extant theory so that it has greater relevance in today’s diverse international business environment. From a managerial standpoint, the thesis helps managers to recognize the opportunities and limitations posed by different aspects of decision context so that they are able to tailor their FDI location decision strategies to best suit their needs. Finally, from the perspective of policy markers, research findings provide great support for the use of investment attraction schemes through the use of targeted location marketing and investment incentives.

The Foreign Direct Investment Location Decision: A Contingency Model of the Foreign Direct Investment Location Decision-Making Process

Despite considerable prior research into foreign direct investment (FDI) location decisions, our understanding of the processes underlying such decisions is still limited. Findings from work based in the economics and behavioral theories of the multinational enterprise (MNE) both acknowledge that FDI is not a point-of-time decision but a gradual process that yields important changes over its duration. However, these competing traditions both fall short when attempting to portray the actual process by which FDI location decisions are made by managers in MNEs. This gap has been recently attributed to two interrelated limitations. Firstly, level of analysis concerns have artificially separated managerial decision-making processes from the organizational and environmental structures within which they are made. Secondly, because of the complexity inherent in the FDI location decision environment, the study of these decisions has not taken contextual factors into consideration. This study addresses three important questions in order to build our understanding of the FDI location decision-making processes: (1) What are the decision-making processes that lead to FDI location choice? (2) What is the impact of contextual variables on FDI location decision-making processes at different levels of analysis, and are there any patterns of variation in decision processes under different decision conditions? (3) What factors drive final FDI location choice, and can a useful framework or theory be developed that links FDI location decision-making processes and context to drivers of FDI location choice? In order to address level of analysis concerns, the study places the manager at the center of the FDI location decision in modeling and in research, a strategy recommended by an emerging stream of behavioral-focused international business research (Aharoni, 2010; Buckley et al., 2007; Devinney, 2011). By examining FDI location decisions from the perspective of the managers who implement them, it is possible to clarify the nature of processes that lead to FDI location choice, and identify the impact of different elements of decision maker, firm and environmental context on such processes. The conceptual framework builds on Aharoni’s (1966) pivotal research while incorporating findings from broader behavioral managerial decision models and international business research. The framework is based on the assumption that FDI location decision-making processes and final choice are contingent upon interactions between the environmental, firm and decision maker context under which the decision is made. The research was undertaken in three phases. Phase 1 included a literature review that covered research on the MNE, internationalization, and decision making. The findings of the review identified key aspects of FDI location decision context and led to the development of an initial contingency framework of strategic decision making. Phase 2 consisted of an exploratory case study of twenty four FDI location decisions. The initial contingency framework developed during the literature review was used during this stage to identify the relationship between decision-making processes and contextual variables at the case decisions. By drawing on results from the exploratory research, an initial conceptual model and a set of propositions were developed. In Phase 3, twenty case studies were theoretically sampled from a pool of MNEs of varying size and parent-country nationality within the knowledge-based industries. The data collection and analysis followed a process, event-driven approach to case study research involving the mapping of key sequences of events as well as within- and cross-case analysis. The results identify the key elements of the decision process that explain FDI location behavior and develop a framework that links them together and makes them sensible. The four key elements of the FDI location decision that comprise the framework include: (i) the process, (ii) the context, (iii) patterns, and (iv) location. Research findings show the FDI location decision process as comprising of five broad stages, the content of each driven by a dynamic and evolving interpretation of maximum subjective expected utility. Utility preferences are identified as the consequence of shifting and opaque goals, founded upon imperfect information, operating in an environment marked by uncertainty. Five variations in the overall orientation of utility at case decisions, classified in the study as ‘decision rules,’ proved to be more useful predictors of decision-making behavior than traditional notions of bounded rationality seeking rent extraction and profitability. Decision processes were found to vary in five prototypical patterns, according to clusters of contextual variables that together moderated the level of decision-maker autonomy, hierarchical centralization, rule formalization, commitment to strategy, and politicization of the decision. Patterns are described as FDI location decision-making models, and proposed as an initial step towards the development of a taxonomy of FDI location decision-making processes. Because of the dynamic and staged nature of the process, findings showed that factors that were important at one stage of the decision were not as important at the next. As such, the task of identifying universal drivers of FDI location was deemed an unfeasible one. In place of universal drivers, the initiating force of the investment, the purpose of investment and information sources and networks are identified as the key context-specific determinants of location in FDI decisions. Bounded by uncertainty, chance, the dynamics of the process and decision-maker effects, each of these aspects of the decision served to limit the possible consideration set for investment, and formed the value basis and measures from which to select the most attractive location choice. Despite the contextual differences in these drivers, however, the study revealed a strong pattern that showed that the importance of specific location considerations differed in much the same way across case decisions. During the first stage of case decisions primarily strategic aspects of locations were considered; during the second, considerations relating to the system; operational concerns in the third; implementation concerns in the fourth; and added value factors in the final choice. How each of these concerns was interpreted to reach final location choice differed according to the drivers mentioned previously, although the patterns were the same. This study develops a contingency framework for examining the FDI location decision-making processes of MNEs under different operating conditions. By identifying the four key components of the FDI location decision, their interrelationships and many sources of variance, this thesis shows that despite its complexity, the FDI location decision is amenable to useful conceptual structuring. From an academic standpoint, the framework answers Aharoni’s most recent call to action in ‘Behavioral Elements in Foreign Direct Investment’ (2010) by developing a replicable structure within which to think about incorporating managerial decision models and context into the theory of the MNE. These findings enhance understandings of decision making at MNEs, reconcile a number of inconsistencies between opposing perspectives of MNE theory, and thereby update extant theory so that it has greater relevance in today’s diverse international business environment. From a managerial standpoint, the thesis helps managers to recognize the opportunities and limitations posed by different aspects of decision context so that they are able to tailor their FDI location decision strategies to best suit their needs. Finally, from the perspective of policy markers, research findings provide great support for the use of investment attraction schemes through the use of targeted location marketing and investment incentives.

Transcranial Direct Corrent stimulation (tDCS) of the anterior prefrontal cortex (aPFC) modulates reinforcement learning and decision-making under uncertainty: A doubleblind crossover study

Reinforcement learning refers to the ability to acquire information from the outcomes of prior choices (i.e. positive and negative) in order to make predictions on the effect of future decision and adapt the behaviour basing on past experiences. The anterior prefrontal cortex (aPFC) is considered to play a key role in the representation of event value, reinforcement learning and decision-making. However, a causal evidence of the involvement of this area in these processes has not been provided yet. The aim of the study was to test the role of the orbitofrontal cortex in feedback processing, reinforcement learning and decision-making under uncertainly. Eighteen healthy individuals underwent three sessions of tDCS over the prefrontal pole (anodal, cathodal, sham) during a probabilistic learning (PL) task. In the PL task, participants were invited to learn the covert probabilistic stimulusoutcome association from positive and negative feedbacks in order to choose the best option. Afterwards, a probabilistic selection (PS) task was delivered to assess decisions based on the stimulus-reward associations acquired in the PL task. During cathodal tDCS, accuracy in the PL task was reduced and participants were less prone to maintain their choice after positive feedback or to change it after a negative one (i.e., winstay and lose-shift behavior). In addition, anodal tDCS affected the subsequent PS task by reducing the ability to choose the best alternative during hard probabilistic decisions. In conclusion, the present study suggests a causal role of aPFC in feedback trial-by-trial behavioral adaptation and decision-making under uncertainty