[MUSIC] So, during the course, we discuss the functional role of various brain regions. So, we know now that the ventral striatum plays an important role in the processing of anticipated values. Also, the orbitofrontal cortex integrate values into our decision values and also plays an important role in the learning. Insular cortex meets an emotional arousal signal that is taken into account during the decision making process. Amygdala plays a vital role in the calculation of the anticipated cost of our decisions. So dorsolateral prefrontal cortex is a key region for the self-control during the decision making. But today, we will discuss the role of these regions in decisions and the risk. So already, the expected utility theory suggested that we take to account the uncertainty of the outcomes during the decision making process. We are never certain about the outcomes of our decisions. So really, the expected utility theory suggests that expected utilities are a product of the probability of the outcome and the utility of the outcome. So, it acknowledges that we are never certain about the outcomes of our decisions. As Benjamin Franklin nicely stated, in this world, nothing can be said to be certain, except death and taxes. So, we're never certain about the outcomes of our decisions. Let's come back for a moment to the very beginning of our course. I hope that you remember the activity of LIP neurons. The decision making neurons that are critical for the perceptual decisions. In this case the monkey is making the decision, a perceptual decision. This monkey has to switch gates left or right, depending on the visual material presented on the screen. So as you remember that activity of the LIP neurons is rising slowly til a certain decision's threshold. We see how this neuron's accumulating information over time and the activity of these neurons increases faster if the decision is easier and more slower if the decision is more difficult. But in all cases, the activity of these neurons reach a certain decision threshold when the decision is finalized and monkey switches his gaze in a certain direction. Two prominent neuroeconomists, Platt and Glimcher, first investigate the activity of LIP neurons. So they conducted another study that simplifies part of that. This program, monkeys had to switch gates left or right depending on the color of the visual cue. So when cue changed color animals had to switch gates, left or right. And their correct decisions were rewarded by an amount of juice. In condition one, you're economist manipulated the amount of juice cessated with certain decisions. So, some decisions were cessated with large gains, with a larger amount of juice. Other decisions were associated with the smaller gain, with the smaller quantity of juice. So on the left side of the graph you see the histogram of the activity of this LIP neurons during the decisions making process. So, these results clearly show that activity of the LIP neurons during the decision making process, when monkey anticipates a large gain, he's dramatically modulated by his expectation. So activity of the LIP neurons is stronger, and as you see here in this graph indicated by the black line, during the expectation of the larger viewpoint as compared to the expectation of the smaller viewer. In the second condition, neuroeconomists manipulate the probabilities of the outcomes associated with their correct decisions. So some decisions were associated with a high probability of the reward. Others were associated with a small probability of reward. You see on the right side of this graph the activity of the LIP neurons was also stronger when monkeys expected the rewards with a higher probability. So, already in the decision making process, a very fundamental decision making process, the neuron level is modulated both by expected gains and probabilities of outcomes. So, our decision making metrics do take into account the variation of the outcomes during the decision making process. But the simple concept of the probability doesn't capture other aspects of the outcome variation. For example, it doesn't really nicely capture the idea of risk. So, we do make decisions on the risk and the outcome uncertainty, dramatically affects our decisions. So, we do make decisions on the risk. For example, when we're playing roulette. Or we make our decisions under very strong uncertainty, when we invest money into the stock market. We are never certain in real life about our outcomes, and this uncertainty dramatically affects our decisions. So, we can define risk in various ways. For example, we can use a general common sense definition of risk. So risk increases with the perceived chance that the bad outcome will occur. According to this definition, animals also experience risk and for them risk increases with the perceived chance of death, either through predation or starvation. But for economists, and also for decision theorists, the concept of risk is closely related to the concept of uncertainty. So as illustrated by this graph, the risk is highest around the probability 0.5. And it makes, because the risk is really small at 0 around the probability 0 of probability 1. Because we are almost certain about the outcome of our decisions. Risk here, is an inversely quadratic function of probability, that is minimal at p equal to 0, or 1. And maximal at p equal to 0.5. So risk is a form of uncertainty or variance of outcome. But now let's come back to the studies of the dopamine neurons during the processing of rewards. I hope that you remember this experiment when the activity of dopamine neurons was recorded during the conditioning procedure. So here, on this graph, the activity of the dopamine urine is represented during the conditioning procedure. You remember that at the beginning of the conditioning procedure, neurons primarily reacted to the presentation of the reward. But during the conditioning procedure activity of these neurons jumped, shift to the presentation of the cue indicating the reward. So at the end there was a conditioning procedure dopamine neurons primarily react to the cue that predicts the reward. So, it gives us an idea that neurons, dopamine neurons are encoding the expectation of the reward as if, you remember, the activity of the dopamine neurons is proportional to the anticipated gain. So, here on this slide, you see a histogram of the activity of the dopamine neuron. So you see a peak of activity after the presentation of the condition stimulus indicating the presentation of the reward later on. So, we nicely know this fact, this transient activity of the dopamine neurons, to the cue predict angry words. But also, what we can notice with this graph, there is a sustained slow activity later on, somewhere between the conditioned stimulus and the reward. We see a slow increase of activity of the dopanuerologic neuron til the presentation of the reward. If we will make a closer look to this sustained slowed activity. We will find that this activity encodes risk. So, in an interesting new economic study, the probability of the outcome was manipulated. So, here, you see activity of the dopamine neurons, in different conditions. When the q predicted reward was 0, 0.25, 0.5, 0.75, and was a probability of 1. So we see here is this first, the dopamine neurons react to the presentation of the cue, of the condition stimulus predicting the reward. And this reaction, this transient, very fast reaction is proportional to the expected value, but later, as indicated by the red arrow, we see in the sustained slow activity produced by dopamine neurons, and this activity peaks as a probability of 0.5. So this activity, slow, sustained activity dopaminergic neurons between the transient response to the cue, and the reward encodes risk. To sum up, the sustained risk-related response occurs between the stimulus, between the conditions stimulus and the reward. And it occurs after this phasic, fast response to the conditioned stimulus. And this activity is sustained very slow, and this activity encodes the risk associated with this cue. We can also study neuron correlates of risk in human brain. So, we can apply neuron imaging techniques and, quite simply, your economics paradigms. For example, here's this gate. Subject has to guess which of two cards is higher than the other one. So, at the beginning of the trial subject has to place a $1 bet on one of the options, second card higher or second card lower than the first card. So, next subject is exposed to the first card, and after a few seconds subject sees a second card. So, if subject guessed correctly, subject collects $1. This is a very simple paradigm, but it's already clear that the first card immediately codes the risk associated with the decision of the subject. Of course, in this case for example, subject decided the second card will be lower than the first one. If the first card will be nine, it indicates a very high chance of the second card will indeed be, be lower than this card. Of course cards used in this study are between one and ten. So, the first card nicely signals the risk associated with the subjects decision. And the risk is highest around the probability of outcome of 0.5. So basically risk will be highest if the first card will be five. So we can discuss the brain activity associated with different levels of the risk in this study. Neureconomists separately analyzed early and delayed neuro activity in the ventral striatum, and here you see the results for the early activity in the ventral striatum. You see that the activity is proportional to the expected value. In this case it is proportional both to the expected value and to the probability of the outcome, because the outcome was fixed $1. You see here on the graph where blue dots indicate the activity of the ventral striatum, the activity is proportional to the expected value. If we will analyze the delayed activity in the ventral striatum we will see that this activity peaks around the probability 0.5. So, delayed activity indeed, encodes the risk of variance, of the outcomes. So, it supports the idea, that dopaminergic neurons both encodes their expected value and the risk associated with the decision. So a really fast, transient response of the dopaminergic neurons encodes the expected values and later sustained slow activity encodes the risk associated with the decisions. So, expected reward is immediately encoded in the ventral striatum. Risk also is coded in the reward-sensitive dopamine neurons, but this signal is delayed. So, overall, dopamine neurons show a slow, sustained reaction to the risk. So, letâs now introduce a formal definition of risk. So economists and decision theorists, they divide uncertainty into two distinct concepts. Risk is the situation when probability of the outcome's unknown and ambiguity is the situation when we do not know precisely the probabilities of our outcomes. So, the situation when you play roulette will be a decision on the risk. Our situation when you invest money into the stock market will be a decision on ambiguity. So in the first case you fully know the probabilities of the outcomes. In the second case, in the stock market, you didn't know the probabilities of the outcomes. So, to make the story even more complicated, [COUGH] we can say that uncertainty can be divided into ambiguity and risk, so depending whether the probabilities are known or unknown. But risk can be determined by various aspects of the outcome variability. For example, risk can be modulated by the variance of the outcomes. Also, risk can be modulated by the symmetry of outcomes. By the skewness of outcomes. Or by the peakness of outcomes, by kurtosis. So different aspects of the outcome of the ambiguity can modulate risk. But most of the studies talk with some of the variants as a determinant of the risk. And finally we have to say that concepts of ambiguity and risk are closely related. So all animal's for example, they do not have enough medical skills to calculate the probabilities of outcomes. Animals, and also humans, have to learn the probabilities of outcomes through repeated sampling gradually turning ambiguity into risk. [MUSIC] [BLANK_AUDIO]