[SOUND]. So, let's make a stop and come back to the Decision theories. So, I suggest now to use decision matrices. Decision matrices, are standard ways to represent simple decisions. So, here we can represent our choices for example, on the left, in case we'd like to take this umbrella today or not to take the umbrella today. Of course, the outcome of our decision depends very much on the states of nature. If we take an umbrella, and if it doesn't rain today. We will have dry clothes but very heavy suitcase. If we not take an umbrella and it rains, of course we have soaked clothes and very light suitcase. So, making this decision matters, we can try come up with a normative solution for the decision in this particular situation. So, for example we can assign numerical values to different outcomes. For example, we can like very much when we do not take an umbrella and it doesn't rain. And we do not like the situation when we don't take an umbrella and it rains. So, we can assign numerical numbers for their utility of possible outcomes, and we can come up with a normative solution for this particular decision. So, if we simply sum up outcomes for taking an umbrella and not taking an umbrella, we would see that perhaps expected value for taking an umbrella is higher than for not taking an umbrella. But the values or utilities of outcomes are not only aspects of our decision making, that affect our decisions. So for example, if I offer you for free, to select between two lottery tickets. In one lottery ticket you actually can win $28 million. In another lottery you can $75 million dollars. So, which lottery ticket you would pick for free? So perhaps, most of you will take the second lottery ticket, but if I will tell you the number of tickets issued in this lottery. So in this case, there is a chance to win lottery is one to 1,000,000. And for the second lottery, the chance to win this lottery is one to 1,000,000,000. So which lottery ticket you would take? If you will simply multiply values by probabilities, you can see that, actually, expected value. For the first lottery is, lottery is higher as for the second one. So, I have a very rational person who actually select the first lottery. So, this example illustrate that when we make a decision. We not just pay attention to the possible outcome in terms of, the expected value but those who integrate this well you're with the probability of this outcome, so this idea in economics called expected utility theory, so whenever we every way it's not an option we integrate value and the probability of the outcome. For example, if there is a very small probability of rain. Now in this case, I just integrated the probability into the decision matrix. If you will calculate the expected utility you will find then with the probability, there's a low probability of rain today. It makes sense actually then to not take an umbrella. If the probability of outcome is different, for example if there is a 50 chance of raining today, it will change the metrics. So, in this case, it makes sense, from normative perspective to take an umbrella. So, the idea is that during the decision making process we integrate probabilities of outcomes. And the values of outcome so its called expected utility theory. This is very influential normal to economic theory so just as we pay attention to the probabilities and the values of our outcomes. So, this is very influential theory but of course as we know from the number of behavioral economic studies this theories doesn't explain. Our behavior, our decisions perfectly well. There are very serious deviations from the predictions of this theory. But, this theory nicely captures that we integrate probabilities and values during the decisions we make. So how to investigate, the process of integration of probabilities and values in our brains. We can use paradigms suggested by Brian Kinutson word so here at the beginning of the trial, subject can see a cue and vertical line codes the magnitude of the expiatory word and horizontal line codes the probability of the expiatory word, so here. We can investigate how brain process expected probabilities, and expect the three words of how braids integrates both aspects through the decision making. So, subject has to press the button when the white square is presented from the screen. And in this case, to indicate the subject can actually get a very high reward was a very high probability. So as you see, at the end of this trial, the subject collected $5. So what Brian Knutson found, that nucleus accumbens really could expected values. So, activity of the eventual straight of the circumference is proportional correlates with the expected values. As you see on the right slide, activity of nucleus accumbens, perhaps not ideally correlated with expected value, but still correlates with expected value in certain way. So, it looks like nucleus accumbens codes expected values during the decision making process. We can actually investigate the same aspects of decision making using different paradise. For example, in this case participants play cards and then one case on the left, participant can guess where the red card is located so subject in the first case can open four cards and in this case can correctly predicted where the red card is located on the right side of this slide you can see another condition when subject can only open one card and guess where the red card is located. With this manipulation, we can actually manipulate the probability of outcome. In the first case, there was a high probability to get positive outcomes, then in the second place. We can also manipulate the amount of money subject expects to get during this game. So with this game, this paradigm, we can make a look what is going inside the nucleus accumbens. So here, you see that activity of nucleus accumbens is proportional to the expected magnitude of the reward. On the right side of the slide you see that nucleus accumbens particularly strongly activated when subject is expecting to get higher reward. At the bottom of this slide you'll see that also nucleus accumbens reacts to the probability of the outcome. So, activity of the nucleus accumbens is particularly strong when subject expect to get rewards with highest probability. So actually, the same region encodes probabilities and values. If we will make a look to this map of the activity of the nucleus accumbens, you see that different regions' coding probabilities and reward magnitudes are presented here by different colors and this regions are overlapped. Look. So, overall it looks like nucleus accumbens is involved into the calculation of utility. It processes expected rewards. So, it actually estimates the probability of the outcome. And it also estimates their amount of values related to the outcomes. So, we can make some intermediate conclusions about the functional role of the nucleus accumbens. So, first of all, as I suggested, from neuroeconomic perspective, our values are simply the firing grades of certain neural populations. So, it looks like nucleus accumbens code anticipated gains. Anticipated gains magnitude during the decision making. And also looks like, that certain neural populations of nucleus accumbens. The code expected magnitude of the reward. In some populations, code probability of getting the reward. So, it looks like, this is a key region for the calculation of the expected utility during the decision making process. [SOUND EFFECT]. [MUSIC]