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Why do children pass in the centipede game? Cognitive limitations v. risk calculations

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Behaviour in strategic games results from the combination of cognitive ability, inferences about others and preferences. The centipede game is an excellent example of a game where theoretical predictions yield low payoffs and are counterintuitive to most individuals. Isabelle Brocas discusses a game of strategy where payoffs monotonically decrease with age.

Image courtesy of interviewee. June 1, 2024

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The speaker discusses a line of research aimed at understanding decision-making in strategic contexts, particularly focusing on how adults often make irrational decisions and how strategic skills develop over time. Two key components of strategic decision-making are identified: logical reasoning, supported by cognitive abilities and the executive functions of the prefrontal cortex, and theory of mind, which is the ability to understand others' intentions and perspectives.

The speaker illustrates these concepts using decision-making games, such as a sequential game where players must decide whether to take immediate rewards or possibly larger future rewards, with the risk that their opponent may take the money first. The exploration of backward induction—a reasoning process where future outcomes influence current decisions—reveals how players tend to make counterintuitive choices that lead to suboptimal outcomes.

Additionally, experiments conducted with children aged 8 to 16 show how decision-making skills evolve. Younger children typically struggle with backward induction and often fail to anticipate others' actions, leading them to pursue lower payoffs. As they grow and develop their theory of mind, they learn to navigate these strategic decisions more effectively.

The research highlights the role of environmental factors and socioeconomic status in the development of these cognitive and social skills, suggesting that different backgrounds might influence how children perceive and engage with others in decision-making contexts. The findings emphasize the complex interaction of cognitive and emotional elements in strategic behavior across different age groups and populations.

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What I wanna do really with this line of research is

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to understand how people make decisions

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in strategic settings in particular.

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And we do know that adults make a lot of irrational

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decisions very often in very various settings.

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And one key question is how we develop our strategic skills.

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And from a general perspective,

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strategic decision making relies on two critical components.

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One is logic. So each time, for instance, we strategize,

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we need to use some logic in order to determine the course

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of action that is likely

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to maximize our goals and our rewards.

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So for instance, suppose that you're playing chess,

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you can replace any piece anywhere on the board.

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So you need to anticipate what may happen in the future,

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and find what is the best way

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to avoid some particular scenario you don't like,

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or to promote another scenario that you,

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you would like to get to.

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So geological ability for this kind of, game

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for instance, is gonna be backward induction.

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You have to work backward, you have to, you have

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to figure out what kind of goal you would like

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to reach in several moves.

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And then to reach that goal in several moves, there is,

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there is a trajectory that you should try.

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So you should try to figure out to anticipate

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where you should be, the move before

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and how you should be, where should be positioned

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the move before.

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And that way, by working down backwards, you can determine

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what is the best way right now to place a piece

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and which piece this should be

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and where this piece should be.

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So, this logical ability is very important

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and it relies on cognition.

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So cognitive abilities are supported by executive functions.

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And what we do know is that these

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functions are depend on brain regions located

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in the prefrontal cortex.

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And these develop relatively late.

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They match you up very late.

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So, but another key ability is

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what is called theory of mind.

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And theory of mind is this ability

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to put yourself in the shoes of another person in order

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to form beliefs about their intentions,

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what you think they're gonna be doing.

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So in the case of chess, for instance, you need

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to read the mind of your opponent

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to anticipate the future moves.

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And this might rely understanding how good this person is,

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or if it is an aggressive person.

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Uh, know a little bit this personality as well.

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So fear of mind is a kind of complex concept, that has

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some cognitive elements,

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but not only that, it has also some effective elements

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and it is somehow related to, some other parts

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of the brain that are called, normally the structural brain.

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And these parts

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of the brains have also their own

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developmental trajectories.

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So in strategic setting, we're gonna be using both things.

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We're gonna be using logic and three of mine,

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and these two are going to contribute.

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And what we're trying to do in the research as a whole is

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to look at variation in

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Behavior, in cognition

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and in effective processes in order to understand

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how this interaction develop in order

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to produce some particular kind of,

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behavior in children, teenagers, and adults.

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And why these behaviors are different.

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So this is a scientific game,

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and this is a game where there are two players

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and they take turn making a decision.

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Um, so one player, we're gonna call them Sam,

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and Larry is playing first.

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And when it starts playing,

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there is an amount of money, right?

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And Sam has to make a decision whether to take and to pass.

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So Sam can decide to take, if Sam takes,

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he's gonna get the full amount of the, of the, of the money

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that is available, and Larry would get zero.

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But if Sam passes, it's gonna be the turn of Larry to take.

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But what's happening in the meantime is

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that the amount of money grows.

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So here we have $4, let's say,

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and now the allocation changes.

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So when Larry makes the decision, Larry might have three,

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and in that case, Sam would get one, okay?

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So he can decide to take, but he can decide to pass.

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And then it is the, the, the, the, the turn right now of Sam

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to take and to pass.

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And the same occurs. The amount has grown again.

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Sam can have now four points or $4

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and Larry is gonna get two points

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and the game goes over.

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So each time somebody takes the game ends.

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So when Sam takes here, nothing happened.

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We don't go through this entire game.

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If Larry takes here, we stop here, right?

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But it might be that we want to continue until the end,

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in which case there will be a final point where this is the,

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the payoff that the people are going to have.

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So there is a final, time in this particular game.

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So what is very interesting in this game is that,

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we see that there is an immediate benefit

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for having particular amount of money, which is more than

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what the other person is gonna get if we take immediately,

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however, there is a possibility of getting more money

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if we get the chance to go back

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to another situation in the future where,

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we're gonna be given, again, the ability to choose

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and the money we can get in the future is bigger.

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However, there is a risk that the person

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who is playing in between might decide to take,

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in which case I'm gonna have a lower reward.

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So this is a game where you have some incentives to go

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on in the game because you can get more money if you do.

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But there is also a risk

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that today you might have more than if you wait one more

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period and the other person takes before you.

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Okay? So this is the interest of the,

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of the scientific game.

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So now what is logic telling us about this game?

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And this is what is really interesting.

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So as we said, this is a game that is going through time.

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It's, there are sequential moves. They taking turns.

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So because there is this aspect,

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we should work backwards in order to solve that game.

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So the way we solve that game is by looking at

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what Larry would do at the end.

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And Larry at the end would have a choice between taking

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and getting five or passing and getting four.

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So what Larry wants to do is to take,

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but now what's happening for Sam, if Sam would ever reach

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that particular stage where some would have

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to decide whether to pass and to take,

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but Sam should realize that Larry will not pass here.

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So these five is not an opportunity for them.

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What they know is that Larry is gonna take

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and is gonna get three at the last round.

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So now he has to choose between passing and get three

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or taking and get four.

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And he will prefer to take Now what's happening, Larry?

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Well, Larry should anticipate these things as well.

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And he would probably realize that

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himself Larry in two periods would decide to take,

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and he should then realize that he should prompt Sam

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to take the next time.

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In that case, Larry has a choice between the two.

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He would get if he passes right now,

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and the three can get right now, okay, by taking,

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Solari wants to take,

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and by unraveling what's happening is

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that at the first round, some want to take right away.

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What's happening in that game?

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Well, the lowest,

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outcome rewards are obtained, right?

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So this is a game where logic pushes you

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to have the lowest amount of money.

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And this is very counterintuitive for most people.

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So obviously we don't find that, when we run these kind

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of experiments with adults, we find normally that people try

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to progress a little bit in the game

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and try to determine

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what is the optimal risk they should take.

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They should try to progress in the game in a way that

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they stop right before the opponent,

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but now everybody's doing the same thing, right?

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So people are going to be,

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never going toward the end of the game.

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They're going to be maybe stopping around here, right?

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Something like this. I mean, normally we play that also

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with, with longer game than this one

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where it's more difficult, to,

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to do these backwards induction logic.

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So this is what we observe normally,

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and you see it is really about understanding

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what other people want to do.

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It is not about logic.

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I mean, of course you need a little bit of logic.

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You have to understand that you have

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to stop before the other person. So there is some element

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Of backward induction,

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but you really need

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to put yourself in the shoes of another person.

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So this ability is something that is due to fear of mind.

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When we work with children, we have

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to simplify things a lot.

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So we have to make sure that, children understand.

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And this is something that in, in traditional economics, we,

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we have very abstract setting normally to play with adults,

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but with children we have to borrow from, development

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of psychology where people have developed some methodology.

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So with children, you have to be careful

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that they don't understand abstractions as well as adults.

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So sometimes some paradigm cannot be really played as such.

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With, with children you have to simplify really a lot

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or you cannot just do some kind of experiments

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because you know, they will not understand.

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For this kind of experiment, it is relatively easy

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to under to to understand.

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So we've been running these experiments with

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children from eight to 16 years old,

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so about third grade to high school.

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And, we have simplified the setting

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by telling them a story.

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And the story we tell them is that there are two children

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and one is an orange kid and the other one is a blue kid.

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And so each person has a role, they can be either the blue

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or the orange kid,

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and they are going together down the street

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and they pass in front of houses.

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And the houses also have the same matching colors.

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So I can show you what we show them here.

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So this is what a kid would see, for instance,

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he would tell them they are, they have the role orange.

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And, so each time that the kid pass in front

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of the blue house, they have to decide whether they want to

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continue to go down the street or entering the street.

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And this is the blue child who makes that decision.

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If they makes that decision, the game is over,

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like in the standard TP if the blue child decide

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to not enter, then this is gonna be,

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they continue going down the street

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and they're going to pass an orange house.

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And the orange kid is gonna decide whether they want to

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continue going down the street

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or entering the house, in which case Debbie gonna grab

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some points, in that case

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and will tell you what I, what they would

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do with the points after.

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And you see this is exactly the same

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thing as I showed before.

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This is a game that ends

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after a certain number of periods each time the kid,

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make a decision to enter the house,

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the game ends each time a blue kid enters a blue house,

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he has a higher payoff than the opponent.

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And these payoff increase in such a way

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that you always have this advantage of taking,

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the amount of gift

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or points in that case in the house of your color.

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But if you would decide to go down the street,

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you have a possibility of getting more points down the road.

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But the risk also that the other kid decide to enter the,

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the, the house of his color before.

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Okay? So this is exactly the same thing,

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and we play that with, with children,

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starting in third grade.

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When we work with children, we have to be careful

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that there is no too much sciency effect, have number

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that is really too big, for instance.

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Um, and we have some time to simplify, some numbers

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to make sure that the comparisons are are easy.

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We have to tell a story in simple terms,

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we have to use colors.

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So these things are less important for adults, even though

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actually I think it is also when we run these experiments

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with adults, we find that normally they have more fun

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and and they understand better.

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So we have, we have less noisy data,

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we find different things here.

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And this is really interesting.

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Um, first of all, we do find,

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and this is expected, so actually I i, I don't

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remember if I said that, but there are,

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we play different versions of the scientific games.

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We play a long scientific game,

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which would be the similar that we would play with adults.

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And then we play a very short scientific game where the risk

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of passing is so big that anyone

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who understands backward induction would stop immediately.

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So this version of this small spend specific game, it

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for us a way

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of testing whether the participants understand backward

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induction because they should do backwards induction in

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that case and, and stop right away.

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And, what we're gonna do, we are going

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to control somehow for these logical element

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and we're gonna see what they do.

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And, in the centipede, game,

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the long centipede game,

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and this is for us a way of figuring out when they, the,

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the, the, the element of fear

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of mind enters into playing their behavior.

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So what we do find with little kids is

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that they do not master backward induction.

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So even in the very small Centipede game

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where there is huge risk of passing,

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and they should not, they try to go to the end

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of this short game,

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so they don't understand the logical argument.

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Uh, and in the long scientific game,

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we do exactly the same thing.

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So they go towards the end.

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What is interesting about it is

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that given everybody is doing this very rational play,

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they get high payoff.

14:06.005 --> 14:07.535
Obviously not everybody wins,

14:07.595 --> 14:10.015
but those who win, they get the highest possible payoff

14:10.015 --> 14:11.295
because they go very, very far.

14:12.315 --> 14:14.575
So this is what happens with the smallest kid,

14:14.575 --> 14:18.055
let's let's say third grade, starting fourth, fifth grade.

14:18.635 --> 14:22.415
Um, we start seeing some kids

14:22.995 --> 14:24.535
who do understand the logic,

14:25.035 --> 14:28.255
and in the small scientific game, they take right away,

14:28.325 --> 14:30.615
they know exactly that they have to do backward induction.

14:30.615 --> 14:31.775
They master that,

14:32.195 --> 14:35.775
but not everybody at that age range is mastering that skill.

14:36.635 --> 14:38.095
So what's happening

14:38.095 --> 14:40.575
however, is that these particular kids

14:40.955 --> 14:43.815
who master backward induction, they tend to

14:44.845 --> 14:46.575
over-rely these logical abilities.

14:46.755 --> 14:50.535
So even in the big, they're gonna start immediately.

14:51.075 --> 14:53.525
This is interesting because somehow they behave

14:53.525 --> 14:56.085
as if they think everybody understands the logic, right?

14:56.305 --> 14:58.845
And this is something we found also in adults, in other,

14:59.065 --> 15:02.285
in other setting, people who tend to understand how

15:02.285 --> 15:03.485
to apply logic, how

15:03.485 --> 15:06.765
to make a complicated reasoning in strategy settings.

15:06.995 --> 15:09.925
They also think that others can do the same reasoning

15:10.505 --> 15:12.965
and they fail to exploit the rationality of others.

15:13.875 --> 15:16.655
So we see in those games, some of the kids,

15:17.485 --> 15:20.015
they over exploit backward induction,

15:20.015 --> 15:22.055
they stop immediately in the center game,

15:22.355 --> 15:24.175
in which case they get low payoff

15:24.635 --> 15:26.095
and the other kids continue

15:26.095 --> 15:27.935
to go towards the end of the game.

15:28.155 --> 15:29.535
So there is, there is this phase

15:29.535 --> 15:32.295
where we see this heterogeneity in two kids,

15:32.475 --> 15:34.895
and we have these effects of these kids

15:34.895 --> 15:37.135
who develop the logic and overly the logic

15:37.365 --> 15:41.535
because they have not developed so far, the ability to

15:42.195 --> 15:45.345
understand that others are going to try to be tempted

15:45.345 --> 15:47.345
to go towards the end of the game, right?

15:47.485 --> 15:48.785
And they don't exploit this

15:48.815 --> 15:50.705
because they fail the theory of mind.

15:51.645 --> 15:54.465
So now, over time, and, and,

15:54.605 --> 15:57.105
and during teenage time, kids are going

15:57.105 --> 15:58.745
to develop this theory of mind argument.

15:58.765 --> 16:01.345
And what we're gonna see is that kids gradually

16:02.045 --> 16:04.145
choose stopping points that are earlier,

16:04.645 --> 16:07.145
but they never converge to the beginning.

16:07.485 --> 16:09.345
So they converge to what adults do.

16:09.645 --> 16:11.425
Little by little they understand

16:11.425 --> 16:13.625
that there is this incentives of going

16:15.145 --> 16:16.755
farther away in the game.

16:17.505 --> 16:18.995
That backward induction,

16:18.995 --> 16:21.235
however, tells them that they should stop immediately

16:21.235 --> 16:22.635
and they understand that logic.

16:23.535 --> 16:28.315
Um, but they know that the others might try

16:29.175 --> 16:32.155
to reap these benefits and,

16:32.155 --> 16:34.435
and try to, to to get to the middle of the game.

16:34.895 --> 16:38.315
So the point is to try to anticipate where others are going

16:38.315 --> 16:40.515
to stop in order to undercut them.

16:40.815 --> 16:43.795
And gradually they learn that during adolescence.

16:44.575 --> 16:46.395
So now something interesting as well is

16:46.395 --> 16:48.235
that we have played different time this game.

16:48.855 --> 16:53.115
And what we do see is that as they play the game,

16:53.855 --> 16:57.115
the kids start converging also with to these kind

16:57.115 --> 16:59.275
of intermediate stage stopping time.

16:59.975 --> 17:02.715
Um, so they learn through the game, how do they learn?

17:02.905 --> 17:06.515
It's difficult to know the little kids probably they

17:06.515 --> 17:08.315
understand that if they go too far, they lose.

17:08.335 --> 17:09.355
So they try something else

17:09.815 --> 17:12.395
and by trying an error, they realize

17:12.665 --> 17:13.915
that they should stop elsewhere.

17:14.535 --> 17:17.435
Um, all the kids maybe understand that,

17:17.995 --> 17:21.395
actually I overestimate what were doing,

17:21.595 --> 17:22.795
I overestimate the risk.

17:22.935 --> 17:25.395
Or, and they, and they refine their, their,

17:25.605 --> 17:26.995
their, their strategy.

17:27.615 --> 17:29.395
The, the, the, we don't know that we don't know

17:29.395 --> 17:31.635
because we cannot test the reason for this learning.

17:31.695 --> 17:34.115
But we do see that this learning takes place in the game.

17:34.775 --> 17:39.035
The literature on decision making in children,

17:39.215 --> 17:41.595
in the context of individual decision making

17:41.775 --> 17:43.675
or in the context of strategic games,

17:44.535 --> 17:46.715
is increasingly interested in

17:46.935 --> 17:49.450
how the different underlying abilities, like theory

17:49.450 --> 17:51.620
of my cognitive abilities, effective skills,

17:51.620 --> 17:53.605
emotional development,

17:53.985 --> 17:55.485
how they interact with decision making.

17:56.225 --> 17:58.565
And, the scientific game is really interesting

17:58.565 --> 18:01.925
because it's one of these rare games where theory

18:01.925 --> 18:04.405
of mind is really the driver of behavior.

18:05.185 --> 18:09.565
Um, and by observing the developmental trajectory

18:09.665 --> 18:11.205
of behavior in the scientific game,

18:11.265 --> 18:15.645
you can really understand how, this theory

18:15.645 --> 18:18.365
of mind element develop in children and when it develops

18:18.465 --> 18:22.085
and how gradual it's, for future research.

18:23.005 --> 18:26.445
I am particularly interested in, heterogeneity

18:26.665 --> 18:29.125
and through many of these studies, including this one,

18:29.145 --> 18:31.045
but others as well, what we have seen

18:31.045 --> 18:34.085
that some young children can apply very complex logic.

18:35.065 --> 18:36.405
Um, but also we see

18:36.405 --> 18:38.445
that some adults are not able to strategize at all.

18:38.785 --> 18:39.965
And this is really interesting.

18:40.225 --> 18:42.565
But there are other variants, all sources of,

18:42.835 --> 18:44.045
heterogeneity as well.

18:44.225 --> 18:47.405
So we have seen some studies where if we compare

18:47.925 --> 18:49.365
strategy behavior in different schools

18:49.675 --> 18:52.885
that have different socioeconomic factors, backgrounds,

18:53.385 --> 18:56.725
or, children who have different curriculum, it seems

18:56.725 --> 19:01.345
to have strong effect on both the development

19:01.345 --> 19:04.505
of cognition and development of strategic decision making.

19:05.255 --> 19:07.825
However, we know very little about differences.

19:08.095 --> 19:10.305
Heterogeneity in the context of theory of mind

19:10.885 --> 19:14.065
and theory of mind is, is kind of different from cognition

19:14.065 --> 19:17.015
because it's a social skill.

19:17.515 --> 19:20.815
So naturally it seems to be the case intuitively

19:20.815 --> 19:23.775
that environmental factors might have a lot to do

19:23.805 --> 19:27.735
with developing these, kind of emotional intelligence,

19:27.735 --> 19:28.855
these affective components

19:29.165 --> 19:31.135
that might be very different for cognition.

19:31.135 --> 19:34.375
We do know that high SES kids do better normally

19:34.485 --> 19:35.615
than low SES kids.

19:36.235 --> 19:39.415
Um, but for social skills it might be completely different.

19:39.995 --> 19:44.335
Um, maybe some low SES kids rely on

19:45.165 --> 19:49.975
some social, networks that make them more able

19:50.035 --> 19:51.335
to read intentions of others

19:51.435 --> 19:53.935
and to have more, more, more fear of mind than other kids.

19:53.935 --> 19:56.575
So we don't know about this, so I believe that looking at

19:57.455 --> 19:59.775
a heterogeneity in that context will be very interesting

19:59.775 --> 20:01.175
to understand a little bit better

20:01.675 --> 20:03.815
how people make decisions in different contexts

20:03.915 --> 20:06.295
and in different, different population as well.

"Understanding Strategic Decision-Making: The Roles of Logic and Theory of Mind in Human Behavior"

00:00:00 - What I wanna do really with this line of research is to understand how people make decisions in strategic settings in particular. And we do know that adults make a lot of irrational decisions very often in very various settings. And one key question is how we develop our strategic skills. And from a general perspective, strategic decision making relies on two critical components. One is logic. So each time, for instance, we strategize, we need to use some logic in order to determine the course of action that is likely to maximize our goals and our rewards. So for instance, suppose that you're playing chess,
00:00:44 - So you need to anticipate what may happen in the future, and find what is the best way to avoid some particular scenario you don't like, or to promote another scenario that you, you would like to get to. So geological ability for this kind of, game for instance, is gonna be backward induction. You have to work backward, you have to, you have to figure out what kind of goal you would like to reach in several moves. And then to reach that goal in several moves, there is, there is a trajectory that you should try. So you should try to figure out to anticipate where you should be, the move before and how you should be, where should be positioned
00:01:24 - And that way, by working down backwards, you can determine what is the best way right now to place a piece and which piece this should be and where this piece should be. So, this logical ability is very important and it relies on cognition. So cognitive abilities are supported by executive functions. And what we do know is that these functions are depend on brain regions located in the prefrontal cortex. And these develop relatively late. They match you up very late. So, but another key ability is what is called theory of mind. And theory of mind is this ability to put yourself in the shoes of another person in order
00:02:05 - what you think they're gonna be doing. So in the case of chess, for instance, you need to read the mind of your opponent to anticipate the future moves. And this might rely understanding how good this person is, or if it is an aggressive person. know a little bit this personality as well. So fear of mind is a kind of complex concept, that has some cognitive elements, but not only that, it has also some effective elements and it is somehow related to, some other parts of the brain that are called, normally the structural brain. And these parts of the brains have also their own developmental trajectories.
00:02:47 - We're gonna be using logic and three of mine, and these two are going to contribute. And what we're trying to do in the research as a whole is to look at variation in Behavior, in cognition and in effective processes in order to understand how this interaction develop in order to produce some particular kind of, behavior in children, teenagers, and adults. And why these behaviors are different. So this is a scientific game, and this is a game where there are two players and they take turn making a decision. so one player, we're gonna call them Sam,
00:03:27 - And when it starts playing, there is an amount of money, right? And Sam has to make a decision whether to take and to pass. So Sam can decide to take, if Sam takes, he's gonna get the full amount of the, of the, of the money that is available, and Larry would get zero. But if Sam passes, it's gonna be the turn of Larry to take. But what's happening in the meantime is that the amount of money grows. So here we have $4, let's say, and now the allocation changes.

"Strategic Decision-Making: A Case Study on Payoffs and Logical Anticipation in Competitive Games"

00:04:09 - and in that case, Sam would get one, okay? So he can decide to take, but he can decide to pass. And then it is the, the, the, the, the turn right now of Sam to take and to pass. And the same occurs. The amount has grown again. Sam can have now four points or $4 and Larry is gonna get two points and the game goes over. So each time somebody takes the game ends. So when Sam takes here, nothing happened. We don't go through this entire game. If Larry takes here, we stop here, right?
00:04:50 - in which case there will be a final point where this is the, the payoff that the people are going to have. So there is a final, time in this particular game. So what is very interesting in this game is that, we see that there is an immediate benefit for having particular amount of money, which is more than what the other person is gonna get if we take immediately, however, there is a possibility of getting more money if we get the chance to go back to another situation in the future where, we're gonna be given, again, the ability to choose and the money we can get in the future is bigger.
00:05:33 - who is playing in between might decide to take, in which case I'm gonna have a lower reward. So this is a game where you have some incentives to go on in the game because you can get more money if you do. But there is also a risk that today you might have more than if you wait one more period and the other person takes before you. Okay? So this is the interest of the, of the scientific game. So now what is logic telling us about this game? And this is what is really interesting. So as we said, this is a game that is going through time.
00:06:14 - So because there is this aspect, we should work backwards in order to solve that game. So the way we solve that game is by looking at what Larry would do at the end. And Larry at the end would have a choice between taking and getting five or passing and getting four. So what Larry wants to do is to take, but now what's happening for Sam, if Sam would ever reach that particular stage where some would have to decide whether to pass and to take, but Sam should realize that Larry will not pass here. So these five is not an opportunity for them. What they know is that Larry is gonna take
00:06:55 - So now he has to choose between passing and get three or taking and get four. And he will prefer to take Now what's happening, Larry? Well, Larry should anticipate these things as well. And he would probably realize that himself Larry in two periods would decide to take, and he should then realize that he should prompt Sam to take the next time. In that case, Larry has a choice between the two. He would get if he passes right now, and the three can get right now, okay, by taking, Solari wants to take, and by unraveling what's happening is
00:07:40 - What's happening in that game? Well, the lowest, outcome rewards are obtained, right? So this is a game where logic pushes you to have the lowest amount of money. And this is very counterintuitive for most people. So obviously we don't find that, when we run these kind of experiments with adults, we find normally that people try to progress a little bit in the game and try to determine what is the optimal risk they should take. They should try to progress in the game in a way that they stop right before the opponent,

"Understanding Strategic Decision-Making: Simplifying Complex Concepts for Children's Cognition"

00:08:20 - So people are going to be, never going toward the end of the game. They're going to be maybe stopping around here, right? Something like this. I mean, normally we play that also with, with longer game than this one where it's more difficult, to, to do these backwards induction logic. So this is what we observe normally, and you see it is really about understanding what other people want to do. It is not about logic. I mean, of course you need a little bit of logic. You have to understand that you have to stop before the other person. So there is some element Of backward induction, but you really need
00:08:59 - So this ability is something that is due to fear of mind. When we work with children, we have to simplify things a lot. So we have to make sure that, children understand. And this is something that in, in traditional economics, we, we have very abstract setting normally to play with adults, but with children we have to borrow from, development of psychology where people have developed some methodology. So with children, you have to be careful that they don't understand abstractions as well as adults. So sometimes some paradigm cannot be really played as such. With, with children you have to simplify really a lot or you cannot just do some kind of experiments
00:09:41 - For this kind of experiment, it is relatively easy to under to to understand. So we've been running these experiments with children from eight to 16 years old, so about third grade to high school. And, we have simplified the setting by telling them a story. And the story we tell them is that there are two children and one is an orange kid and the other one is a blue kid. And so each person has a role, they can be either the blue or the orange kid, and they are going together down the street and they pass in front of houses. And the houses also have the same matching colors.
00:10:24 - So this is what a kid would see, for instance, he would tell them they are, they have the role orange. And, so each time that the kid pass in front of the blue house, they have to decide whether they want to continue to go down the street or entering the street. And this is the blue child who makes that decision. If they makes that decision, the game is over, like in the standard TP if the blue child decide to not enter, then this is gonna be, they continue going down the street and they're going to pass an orange house. And the orange kid is gonna decide whether they want to
00:11:02 - or entering the house, in which case Debbie gonna grab some points, in that case and will tell you what I, what they would do with the points after. And you see this is exactly the same thing as I showed before. This is a game that ends after a certain number of periods each time the kid, make a decision to enter the house, the game ends each time a blue kid enters a blue house, he has a higher payoff than the opponent. And these payoff increase in such a way that you always have this advantage of taking, the amount of gift or points in that case in the house of your color.
00:11:46 - you have a possibility of getting more points down the road. But the risk also that the other kid decide to enter the, the, the house of his color before. Okay? So this is exactly the same thing, and we play that with, with children, starting in third grade. When we work with children, we have to be careful that there is no too much sciency effect, have number that is really too big, for instance. and we have some time to simplify, some numbers to make sure that the comparisons are are easy. We have to tell a story in simple terms, we have to use colors.

"Understanding Strategic Decision-Making: The Role of Backward Induction and Theory of Mind in Game Behavior"

00:12:28 - actually I think it is also when we run these experiments with adults, we find that normally they have more fun and and they understand better. So we have, we have less noisy data, we find different things here. And this is really interesting. first of all, we do find, and this is expected, so actually I i, I don't remember if I said that, but there are, we play different versions of the scientific games. We play a long scientific game, which would be the similar that we would play with adults. And then we play a very short scientific game where the risk of passing is so big that anyone who understands backward induction would stop immediately.
00:13:09 - for us a way of testing whether the participants understand backward induction because they should do backwards induction in that case and, and stop right away. And, what we're gonna do, we are going to control somehow for these logical element and we're gonna see what they do. And, in the centipede, game, the long centipede game, and this is for us a way of figuring out when they, the, the, the, the element of fear of mind enters into playing their behavior. So what we do find with little kids is that they do not master backward induction. So even in the very small Centipede game where there is huge risk of passing,
00:13:49 - of this short game, so they don't understand the logical argument. and in the long scientific game, we do exactly the same thing. So they go towards the end. What is interesting about it is that given everybody is doing this very rational play, they get high payoff. Obviously not everybody wins, but those who win, they get the highest possible payoff because they go very, very far. So this is what happens with the smallest kid, let's let's say third grade, starting fourth, fifth grade. we start seeing some kids who do understand the logic, and in the small scientific game, they take right away,
00:14:30 - They master that, but not everybody at that age range is mastering that skill. So what's happening however, is that these particular kids who master backward induction, they tend to over-rely these logical abilities. So even in the big, they're gonna start immediately. This is interesting because somehow they behave as if they think everybody understands the logic, right? And this is something we found also in adults, in other, in other setting, people who tend to understand how to apply logic, how to make a complicated reasoning in strategy settings. They also think that others can do the same reasoning
00:15:13 - So we see in those games, some of the kids, they over exploit backward induction, they stop immediately in the center game, in which case they get low payoff and the other kids continue to go towards the end of the game. So there is, there is this phase where we see this heterogeneity in two kids, and we have these effects of these kids who develop the logic and overly the logic because they have not developed so far, the ability to understand that others are going to try to be tempted to go towards the end of the game, right? And they don't exploit this because they fail the theory of mind.
00:15:54 - and during teenage time, kids are going to develop this theory of mind argument. And what we're gonna see is that kids gradually choose stopping points that are earlier, but they never converge to the beginning. So they converge to what adults do. Little by little they understand that there is this incentives of going farther away in the game. That backward induction, however, tells them that they should stop immediately and they understand that logic. but they know that the others might try to reap these benefits and,

"Understanding Decision-Making and Theory of Mind Development in Children: Insights from Strategic Games"

00:16:34 - So the point is to try to anticipate where others are going to stop in order to undercut them. And gradually they learn that during adolescence. So now something interesting as well is that we have played different time this game. And what we do see is that as they play the game, the kids start converging also with to these kind of intermediate stage stopping time. so they learn through the game, how do they learn? It's difficult to know the little kids probably they understand that if they go too far, they lose. So they try something else and by trying an error, they realize
00:17:14 - all the kids maybe understand that, actually I overestimate what were doing, I overestimate the risk. Or, and they, and they refine their, their, their, their strategy. The, the, the, we don't know that we don't know because we cannot test the reason for this learning. But we do see that this learning takes place in the game. The literature on decision making in children, in the context of individual decision making or in the context of strategic games, is increasingly interested in how the different underlying abilities, like theory of my cognitive abilities, effective skills, emotional development,
00:17:56 - And, the scientific game is really interesting because it's one of these rare games where theory of mind is really the driver of behavior. and by observing the developmental trajectory of behavior in the scientific game, you can really understand how, this theory of mind element develop in children and when it develops and how gradual it's, for future research. I am particularly interested in, heterogeneity and through many of these studies, including this one, but others as well, what we have seen that some young children can apply very complex logic.
00:18:36 - that some adults are not able to strategize at all. And this is really interesting. But there are other variants, all sources of, heterogeneity as well. So we have seen some studies where if we compare strategy behavior in different schools that have different socioeconomic factors, backgrounds, or, children who have different curriculum, it seems to have strong effect on both the development of cognition and development of strategic decision making. However, we know very little about differences. Heterogeneity in the context of theory of mind and theory of mind is, is kind of different from cognition because it's a social skill.
00:19:20 - that environmental factors might have a lot to do with developing these, kind of emotional intelligence, these affective components that might be very different for cognition. We do know that high SES kids do better normally than low SES kids. but for social skills it might be completely different. maybe some low SES kids rely on some social, networks that make them more able to read intentions of others and to have more, more, more fear of mind than other kids. So we don't know about this, so I believe that looking at a heterogeneity in that context will be very interesting
00:20:03 - how people make decisions in different contexts and in different, different population as well.

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