Skip to main content
Loading Explore guides…
Game Theory · Acedra
Home
Explore
Economics
Game Theory
Sign in to save
Chat
If YouTube asks you to sign in, open the video on YouTube.
Watch on YouTube
Reload player
Transcript
217 segments
Copy
Hide video
0:04
We're looking at the fact that people make decisions, but when we make decisions, we're often affected by what other people do or what we do affects what they do, so we have social interactions all the time. If I choose to finish the cornflakes in the morning, that's going to affect the rest of my family. If they choose to finish it, then that affects me. Every single thing that we're doing in life normally involves social interactions,
0:29
so we're focusing on social interactions. In the live session we're not going to go through all the detail of how to solve the games, although we will talk about how we do that while we're looking through the examples, but hopefully from working through the book and also the assignment, and when you get to the quiz if you haven't started it yet, you'll get some ideas on how to solve these games. It's really important that you get
0:56
your heads around this game theory tool, it is one of the main tools of economics.
1:02
As somebody mentioned in the chat, the thing that we associate most with John Nash, but also with lots of Nobel prize winners is game theory, which is actually a mathematical invention that economists then adopted (or many mathematicians became economists off the back of it)
1:22
but we're really trying in Week 4 to take you away from the maths and to get you to think intuitively about how things work, how decision-making works. I really need to think about, you know, if I was in the shoes of the row player or the column player, what would I do? That's why we're doing this through classroom experiments today, to get you to start thinking about all the hypothetical situations that people think about, and that's how we solve the games. It's a bit like
1:50
with the decision making, where we said we're always thinking about what if this happened? How would I respond? That's exactly what we do in game theory, we think about: if I choose action A
2:04
given that the other player is using action A, what's my outcome? If the other player chooses action B, do I still choose action A? And we look through all the different scenarios essentially, and then use that to think about what is the desirable outcome from my perspective, so what's my best response strategy. I think about what the other player will do, so we tend to assume that we have information about what the other player knows
2:29
and then we think about what's the outcome going to be of the game. So we're really here today, particularly in the live session, trying to get you to think about how to use your economics, your knowledge of decision-making, your knowledge of social interaction.
2:49
So let me move to the next slide, so we're going to be running three games and in each of them I'm going to explain to you what we'll be doing, then we're going to look at what happens. Before I show you the results of the games I'm going to ask you what kind of game you thought it was, what you expected to happen, so this is where you're going after your Unit 4, thinking about how it all works.
3:15
Then we're going to look at the results and think about whether you behaved the way that we expected you to behave as a group and why maybe we got outcomes different to what we expected, and hopefully we'll be able to finish with some good lessons learned about how games work in theory, how experiments work, and how first-year undergrads at UCL and economics behave.
3:39
So you will have a few minutes to log in while I talk you through the first game but once we start a game you won't be able to join it late so do try now while I'm talking you through the first game to make sure that everything's working okay. So this is the first game that we're looking at and I'm going to tell you that I was inspired last week. So this game is around
4:09
collusion, so imagine that you're in a situation where you and a friend have been accused of copying on an assessed essay which is defined as collusion under UCL's academic misconduct policy, and what would happen if this happened, if we had a suspicion that two students were copying? You'd be interviewed separately by the academic misconduct panel, so the department would hold a panel and they would take you in separately and the rules of the game are going to be as follows.
4:41
If you are the row player, or well either player, if you confess and the other player confesses you're going to get a reduction of 10 marks on your assessed essay, so these numbers in here think of them as 'bads', so the lower the number the better off you are. So if you both confess, you'll both get 10 mark reduction on your assessed essay mark. If one of you confesses and the other person denies the person who confesses is going to get no reduction on
5:12
their academic mark (they're going to be given a reward for confessing)
5:18
however if you're the player who denied you're going to get a 15 mark reduction, so you're going to be penalized by more for not confessing up when the other player did,
5:30
and that will happen either direction. If you both deny that you colluded then you're only going to lose five marks of your academic mark for the essay. So hopefully you understand the game.
5:48
You'll get the instructions again when we go into ClassEx, this is what it will look like in your screen. So when I start the game, you won't see anything until I hit start on the game, you will get a little man and you get to choose whether you confess or you deny and then after everyone has played the game, you'll get your payoffs. Now is the time to say you are not allowed to communicate in the chat. You will be in pairs, obviously you don't know amongst all of you
6:20
who's going to be in the chat anyway and so this is all hidden. Here I'm going to give you about 10 seconds to play, I can see when everybody's played and once we've finished playing I will tell you when to come back into Moodle, so keep the window open that you're in now,
6:41
with Moodle open and me on LectureCast, keep that open, but now you can move into ClassEx
6:52
and wait and see what's happening. Okay so I'm going to start the first, game I just logged in as a user so I can make sure I can see everything that you see.
7:15
Okay so I'm gonna hit start, so remember you're randomly in pairs, you can choose to confess or deny. If you confess and the other player confesses you get 10 mark reduction on your essay, if you confess and the other player denies you get no mark reduction and the other player gets a 15 mark reduction, and if you both deny you get a 5 mark reduction.
7:46
So hopefully your screen will be updating at this point.
7:51
Okay I've got 148, oh, okay more people logging in, everyone make sure you're in,
8:01
so we've got 606 people playing which I think is probably one of the biggest experiments that I've been running in economics, which is quite exciting.
8:32
Okay, we know there are about 40 of you left to make your choices.
9:00
Okay I'm going to count to 5 and then we're going to display the results but I'm not going to show them to you yet, but you will be able to see your own payoff. Okay so 5, 4, 3, 2, 1,
9:17
right if you haven't done yet I'm afraid that's it, so what I need you to do now is to switch back into middle so you can see your own payoff but I'm not going to show you the overall payoffs yet.
9:35
We have a poll question so back into the lecture cast tab please and answer the poll question.
9:44
Well done, okay, so the vast majority of you recognize that this was a prisoner's dilemma game. Remember an invisible hand game is a game that players play where making their choices independently thinking about their best responses. It still gets them to the outcome that's best for both players, so we get to what we think of as a social optimum even without the players interacting with each other or coordinating, so just making their
10:11
own separate decisions, and this of course is Adam Smith's idea of leaving the markets to it, so leading firms to make their own decisions - consumers to make their own decision, he believed that you would still get to optimal market outcomes or welfare-maximizing outcomes.
10:27
So in this game that wasn't what we were playing, we were playing the prisoner's dilemma game
10:33
which is like the Thelma and Louise example in Unit 4, which brings me nicely to the next question, which is based on what you learned about the prisoner's dilemma game in Unit 4: which of
10:51
the allocations or outcomes would you expect to happen in this game as a Nash equilibrium?
10:59
Okay, again most of you have understood the prisoner's dilemma came really well that you can see that we're going to end up with a social dilemma, so let me just switch to the visualizer very quickly because obviously some of you did not fully appreciate that. So I've got some
11:16
shadow coming in through the window, I'll just pull the curtain across. Okay, so
11:25
here's the game, so we've got our row player and our column player, so let's think about the row player. The way that we solve these games is: I'm the row player and I'm thinking about "Should I confess?". What I do is I think about what happens depending on what the other players do,
11:46
so if the column player confesses, I'll get 10, if I confess I'll get 15, if I deny (and remember this is a negative thing) it's 5 marks reduction on my assessment, so if i think the other player is going to confess then I'd rather confess and then I look and say "Well what if the other player denies? Well I can get 0 if I confess and I get 5 if they deny, so again in this context 0 is better than 5". This is obviously... The prisoner's dilemma it's a number of years in jail,
12:18
or marks reduced from your assessment so you can see whatever the column player does
12:25
my dominant strategy is always to confess so no matter what they're going to do I always want to confess, so I'm always going to confess. If you do the same thing for the column player, you'll find exactly the same thing, that their dominant strategy is to confess, so what we have is our best response equilibrium or Nash equilibrium, where the two players are confessing
12:49
and what you're noticing is that we have what we call a social dilemma because both players would be better off if they both denied but their best response, just thinking about themselves and their response to the potential actions of the other player, takes them to (confess, confess).
13:09
But in reality they would be better off if they both denied, but they're not getting there through their own social actions and that's what we call a social dilemma. So this is the equilibrium that we think is being socially optimal or more efficient - it's better - and remember, this is for the players in the game, obviously you might think society would be better off if people who get punished but when we think about the social value of the different strategies and
13:38
the different outcomes we're only thinking about the value to the combined people in the game, we're not thinking about society in the broader term, so we've got what we think of as a social dilemma in our prisoner's dynamic game.
13:54
Now let me just put this down so it's not my face
13:59
and let's go back to our slides. So just as a reminder this is the prisoner's dilemma game, you've seen it in Unit 4 with the Thelma and Louis example of trying to avoid time in prison.
14:19
So let's look at what happened in the game that you played. So we know that according to our model (confess, confess) should be the dominant strategy for all you players. Let's see what you actually found. Now you stay in Moodle, I'm going to share my screen in ClassEx and you can see that we actually had lots of different outcomes. So we had 20 of you playing the dominant strategy,
14:52
nearly... over 50 percent were playing (deny, confess) or (confess, deny)
15:04
and then we had another 28 - so very high proportion, the highest proportion from any of the four allocations - choosing the social optimum. So you haven't played as we might expect from economic theory. So let's go back. I'm going to go back into Moodle, you're already there,
15:24
so we know what happened was that
15:27
most of you either chose deny and I or we had (confess, deny) combinations.
15:35
Why do you think the experiment results might be different to what we expected in the model?
15:53
Okay so we think that first year economic students are very altruistic,
15:59
hopefully, so you're thinking about "I'm going to help the other player out by denying even though I take some risk that they might confess and i'll be worse off."
16:11
Yeah really good point, there's actually nothing at stake here, what you choose doesn't matter at all because this is just a hypothetical situation. Now if I was to apply all your strategies to what you do in the next quiz or in your summer assessment or something then that would be a different thing, so if you're actually thinking about colluding on an assessment, that would have a much more bigger impact on you. Okay some people misunderstood the game and this
16:40
is really important. In a big part of behavioural economics there's something that we call bounded rationality, so people may not understand the game that they're playing and may actually have thought "Oh (5, 5) is better than (10, 10) so that's where I'll go" or actually they may have decided (5, 5) was worse, so they may not have realized these were 'bads' - negative things.
17:01
Solidarity is always good, so you might think of this as being implicit communication, so when we look at collusion in market, something that I look at quite a lot through cartel investigations,
17:14
most collusion that we look at is something called tacit collusion, so people colluding not by meeting in a group room and agreeing to do something but just by recognizing that the collusion outcome is there and it's better off for them and so they get to (deny, deny) themselves.
17:34
Okay, so another really good point... Usually when people run this experiment they run it without
17:41
sort of after/before you've read Unit 4 whereas you guys have a lot more information about how to play games, so you may have already worked out that you should go to the cooperative strategy even without cooperating and you're good people. So you're seeing there, what matters, or the preferences, the understanding of the rules of the game, whether people actually are rational, so whether they go for their best responses all the time, so lots of different reasons
18:11
and obviously I'll have a closer look at all of these when we've finished the lecture.
18:19
Yeah, confusion is a good one. Okay, let's move on and play another game. So far we've seen that you
18:32
are not reaching what's expected from a prisoner's dilemma game, so we're going to change the game and what we're going to play is a game where imagine you're living on a road with three neighbors, so there's four houses on the road, one of which is you, which means in this game you're going to be in groups of four and you've got 20 tokens
18:53
and each household on the road is being asked to contribute towards a flood defense scheme. So you want to make sure that your house doesn't get flooded by having, you know putting, sandbags up or some more and sophisticated flood defense scheme, and you're going to play a round which is like a year, so each year you're asked to contribute some proportion of your 20 tokens - you choose how much to contribute, so anything between 0 and 20 - and if you are
19:24
choosing 0 please type zero in don't just leave it as nothing and anything you don't contribute to flood defense you keep for yourself as your own income to use for other consumption.
19:37
So you have 20 tokens, you decide how much to give to flood defense,
19:42
all the money that's given to the flood defense, so the sum of what the four people give,
19:48
gives a value to all the households so in aggregate the households are better off by 1.6 times the total number of tokens, so 1.6 times total number of tokens is like the monetized value of flood defense and that's shared equally between you, so you will get point four units of the value of the flood defense - you get a quarter of each.
20:13
The way the game will work is, at the end of playing - so everybody chooses their contribution - you will get to see what everyone contributed and how much money you were left with in aggregate, and your payoff at the end is what you started with. So 20 minus the number of tokens that you contributed plus your proportion of the monetized value of flood defense, so plus 0.4 times the total contribution of the four households to the project. This one's
20:48
getting a little bit more complicated so you might just at this point want to scribble down a payoff. At the end you're going to get 20 minus the tokens that you contribute, which obviously can't be more than 20, plus 0.4 times the total contribution to the project so the sum of all the contributions made by the four players including yourself
21:17
and again just to show you what it will look like when you're into ClassEx - you'll be a player, you'll be told you have an endowment of 20 and you're just asked to put in your contribution. Please put in 0 if you're choosing 0. Again i'm going to give you a few seconds to do this, keep your tab open the whole time and in ClassEx... So we're going to move there in a minute and then when the round is finished
21:43
you will find out how much you gained, how much everyone gained in total and you'll see your income and... you'll see your income and the tokens that the other parties contributed.
21:57
Okay so get ready to go back into ClassEx now, I'm going to leave game 1 and play game 2.
22:18
Okay, it doesn't like, me let's try this again... again 2... Okay, I'm gonna start, I play 2 so you're in a round with 3 other players, there're 4 players in total. In your round you're going to be in the same group of 4 for all the rounds so there might be more than one round and at the start of each round you go back to having 20 tokens. Again you decide how much you contribute, you know what your payoff is at the end of each round. Let's get going.
22:56
Okay so you should see your results from that round
23:00
take a quick note of them see how much income you've got off the back of the first round what your payoff was and we're going to play again so take note of what you've got from the first round and we're going to start round two. Now it's exactly the same: you choose your contribution... You might need to refresh your page if it doesn't refresh itself...
23:26
Okay we've hit 550 so I'm going to hit results and again once your page is refreshed in ClassEx you should get information about how many tokens you got in that round
23:42
and also how many you have in total from the two rounds. You should be able to see that.
23:49
We're going to play again, so this is like our third year of investing in flood defense, so you've got the information that happened in year one... round one, what happened with your other households in year two and now you're going into your third year of deciding how much you want to contribute to flood defense.
24:05
When you're playing these games remind yourself of what you're thinking about, you're thinking about what happened before. What do I think the other players in my group are going to do? Remember you're in the same group each time and you're thinking about your own personal payoff
24:22
and maybe you might be thinking about what other people might get as well, and you may be thinking about the flooding and the impact on the whole road of the flooding.
24:33
That's how we solve games, we think through what are the different options that I have, what other people might be doing, what information I have to make these choices.
24:43
Okay so I'm going to let you see what you're getting now. So you should see
24:50
how much income you've got from that round 3, so the third year
24:55
and how much income you've got in total over the three years.
24:59
So are you getting better off, worse off as we go through the rounds? And now we're going to play exactly the same game, you're in the same group of four, same decision to make for the fourth round.
25:12
So now you should see after four years of paying for food defense
25:18
what income you've got in this round, what income you've got in total
25:24
up to here. How are you keeping track of this? Are you just forming a generalised opinion of how you're doing or you've got a spreadsheet open keeping all the information going? Fifth round
25:41
and now we're going to assume that you've all moved, that's going to be the end of the game. I know it says there's another round but we won't play any more rounds so once you've checked in with how much income you've got over those five years paying for flood defense come back into Echo.
26:02
Okay and you have your entire record with you and ClassEx...
26:06
Okay hopefully you've all switched across same question as before...
26:12
Excellent so the vast majority of you recognized that this was a public goods game. What is a public goods game? It's a game where the choice that you make if you make a positive choice would be good for the rest of the people in the game, so the rest of society, but bad for you. So what you want to do is free ride. Your payoffs will be a bit higher for yourself individually
26:40
if you don't contribute to a game like this. I think I'm giving you the answer to the next poll question actually, so this is a public good game, we think about things like flood defense as a public good game, non-rival goods which means that I can consume it and it doesn't prevent you from consuming it so if you think about something like the Thames barrier, the fact that I get flood defense from the Thames barrier - it doesn't prevent anyone else from London from getting their
27:07
flood defense. Very different to if I ate a bar of chocolate - it's gone, nobody else can eat it. We also think of public goods often as goods that you can consume even if you don't pay for them, so if you arrive as a tourist in London you haven't paid any council tax or any income tax, you can still get the value of flood defense from the Thames barrier. So we are looking at public goods, what
27:32
kind of behavior do you expect to get in public good games, so we're moving on to slide 14 now.
27:41
Okay, so a few different views on what might have happened or what the model predicts will happen. So most people think that the model predicts that everyone keeps all their tokens, which means that everyone will choose 'free ride'. Quite a few of you think that there'll be a mix of behaviors, so different people will make different choices and again, third most popular option is
28:06
that some... Everyone donates all their tokens. So everyone thinks about the flood defense rather than their own payoff. The model prediction is B and let me again switch to the visualizer
28:22
to explain why this is so. Because we've got four players I can't draw a two-dimensional
28:29
payoff matrix for you but it's much easier to just look at what the payoffs look like and this may be useful for you and your assignment... The assignment that you're working on as well.
28:40
So there is just... token t_i is the token that player i contributes, t_j is the token that player j contributes, so my payoff is... Player i... Payoff is my endowment minus what I contributed individually plus my share of what everyone
29:04
contributed in total, so this is the total contributions from everyone and I get 0.4 of that. So that was what the rules of the game told me, what my payoff would be. Now remember I'm one of the people who've contributed to the total, so if I pull out my contribution to this total here
29:23
and just leave all the other three players... So player j now is everybody except me player i,
29:32
I can see that my payoff is 20 minus 0.6 of what I've had in tokens so for every token I paid I lose one but I gain 0.4 from the flood defense, so in total I'm only losing 0.6 of the value of each token I spend, and then obviously I get some value from what everyone else has contributed,
29:56
so this is my payoff and I want to optimise... I want to choose what's my best number of tokens to contribute given this payoff and hopefully what you can see is my payoff is always negatively related to the number of tokens that I personally contribute. So no matter what anyone else has done
30:16
my best response is always to make my number of tokens as low as possible or zero. So if I do anything more than zero I've reduced my payoff, so if I'm thinking about my feasible set, my preferences this is the resulting combination of feasible set, preferences, my optimal choice is to make t_i = 0, so I'm always better off free riding, and this is true for any of the four players in the game. And this is why in the public goods game we predict that everyone will free
30:52
ride, and actually the flood defense won't happen at all and that of course is why we normally get government intervention then... Government getting involved in providing something like flood defense because no company is going to choose to provide flood defense in a market because they worry that they're not going to get any income, so this is the public good problem that often results in government intervention for governments providing the public good... Or
31:18
they may use government intervention other ways to persuade people or to require people, so something like council tax, to pay rather making it a choice that people get to make.
31:31
So just as a reminder this is what you have seen in Unit 4, we looked at Kim's payoffs and you could see that she was always better off not contributing relative to what would happen if she did contribute. So again it was always in Kim's interest to not contribute, if one other farmer was contributing she was better off not contributing and and if three other farmers contributed, so if all three other players in your road were contributing to flood defense, you're
32:05
again better off not contributing. Of course what this means is we end up with flooding and I don't want to make the impression that in reality flooding happens because people are free riding. Obviously, there's a lot more going on because we don't depend on people to do it individually and what we ideally wanted, so our social dilemma from the public goods game, is that we get the flooding... Our social optimum is the people actually invested in a flood defense system
32:36
like this to prevent the flooding from happening and this is of course the public policy dilemma: how do we get people to make choices to contribute to ensure the flood defense gets built?
32:48
And obviously the public goods game tells us, leaving them to choose it for themselves is not going to get you there, so let's see if what you did corresponds to what we expected.
33:03
So this is all your different groups, I'll have a closer look at them later, obviously a nice multi-colored rainbow, but let's look at the average contributions,
33:14
so what we can see is, you've got fairly low contributions, you're coming down towards the idea that you're better off paying as little as possible
33:24
but you're not at zero, there are people in the group making positive contributions which is not what we would predict from the public goods game. You can also see that there's been a slight decline in the contributions in the game in the first two rounds, a little increase around four and then more or less flat so 6.18, 6.17, so some variation as you play the game over time. Now when we play it over time what we expect is a little bit of response to what happened last time,
33:59
which can work in two directions. So you've got some information about what your households did. It doesn't affect your payoff in the new round at all but it might affect your behavior even though it doesn't affect your payoff and this came up quite a lot in the discussion forum - people saying well why do people make choices when their payoff is zero? So if the payoff is zero there're two options: why do they choose one thing over another ? And of course it's to do with the fact
34:25
that we can be influenced by more than just monetary payoff when we're making choices, so this is what you did, you're fairly close to the public goods game which I'm not surprised by because you've obviously read the unit, but not everyone's down at zero
34:43
and you can see that there's quite a lot of variation across the groups and some groups are paying very high contributions, some groups are operating much closer down to the zero.
34:56
What I'll do is, after the lecture I'll try and download the data and produce some summary results so that we can share them on Moodle as well, so you can see them.
35:07
So that's what you... How you played the public goods game. Let's go to slide 17 and I just want to show you how people in another university played this game three weeks ago. So in Pompeu Fabra one of our colleagues on the CORE team played exactly the same experiment, in fact I used his experiment, he had 99 students and we have a great sample for our experiment
35:42
and what you can see in their game is, he played for more rounds but if we just look up to round five you can see they tended to start off by making more contributions. Do we think the Spanish students or the students in Spain are more interested in flood defense
36:00
and then as they went over time they started contributing less and less?
36:05
He played the game in exactly the same way as I did with you, the one big difference was that he played this game before the students had read Unit 4. So think about whether that might have affected how they played the game or maybe more importantly how you played the game.
36:24
So what we saw was, your behavior was close to public goods outcome but not exactly the same.
36:35
So any thoughts on why it might have been similar or different
36:42
how you played relative to what we'd expect from the public good game?
36:48
Okay, so some of you think that you're more altruistic again and so the fact that you
36:56
want to contribute to flood defense even though that's not the best response for you individually, which is exactly what altruism is, so you're trying to benefit the whole community by contributing to the flood defense even though that creates cost for you.
37:10
And yes, you may be punishing each other even though this isn't a game of punishment, so there's no formal punishment strategy but because you're playing over time you might just be annoyed with your neighbors for not contributing in line, but if you're not going to contribute I'm not going to contribute, so kind of negative reciprocity.
37:36
As we started playing you probably began to realize that you were in a repeated game
37:42
that you were playing over time, so you maybe started thinking about actually I might be careful about how I'm playing here because people might respond to that in the next game. And again it is about each game on its own should not be influenced by the other games because the payoffs in the other games don't affect your payoff in each game but behave really. You're thinking about "How can I punish people? How can I reward people? How might they punish me?
38:08
How may I be rewarded?". Some of you may be thinking about flooding, you may be genuinely worried, more risk averse, essentially thinking about I really don't want the flooding to happen so I'm definitely going to contribute, and again people noting that this is just an experiment there's no consequence to you whatever number you put into that and that would of course affect you.
38:36
And yes again, because you've read it that will affect your decision, you kind of are influenced by the fact that you know what you're supposed to do according to theory and that is one of the consequences of being an economist, that we often know that we're supposed to behave in a particular way according to our models and we might actually start behaving like that although there's lots of empirical evidence that economists are not the most rational people in the world.
39:00
In the sector I work in, in economic in energy, if you look at the different disciplines and whether or not they switch energy supplier, economics is actually the worst, so economists are less likely to switch supplier even though they're better off by switching supplier. In the energy market empirical evidence is based on very small samples but it's an interesting thing to think about
39:24
whether economists are actually better at playing games than other players. Okay, and of course the fact that you knew the game and the people in Pompeu Fabra didn't is very important. Okay and nice to know that you're... Some of you at least are thinking about the betterment of society.
39:46
Okay so this is the final game, this can get a little bit long and i know most of you haven't made it straighten house yet, but we do actually have an experimental lab on the first floor of Drayton House and hopefully some time in the future, not too far in the future, you will get the opportunity... When we run experiments in the lab we ask for volunteers... The researchers running experiments for their research and you can play more experiments that way.
40:18
So in our third game, the game is very similar to what you just played, your four households contributing to flood defense, but now we're going to have two stages in each round. In the first round you choose your contribution just like you did before, so you choose how much you want to contribute to the flood defense and you see what others have contributed
40:40
and after that in the same round there's a second stage, so after you've seen what your neighbors have contributed you can pay a token or up to 10 tokens to punish your neighbors and for every token you pay they get minus three tokens and the maximum you can punish them is 10 tokens. If you have 10 tokens, if you've contributed 20 token in stage 1, you have no money left to punish so your maximum is either the amount you have left after contributing or 10. If you get punished by
41:17
the others you obviously lose minus three times the number of tokens that they spend punishing you and you're also going to spend tokens punishing them so your payoff now at the end of each round, so after the two stages, is going to be 20 - what you started with, minus the tokens you decided to contribute to flood defense, plus again 0.4 of the total contributions to flood defense. So this part of the payoff is exactly the same as it was in the second game but at the end of
41:49
a round, so after stage two, you're also going to lose any tokens that you spend punishing others
41:56
and you're going to face a fine or a penalty of three times the tokens that others spent punishing you. Okay, so where before you talked about the fact that in the game when you knew there were multiple rounds you were punishing each other by your choices, you were just trying to let people know, send signals here there's an actual scope to punish people, to find people,
42:23
but you're still worried about the flood, and you still want to make sure there's a defense potentially or you're only focused on your own payoffs,
42:32
so again just to show you what it will look like in ClassEx. So you'll start and it'll look like what you played before, so the first stage you'll be asked how many you want to contribute, then you'll be shown what you were shown before, how much everybody's contributed and then you'll move on to a second stage which will ask you how many tokens you want to pay to punish each of the other three players, and again please put in zero if you want to punish them zero, don't leave
43:01
a blank. And then that's the end of a round, once you've done that, when everybody's played you will get to see the total payoff that you get including the punishment strategies.
43:15
Okay so into ClassEx, move on to a new game, so this is game three, our final game
43:28
and just check my test participant is awake.
43:35
Okay so we're gonna start. Fine okay so now we're gonna finish stage one, you're still in round one but we're finishing stage one and you're moving on stage two which is where you're gonna get asked
43:59
how many people you want to punish or how much you want to punish people. Remember the maximum you can punish is 10 for each person,
44:08
sorry 10 in total but also how much you actually have in tokens
44:17
and you can see that we're going to be playing a second round, so again we're in multi-rounds. Okay we've just passed our 500 mark, so we're gonna end round one and you should see in a minute... Yeah you should be going into round two and you've seen what you've got after round one.
44:43
Right, let's finish round two when... I'm sorry let's move to stage two round two. Now you're getting to punish again, if you want
44:54
so, you finish round two and go straight into round three, so get asked about contributions again but you will get the information about what happened at the end around two as well.
45:06
So now you should be able to see your feedback from the end of round two and you're getting asked for your contribution for round three...
45:24
Gonna move on stage two of round three so the punishment stage of this round.
45:31
Now you're getting nicer or you're getting less nice as you move through your ends.
45:36
Okay moving into round four this is going to be your second last round I didn't tell you that last time so this time I'm telling you.
45:49
Round four is the second last round, see if that changes your choices at all.
46:01
Again this is a two-stage round with punishment, in the second stage as the fifth round will be a two-stage game...
46:10
Interested to know if any of you are thinking about what happened in the game two, when you're playing game three you are with a different group of three people... Well you with another random group, you might have been the same but you don't know but obviously for each of these five rounds in game three you are the same four people playing together, same four households on the road.
46:33
Okay so now we get to punish... Okay nearly there, starting our last round round five.
46:44
So your final round, how much do you want to contribute and there will be a final stage two of punishment as well. Okay final stage, two final round punishment choices.
47:05
Okay, so we're going to stop there, I'm not going to hit the start round six button because we don't wanna play round six, so please go now back into Echo, into Moodle, so that we can have a chat about what game you think you were playing. So on slide 22
47:26
you know you were playing the good... perfect good game, we already worked that out
47:31
but what kind of public good game were you playing?
47:36
Okay, so you all recognize that we were obviously playing a public good game with punishment, it was set up to be a public good game with punishment. By having punishment we've also built in reciprocity and almost automatically, so the punishment is about being reciprocating behavior on each other. Now I didn't specify anything about preferences, or I didn't set up the game to be altruistic or to have social preferences - so altruism is where your preference
48:06
is to help others at your own expense, social preferences is where you're focused on getting the thing that is the social outcome, the thing that's most efficient for society.
48:18
In this case altruism and social preferences may overlap and it's not a game of cooperation, so there was no way in which you were able to cooperate with the other players and even if you'd attempted in the chat you don't know who you're playing with, so definitely not a game of cooperation. Explicitly set up to be a public good game with punishment. Once we have punishment we have reciprocity built in but as you found in the previous game, you might build that in yourself.
48:46
Anyway, when you know you're playing a repeated game, when you're playing multiple rounds,
48:52
you may have altruistic and social preferences when you're playing, but I didn't build the game up to assume that in any way, so given it's a public good game of punishment
49:04
and based on the theory and the models that you looked at in Unit 4, what would you expect to happen in this game relative to game 2?
49:15
So where do you expect people to be contributing more tokens less tokens and would you expect punishment to have no effect relative to game 2? And do you think it's the repetition that matters
49:29
so what people did the reciprocity that matters or the scale of the punishment?
49:38
Okay, so most of you think that the threat of punishment is going to make people contribute more because they're worried about the cost of the punishment on themselves and also a lot of you recognize that you may play a sort of reciprocal game here, so what you do depends on what other players did the last time and that is important. So the information you're getting about what other players did is going to influence the extent to which you expect to be punished next time,
50:08
so you form expectations about what will happen in the next game based on what you observed in the previous round and me telling you that it was the last round coming up may have affected your decisions in the last round, and we will have a look in a minute because then you know that there's no more punishments coming up, there's no more future rounds, there's no need to develop a reputation, so reputation matters in these games
50:35
and people know you're player 1 or player 2 or player 3. C is the one that we know for sure isn't going to happen, we know that having the explicit punishment will affect behavior. B is a possibility depending on how people think strategically through the game, so if their preferences are that they like to punish people, then they may save up some money for punishment, so there may be people who have a preference to punish which is sort of the opposite of altruism.
51:07
But generally, we would expect... People are going to be more protective of themselves and try and avoid being punished more than they're going to try and punish other people, but behavioral economics tells us that you can get all these different types of behaviors happening so C is the only one I would say is a definitely wrong answer, and A and D we would certainly expect, B is a possibility depending on people's behaviors.
51:35
So again this is a game that you've seen in Unit 4, the public goods game with punishment and you were talked through an example of introducing fines for parents showing up to late to pick up their children and seeing that the fact that fines were introduced had an immediate effect people behaved differently.
51:58
So when you didn't have fines introduced and when you did, you had different types of behaviors, but as people get used to the fines and the punishments they start to behave differently, and so you can see their fines have different effects. In this case... Was this the average number of parents arriving late? When you introduced the fines more parents were arriving late, that obviously wasn't the intended effect,
52:20
why? Maybe parents thought they were willing to pay the fine and have 10 extra minutes at work and certainly when my kids were young that was probably a trade-off I would have made, and so that's about the design of the incentive. Is it not high enough? Is the fine maybe the thing that affects people's behavior? Maybe if you were told that your child was going to be put out in the street that might make you behave in a different way rather than a financial fine
52:46
and of course in our case what it means is, are we more likely to get the flood defense or are we more likely to still be ending up with flooding now that we're able to fine our households?
52:57
So let's see what you did, so I'm gonna press start round six, please don't play it,
53:06
so that I can see the results after round five and you should also be able to see... what you got at the end so after five rounds, I got 7.2 tokens, people seem to punish me a lot in my game,
53:26
so I didn't do very well but let's see what we did on aggregate. So the average contribution in this game and this is the game with punishment - first note much higher than before, so our axis here is starting on 8, remember before we were down fairly close to zero, not at zero, so people are making much higher contributions in this game. The contributions are going up over time but then when you recognize you were coming back towards the last round,
53:57
no need to be sending signals about your behavior, no need to be sending signals about your choices, and we fell back down again, not quite as low as we began with.
54:08
Again you can see a huge variation across the groups: some people playing a very special preference type approach where you're focusing on getting the flood defense, others still playing low amounts and quite a big variation, so if you look at group 149 playing low all the time then the middle big jump up... That's a different group. See if we can trace 149.
54:40
Anyway I will have a look at this. And here we've got information on the punishment, so you can see the punishments, people didn't go up to the maximum very much at all apart from group 55.
54:54
So people were using sort of half their maximum ,some people choosing not to punish at all,
55:01
and certainly not much movement. I think it's a bit hard to see, it's a shame I'll have to give feedback to these people that we should have a punishment line here on the average as well but I will work it out and see what was going on. But we can see some variation, but actually quite a lot of clustering around the low punishment levels between the students in this class, but again big message here, that your contributions are higher
55:31
when you have punishment built into the game. And again I've got the data from Pompeu Fabra, and you can see again... I mean these guys in Spain are making much more significant contributions when there was penalties but again dropped off towards the last round, so this time they played six.
55:55
So I'm not going to do what you... Well I'm going to run this very quickly you can do this in the background and I'm going to switch to the visualizer, just to explain to you how complicated it can be to solve these games and that you really do have to think through them
56:14
step by step. I guess this is the best way to think about this, so let's try and draw a game tree of what's going on here in this third game that we played. So imagine this is me as a player
56:27
and I've got a choice between contributing, 0, 1, anything up to 20, so I have all these choices,
56:37
that's my contribution and this is stage one. In parallel we have three other players,
56:50
so let's just say this, say I'm player one and we've got player two, three and player four and each of those players gets to choose zero one or twenty. Now they don't know what I've done when they're making their contribution choice and I don't know what they are doing so although it looks like we're moving sequentially we're not, this is all simultaneous,
57:16
so stage one is all simultaneous and then we move to stage two,
57:23
and in stage two I get to decide... So imagine player one has chosen one, back to me again and I get to decide "Do I want to punish player one zero, one, or anything up to 10?" So my game tree is getting a bit complicated now, but what you can see is, I get a set of information at the end of stage one which is basically what I contributed and what the other people contributed and with that set of information I get to... So this is my contribution choice
58:02
and this is my punishment choice and then again I'm making those choices but player two,
58:11
player three, and player four are also making their punishment choices in parallel
58:17
and what we end up with is that I get a payoff at the end of the game.
58:25
Not sure how clearly this is which is 20, my original endowment
58:35
minus 0.6 what everyone contributed, well I contributed in stage one, so I'm going to call it the power just t_1 so this is the same payoff as we got with game two and
58:55
so there should be a point four there,
58:58
a portion of what everyone else contributed. So this is what... The game we have for game two, the payoff, but now I'm also going to be paying an amount of penalties so called t_2, the penalties
59:14
and I might have penalties imposed on me by the other three players.
59:23
So I've got a more complicated payoff function, the same payoff function at the end of stage one as we had in stage two, or as I gained, but now we're adding in the stage two payoffs, which are taking away anything I pay in punishment and taking away anything that other people punish me.
59:43
To really work out what my optimal strategy here is, I need to think about what the interconnection between these choices might be, so in round one is the punishment choices of other people
59:59
a function of my choices in stage one? If I believe it is so, if I believe the choices of penalties that other people impose on me depends on what I did in round one then of course when I'm thinking about my optimal payoff I'm going to have to think about that function,
1:00:19
and they'll be doing the same thing thinking about whether the penalties I impose on them are a function of what they did in round... Stage one, and then of course I'm realizing that we're playing a repeated game so I'm thinking "Hang on, I've got round one and round two and round three to think about, so I actually have to think about the payoffs over time. Does the fact that I punish
1:00:42
somebody in round one kind of mean they punish me in round two?" So I have to think about my choice, the penalty around one, what impact it might have on round two, and I will make different choices, if I expect there to be another round or not. So you can see that the rules of the game really matter and this is something that we're going to focus on a lot in Unit 5, looking about how
1:01:10
the institutional arrangements work. So if I know that there's an end game, there's a last round to the game that will affect my choice about whether I punish in that game because I know there's no more scope for reciprocity, on the other hand, if I don't know there's an end to the game
1:01:28
that will change my behavior. These rules are what we call institutions, so institutions don't just mean the buildings, they're anything that influences how the game is set up, who the players are, what the players preferences are, what the payoffs are, and and they may come from government or from external sources, but they can also come from the inherent features of the game itself and these institutional... These institutions or rules
1:01:55
of the game have a big impact as you've already seen from these experiments, so things like what information you have, whether there's an end game and what information you're provided with.
1:02:09
So again the fact that we are seeing one kind of behavior, one type of preferences, and if they're different and that will affect things.
1:02:19
And you know there are people out there who just have a preference to punish and other people out there who don't like punishing other people, so there's a lot of behavioral going on in these experiments and that's definitely worth thinking about going forward.
1:02:36
So what did we learn about this week? Well we learned that our models are reasonably good predictors of how people behave but not absolutely perfect, why? Because people don't always make the assumptions of the models, so every model has a set of assumptions built into it, assumptions like perfect information, fully understanding the rules of the game. The other reason is of course that people playing games don't always know the detail
1:03:02
of the game beforehand and whereas you've read through Unit 4 you understand it. We also learned that people make choices for many different reasons which go beyond the monetary payoffs or the sort of what you see in the payoff matrix, and that is important that you think about, why people may be doing things differently. Obviously, when you look at Anil having altruistic preferences or very selfish preferences,
1:03:28
understanding what that does for his choices about how to share things between him and Bala is really important to understand. We understood that repeating again affects the outcomes and knowing whether or not there's an end game matters
1:03:45
and of course always remember that these are models and they're based on a particular set of assumptions that makes them very useful as a way of understanding how people might play games and for understanding how the rules of the game affect... It will lead to different changes. So the models really help us. If we tweak one thing in the model how do the outcomes change? But we're not going to pretend that they can tell us everything about how
1:04:11
every individual makes decisions, so people will do things for different reasons and we might need to understand that through experiments, through surveys through other kind of behavioral analysis.
Here to help you learn
Sign in to keep a private conversation with your course tutor.
Ask me anything about the material…
Sign in to chat