As advances in technology drive globalization and digital transformation, the importance of the use of technology in education is again on the front burner. At the tech summit on the new past to education held in Lagos, a group, EF's catalyst has stressed the need to reposition education through technology, Jacinta Obuco-Hosmore. The world today is changing, positioning humanity with uncertainty, take for instance the heat of coronavirus pandemic, where the importance of technology is clear in responding to the novel disease. With regards to Nigeria educational system, thus gathering and chatting a new path, point that the growing importance of technology in the sector is alarming, as gone are those days education take place only in classroom. So technology is at the heart of everything we do. This is the age of technology. If we are not riding with this wave, we might just miss it completely. If you give a device to a small child, the first thing is to unlock and look for game and everything. This is natural with them. We can change that. So what we need to do as adults and teachers and school owners is to flip things around to say how are these games and all these videos engaging the students and how can we structure our pedagogy, our curriculum, our content in a way that we can actually engage them. Teaching is no longer the usual thing. It should be that you're teaching with the script, you're dramatizing, you're getting the students engaged. These students, when they were online, a couple of them complained that the teachers bored them, that the teachers didn't engage them very well. But if you give them a phone, they can watch Netflix movies for two hours, three hours and they won't stop. We don't have options anymore because we are dealing with what we call the Generation Z and Generation Z children were born into technology. How many classrooms will you go? And you see teachers teaching students modern things using native languages. Language is a technology. Well, we don't do that. We use English and that's why our people are confused. Technology introduces lots of great tools. But Iran needs for local developers of softwares, a call for youths to engage in technological innovations. It is very important that we encourage our youths to learn to develop applications, to code applications, to invest in their education. Not only will that help them, but it will help the nation. The Lagos State Government revealed they are also taking part to ensure no one is left behind in modern digital connectivity. We are building the digital divide. We're making sure that whatever we make available for the people in the state will be extended to people in the rural areas. When used well, technology can help improve education for students, parents and teachers, as well train young people to become agents of innovation, to prepare for the future.


Welcome back to Mental Wealth TV, I'm Emmie Golding, Director of Psychology for the Workplace Mental Health Institute. I'm Peter Dears, the CEO of the Mental Health Institute and we welcome you to the new year. Happy new year, I hope you've got a chance for a bit of rest and rejuvenation. Rejuvenation is the key. Most people feel not rejuvenated but a little bit more tired. Maybe we overrate or drunk a little bit too much. Well, that's something we noticed this year actually. A lot of the organizations that we worked with seemed to barely pause for the holiday season. They just kept going. Surprising because that's never happened before which either we should be happy that they're thinking of mental health all throughout or part of me thinking should I be concerned that people are not stopping and taking a break. So I'm ambivalent. I know a lot of HR managers, people in culture, directors that I was speaking with, they really wanted to just get a jump on their planning for the new year and that's where most organizations are at right now looking at what are the initiatives they're going to put in place for 2024, what are the needs of their people, what's going on in the world at the moment is actually impacting hugely on mental health of people as well. One thing to be ready, I think that's commendable. That's really good. Absolutely. So what is the mood for 2024 going into the new year? There's a few things that we've seen out there in the world that are impacting well-being. I think this is a good time for people to sharpen the axe. I'm not sure if you've heard that story about the two logger men. They were cutting trees. Woodchoppers? Woodchoppers. They are cutting trees. And one was cutting the tree and he was putting a lot of effort into it, a lot of effort. And he was listening to his colleague that every few minutes he was stopping and he thought, I'm going to finish much faster than him because he's taking so many rest. And no, as it happened his colleague finished the log first and he asked him, how did you do it? I heard that you were stopping. I thought you were taking it so slow and I was really going for it. And you beat me. And we basically had the same kind of log. And he said, well, I wasn't really resting. I was sharpening my axe. So every time I was using my axe, it was more effective. And this is what we can do now. 2024 is here. Maybe it's time to sharpen air axes. You know, stop for a moment and what have we done in 2023? What has worked? What hasn't worked so well? What can we improve on? And what kind of results and outcomes do we want for 2024? I'm not talking about setting new goals necessarily or putting more pressure on yourselves, more projects. That's not what I'm talking about. I'm talking the thing that you are carrying from 2023 that are important to you and important to your workplace and important to your family. What can you do better in 2024 so you get even better outcomes? It's about being strategic. Yeah, don't add more projects necessarily. You know, there's a lot of people that see that. New year comes along and they put more stuff onto themselves, which is very overwhelming. And I don't want people to be overwhelmed in 2024. Whatever you're going to do, do it well. Yeah. Let's get better at what we do rather than take on more stuff if our life is already full. Absolutely. So one of the things that I'm seeing... Sharpen your axe. Got it. Sharpen your axe. One of the things that I'm really seeing in the conversations I have with workplaces, whether they're in Australia, Asia Pacific area or the US and North America and Europe as well to some extent. Well, to some extent there's a lot happening in Europe at the moment. But one of the big things is there's a lot of uncertainty. And the political environment at the moment is quite on edge. One of the big things happening is we've got the ongoing war with Russia, Ukraine. We've got everything that's happening in Israel and Palestine with that situation. That's creating a lot of uncertainty for a lot of people out there. And of course they bring that into the workplaces as well. You know, just uncertainty. There's a lot of unhappiness and anger associated with that because they're seen as unfair wars. And people don't like unfairness. They like justice. They like things to be fair. And definitely we're not in an even play field at the moment around the world and the wars that have been started.  That's quite usually considered a traumatic experience. But even for us watching it on the news, reading about it, social media, there's a lot of rhetoric about it. And so it's very easy to get caught up in all of that and have a negative impact on our well-being. And I've seen that. We would talk about it when we talk about vicarious trauma. That idea that there's direct trauma when you're physically involved in a difficult event, but then there's also indirect trauma when you're surrounded by that information and it has a very real impact on people and it's very easy to get stuck in that rabbit hole going down news and articles of greater or lesser quality, a lot of that information that we're getting as well. There's also the aspect that when you're watching, if you're watching too much news and you're getting caught up with it, it's very easy for us to hook onto the two main elements of a mental distress problem or a mental illness which are helplessness and powerlessness. You know, that idea that it doesn't matter what I do, it's not going to work and what should I try anyway. What position am I in to do anything about these international conflicts? So you can create an angst in our souls, in our psyche, in our spirits and that can, if we don't address it, it can cause problems later on. So it's good to be aware of this and see how we are coping with this. This is very interesting because a lot of people do start to think, well, what if these situations do start to impact on my actual life, my personal existence in the world? And there's been a lot of movies out lately around the sort of end of world scenarios which I think are very attractive to people because of this uncertainty, because of these fears going on at the moment. And what we know from mental health is that anxiety does serve a purpose. Those fears, those uncertainty, that anxiety, it serves a purpose in that it can prepare us if used correctly, that's the thing. Yeah, anxiety is the body's mechanism letting us know that something is amiss and that we need to pay attention to it. It doesn't tell us what it is, but it tells us that something is not quite right. So what do we do, the average person, if we're aware of all this going on in the world, we're concerned that it may have some impact on us in some way. We've seen articles where people, Sweden, for example, have rushed off panic buying and really in that sort of response mode, is that a good thing to do? Is that a bad thing to do? How do we get the balance right in terms of our well-being within all of this? I think different people need to do different things to feel psychologically protected. If you're fearing that maybe finances will be an issue, it might be good to have a financial cushion of sorts, maybe savings, cash savings at home, or if you fear that water or food is going to be an issue. Because remember, we're not talking just about Australia or New Zealand or Canada, we're talking about the whole world. Europe, the threat of war in Europe this week has become quite real with some countries saying that they're thinking about starting conscription again and preparedness for war. This is quite serious talk. So we're here in Spain, so we're a little bit far away from the front lines. Being the front line is supposed to be in Russia. But those countries that are close to Russia, it's logical that they may have to look at things like water, food, electricity, etc. I think within our communities, within families, within workplaces, when we're having these conversations, some people would look at that and go, wow that's extreme, there's no need for any of that, you're crazy, what are you thinking about? For someone who is concerned about that actually taking actions like you've mentioned could actually alleviate that anxiety. The important thing I think is to say, alright, what can I do that will help me feel better, feel more prepared? And then when I've done those things, stop. Okay, I've done that as ready as I can because who can predict the future, who knows what's going to happen, but it can't be at the expense of our mental health. It should be something that serves our well-being and gives us that sense of safety and security that we have a plan B. Exactly. You can be reasonable about these things and you don't need to preach about them to other people. If having a psychological cushion of sorts is good for you, just do it. You don't need to tell other people that you're doing it. Just be aware that you can go too far in addressing your anxiety. It's okay to have a certain degree of anxiety.  No, you don't want to be so blasé. Yeah, but you don't want to be so blasé then everything goes. But you don't also need other people's approval in order to have a psychological cushion of sorts. You don't need them to approve of what you're doing necessarily. So a balance is the key word here. A psychological cushion is not necessarily preventing everything that could possibly happen in the world. We don't have control of those things. So the question is, what could happen that I'm concerned about? Could happen? And what would be a psychological cushion that if I have it, and even if these things I'm concerned about doesn't happen, well, what's the big one? I've got a sense of control going back to your point about feeling hopeless or helpless. It gives you that sense of control. And it hasn't destroyed my life in the meantime. Exactly. It hasn't made me a hermit. I haven't spent all my money in this preparedness and now if it doesn't happen, I'm ruined. No, there's a balance to this thing. It's a cushion, not a bunker. I think there's another element. That's very good. It's a cushion. It's a cushion, not a bunker. Unless you've got a lot of spare for a bunker. That's a cushion for you. It's with a spare change. With a spare change, you're building a bunker. It's kind of a cushion. So there's another thing that I think I'm seeing is having a huge impact on well-being just generally is, and we've kind of touched near the topic, is those relationships with our friends and family around these kinds of topics. So, and the obvious example, there is what's going on with Israel and Palestine. You know, the level of what might be an interesting political conversation at the dinner table becomes an all-out debate and becomes an unhealthy conversation. And we've seen that on different topics over the past few years as well. There's definitely a lot of division on ideas and people having really hard conversations, which I think are important to have. And yet we've also seen people have damaged relationships because of it and more loneliness because of it. Some people can't handle thinking about things. You know, what we may be really comfortable to look into I'm afraid of war, I'm afraid of this, I'm afraid of that. Some people prefer not to think about it. Because it feels so helpless and it causes pain. So, if we initiate a conversation and people have a reaction, well, maybe that's a cue to stop and not talk about it with them. They're not the person. But some people, you start a conversation and they can't wait, oh my God, I'm so glad someone else is concerned about this and they're wanting to talk, that's good. So, you take those opportunities and you talk with them. As much as you have time and allowance for that. But yeah, it's about having a bit of social, you know, acuity and say, well, is this person connected to their pain around this and they want to talk about it or they don't want to talk about it, if it's a problem. And what about just simply people that do want to talk about it but might have opposing views? That's fine too. But we have seen some people are quite okay to we can have completely opposite ideas politically but we can still be friends. Because other people, that's not possible. We're too misaligned to be able to continue our relationship and that's really difficult. In fact, I think the world is experiencing that polarity at the moment in which people feel that if you disagree with me in a subject, we can possibly be friends.  That didn't happen 30 years ago. People had different opinions and they remained friends. In actual fact, having different opinions and different angles was seen as good diversity. Because it shapes each other. It makes us be more balanced. So that's a good kind of diversity. So if you're out there navigating all of this then you're not alone. That's definitely what we're hearing from having with workplaces and individuals. All around the world. We fear it is. Hi, I'm Emmy Golding, director of psychology for the Workplace Mental Health Institute. We hope you liked the video. If you did, make sure to give it a thumbs up. We have more and more videos being released each week. So when you subscribe, you'll get a notification letting you know when a new one's just been published. So make sure to hit that subscribe button and don't miss out on this vital information for yourself, your colleagues and your loved ones.


So I received an email from this guy a little bit a time ago But he's basically saying that he has a problem. So I asked him what his problem was and it's basically when he brings girls home at night He has no problem during the make-out when they're getting close But as soon as he brings them back home and the pants are coming off He can't get hard and this has happened a number of times and he's actually done the no-fab thing He's done that for months. Okay, so, you know, why is this happening? I've actually talked to a lot of guys with this problem where they have done the no-fab and they feel like this is the number one thing That should be curing my erectile dysfunction and it doesn't so this is kind of a frustrating thing because that's for a lot of Guys, that's the reason why they get into no-fab in the first place So why isn't it working? Well, the simple answer is is that no-fab doesn't solve all your problems Okay, it solves a lot of them I think the no-fab movement is a really really good movement something that's come out of you know all this Over stimulation we get from the modern-day lifestyle But I think it tends to over promise and under deliver for certain areas now If you're having problem getting hard bringing chicks home There's a reason for this. There's a mental insecurity. There's a confidence issue going on that you need to solve And it may or may not be related to your masturbation habits Okay, so obviously I'm not saying that pornography doesn't change your mind I'm not saying that jerking off a lot affects your stimulation It does but it's not the whole picture the whole picture encompasses everything So for this type of guy, it was kind of interesting to hear the way he described it He described it. He was having it was totally fine with the make-out He was getting hard when they were making out when they were kind of getting cozy in the club They were you know, his dick was doing fine. It was upright.  They're scared They're they've never done this before and so they don't really feel confident doing it So how do you get confident doing something that you've never done?  This is totally normal Well, you need to start focusing on is you need to start focusing on the things that actually start turning you on What actually makes you hard when you think about that sort of stuff where you do you feel some blood flowing? Do you feel something happening down there? What sorts of things do you think about where that actually happens now? It might surprise you the types of things that Actually turn you on as opposed to what you think would turn you on because we were all raised to believe That we want a certain thing and I think for a lot of guys out there We're taught to believe that oh we want this kind of sex and that's enough for us But it turns out if you look at actually what this guy was telling me He said he had no problem getting hard when they were making out When they were close to each other he likes intimacy he likes feeling comfort But he doesn't like to feel shame and there's a lot of shame that guys have around their dick There's a lot of shame that guys have around sex They don't want to approach and they don't want to tackle we kind of shove that stuff underneath the carpet We don't really want to talk about it We don't really ask ourselves these questions.  Okay, I guarantee you for a lot of guys out there You might be in the same position as this dude where you feel like oh I have no problem when we're making out at the club But when I bring them home and the pants come off nothing's happening. We'll start with that When you bring the girl home when you're in that situation try and make out with them a little bit more Spend more time doing the sorts of stuff.  There's a lot of psychology going on There's a lot of moods and women are much more attuned to this than men are but just because they're more attuned to it Doesn't mean that it doesn't happen for men as well. So start asking yourselves these questions And start trying to figure out the sorts of sorts of things that you can start doing in the bedroom That's gonna make you more comfortable That's gonna make you actually get hard and then you can move on to the stuff that you're nervous about the stuff They have a little bit of anxiety over and that you're stressed out Move on to that sort of stuff once you're comfortable now This is gonna take some time You might need to be seeing someone for a little bit of time for this to happen The good news is is that women are very understanding. Okay, most of them unless they're like huge bitches They're gonna be pretty understanding about this and they're gonna probably be down to work with you through it They probably have some anxiety about sex as well that they're you know that they're dealing with and stuff like that Women like to feel comfortable as well. So the more comfortable they feel with you the more The more they feel like they can relax the better the sex is gonna be the same thing for you Once you start feeling comfortable with the girl once you start moving on to those other things that stress you out You're gonna be a lot more confident and you're gonna be a lot better in bed So my recommendation is find those things that turn you on think actually think about it Let's start doing those things and move on to the stuff that stress you out That's that actually, you know, you're worried about the stuff that you don't get hard for Move on to there after that and I would recommend that you stick with a girl for a long period of time And when I mean long, I mean you're having sex with her multiple times You're seeing her again and again To try and figure this problem out once you start getting more confident with your sexuality once you start getting more confident with You know With your dick then you're gonna start having a lot more sex You're gonna start having a lot more fun when you have sex and this won't be an issue for you I remember in my life.  You know when she tells her friends or whatever is she gonna think I'm bad Is she gonna think I'm doing this that or the other thing wrong? Try and push all that out of your mind And I know it's really tough at the beginning and I had trouble with this too not with one girl But I actually had mine was kind of a interesting situation I started bringing I started getting a lot of threesomes So I would bring two girls home and with one girl I was totally fine with but with the second girl being in there I just started to get like a little nervous and Like I just I wouldn't happen for me like I wouldn't get hard and if you think you If you think it's bad when you disappoint one girl because you can't get hard try disappointing two girls. Oh my god It's humiliating So what I started to do is I started to focus on the things that actually turn me on which was you know With one girl I've that felt more comfortable and more natural for me So what I did was I would focus on a one girl for a longer period of time Wait for me to start getting hard and then I would move on to that both girls at the same time Or the next girl But I would wait till I was a little bit more comfortable with one of the girls till I moved on to the next one And with that I was able to build up my confidence and now I have zero problems With three some zero problems getting hard during those types of situations and I actually just proved that this weekend So there's a happy ending to these stories Hopefully it's helped if you made to the end consider subscribing and come out videos like this every single week guys If you still have questions about this feel free to email me. I don't mind talking about this sort of stuff It's totally natural. I think when you are comfortable with your sexuality when you are confident sexually That's when you can really attract and get the girls that you want in life Begin with the end in mind if you don't if you aren't confident With the ending if you don't have that in mind then it's gonna be very difficult for you to get to it And hopefully your goal is to have sex with an awesome attractive hot girl So thanks a lot you guys and good luck out there


So, in the previous class, we talked about problems where players were allowed to get into binding contracts with each other and we asked what kind of payoffs that can players achieve or that are attainable by the players under such kind of contracts. So, we were not talking about designing the optimal contracts, but rather asking if players have to get into binding, have the option of getting into binding contracts and arbitrary contracts are allowed, what kind of contracts would they sign and with such contracts being added and augmented to the game, we wanted to know what kind of payoffs can be achieved. So, today what we will do is we will relax the condition that players are allowed to get into binding contracts and we will however still allow players to communicate with each other. So, there will be communication and players will have a wide amount of communication possibilities, but they will not be allowed to get into binding contract. So, that does not mean that binding contracts are impossible, it just means that every contract need not be binding. So, now in order to talk about this, let us consider the following, we will consider the following game as an example. We have a game with two players, player 1, player 2, player 1 has two strategies X1, Y1, player 2 has two strategies X2, Y2, payoffs of the players are 5 comma 1 here, 1 comma 5 here, 4 comma 4 here and 0 comma 0 here. Now, there are three Nash equilibria in this game, you can eyeball them quite easily. The first Nash equilibrium is X1, X2, there is another Nash equilibrium which is Y1, Y1, Y2 and in addition to this, there is also a mixed Nash equilibrium in which player 1 randomizes say half X1 comma half Y1, half X1 comma half Y1 for player 1 and half X2 comma half Y2 for player 2 and the payoffs that they get are, you get 5 comma 1 here, 1 comma 5 here, you can check that they get 2.5 comma 2.5 in this. So, the problem that we now, we are now going to address is where players are allowed to communicate but there is no scope for them to get into binding contracts. So, the question therefore for us is what does it mean, what kind of strategies are now feasible now that players cannot get into, can communicate but cannot get into binding contracts. So, in the absence of communication players were randomizing independently. So, each player was choosing his or her mixed strategy independently. So, and from there we concluded these three as being the Nash equilibria of this game. However, now that communication is allowed, players need not randomize independently means players could potentially do enter into correlated randomizations. All right. So, in particular they can in fact play what is any correlated strategy. So, any correlated strategy you in this, I am using the notation from the previous class. So, any correlated strategy could be used but remember when players say well let us play this correlated strategy what does it mean for example, it would say let us say it could a one correlated strategy would be there are these four possible combinations here. If a correlated strategy could say well we will play each of them with probability 1, 4. So, x 1, x 2 with probability 1, 4 x 1, y 2 with probability 1, 4 etc. Now, or it could be that players could say well let us play x 1, x 2 with probability half or y 1, x 2 with probability half that is another correlated strategy or another possibilities let us play x 1, x 2 with probability half and y 1, y 2 with probability half etc. Now, remember any correlated strategy that they just discuss and talk about is not binding on the players. So, they may say okay let us play this but when they actually go to choose a particular strategy they may not actually stick to that stick to whatever correlated strategy is part of the plan. So, what kind of strategies can actually then be are actually feasible under the fact that players can communicate but there is no binding agreements. So, or rather let us say forget what kind can you give me an example of a strategy that is feasible under binding agreement but without under communication but with no binding agreements. So, you cannot just pick an arbitrarily correlated strategy because that is you know that actually is because there is nothing to bind the player to playing that particular strategy right. They were also see remember let me also point out one more thing. The set of strategies that can be implemented under correlation under communication but no binding contracts. Now, that set of strategies okay how is that related to the set of strategies that were that are implementable with binding contract with communication and binding contract which one is the subset of which one of course one is a subset of the other that is why I am asking this question but see the point is see think about it this way see if a strategy is of the kind that a player would not like to deviate from it even though it is not binding then he would not like to deviate from it even if it is binding right. So, this the set of payoffs that players can achieve with binding contracts is actually larger. So, the point is that once the once players are allowed to get into binding contracts essentially that that widens the scope of the scope of things that they can do. So, in fact the kind of games that will result out of that are the kind of games that we just wrote in the previous class where there is one extra contract and that there is an extra decision then whether to sign is that contract or not right. So, contracts are the so you so what you have is a game that you begin with and then you extend that game with additional options that come from the contract and you ask which contract would you want to sign any of these contracts alright knowing that when you sign it is binding upon you whatever you are signing on alright ok. So, now that so the so the so now with binding contracts out of the question what play what can players achieve with communication. So, here I have to also make precise what we mean by communication ok. So, again once again you can go in two different ways here one you can start modeling the operations of communication where one player says something then the other player responds or third player says some then the first player plays response to this response etc etc that is effectively communication alright or we say well we do not bother about who is saying what we just say what is the result of all of this communication in the sense that in the in the sense that after all of this communication what is the action that you are going to be chosen ok. So, this is what is this way of modeling what it does is it makes communication implicit essentially we are not modeling the actual exchange of signals but we are saying what is the final result of those signals that are exchanged alright. So, now here so here what we are talking about is communication that is happening between in which players are openly then directly communicating with each other directly communicating which I will explain what indirect communication also means in the moment. So, what this means is that players can conduct a joint experiment like a coin toss or whatever all observe the outcome of that experiment and then decide what they should be playing based on an outcome of the experiment which all of them observe alright. So, this is direct communication essentially so they can this is what it would mean to correlate their actions you know by this is what it would mean to correlate their actions alright. So, now what do I mean by this so I will give you an example of a strategy that players can create now with communication any correlated strategy could be used but not every correlated strategy is something that they would want to stick to. So, I will give you an example so here is an example of a strategy that they would want to actually stick to. So, for example they may say let us play the first equilibrium x1, x2 so these are three Nash equilibrium alright. So, you take the first equilibrium x1 play that with probability half and play y1, y2 with probability half. So, what does this mean how are we implementing this players toss a coin everyone witnesses the outcome and everyone has agreed that this is what will be played with based on the outcome. So, if it is heads you will play they would both play x1, x2 if it is tails they would play y1, y2 alright. The question so you can I can this now is another option that is present in the that is now present in the game. Now question is with this option now player has to go back and but before the coin is tossed decide whether he actually sticks to this option or not and so what are we assuming when he sticks to this option there is no this is not a contract. So, what we are only thing what is being assumed is that if a player will now can only unilaterally deviate from this alright. So, this they have come up with this particular distribution and now they can when it when it comes to actually playing they can only unilaterally deviate from this alright when it comes to actually pressing the button they can unilaterally only unilaterally deviate. So, what does this mean for example if player 1 decides to deviate from this he can say let me play a pure strategy x1 or let me play a pure strategy x2 or let me play something else altogether. But he is when he is unilaterally deviating player 2 is still assumed to continue to play according to this experiment that means if it is heads then he is going to play his portion of the strategy which is x2 and if it is tails he is going to play his portion of the strategy which is y2 alright. So, the question for each player is now assuming that the other guy is sticking to this correlated strategy would I want to stick to this okay. So, now if you look at this particular this particular strategy that has been created is this something that players would want to stick to assuming the other guy also sticks to it yeah. So, this is actually a combination of two pure strategy Nash equilibria of the game. So, it has obtained by taking half of this Nash equilibrium and half of this Nash equilibrium. Now, if player 1 suppose deviates from x1 to x instead of playing this suppose he decides to play x1 okay let us take a pure strategy x1 right then what would happen because it is a Nash equilibrium he of course here it remains x1 x2 in this one but here shifting to x1 is actually not profitable because y1 was the best response to y2 because y1 y2 is a Nash equilibrium. Suppose player 1 plays x1 as a deviation from this half x1 x2 half y1 y2 this one okay p2 and p2 continues to play as per let us call this mu as per mu okay. So, that means he is going to play so if since he is playing as per mu what this means is that if it is heads he is going to play x2 otherwise he is going to play y2 which means that essentially he is going to play x2 with probability half and y2 with probability half right. So, player 1 suppose he deviates to a let us say to playing x1 then look at the payoff that player 1 is going to get player 1 that will get a payoff x1 comma whatever it is that comes from whatever it is that player 2 is going to do. So, he is going to do x2 with probability half comma y2 with probability half. So, this is the payoff that player this is the deviation payoff to player 1 deviation utility to player 1. So, player 1 has deviated from his from playing x2 in this in this coin in this in the tails event instead of playing x2 he is now saying he is going to play x1 right. So, then in that not x2 what was I saying y1 instead of saying playing y1 he is going to play x1 right, but then y1 was a Nash equilibrium was part of a Nash equilibrium. So, what this means is this this here is actually less than equal to and the same thing would hold if I said if player 1 instead of playing x1 as a deviation was to suppose playing y1 as a deviation if he instead played if I replace this thing by y1 here I would get y1 here out here and this would remain I would this would remain y1 I would get y1 here sorry not here I would get y1 here in place of this x1. Now the half here is not important at all actually that this is in fact 50-50 probability what is important is that these are convex combinations of the Nash equilibria of the game if there are more Nash equilibria you can put all of them in and you take all the pure strategy Nash equilibria and take their convex combination in fact you can take even mixed value strategy Nash equilibria take their convex combination there will be no incentive for any player to deviate because whenever he deviates he is basically going all these inequalities are only pointing in the in one direction he is going worse off than in each of these terms right and you can deviate to a mixed strategy or whatever does not matter. So, which means then with this kind of direct communication where the mechanism is a joint experiment is conducted everyone witnesses the outcome of the experiment and and and based on that outcome the the strategy this thing is chosen the the strategy is chosen this is this kind of this kind of in this sort of communication the payoffs that can be achieved are is actually the convex hull of this set of Nash equilibria of the game. So, the pay so payoffs that what is what do you mean by a converse so it is in fact so that is the exact set of this thing so it is so that you have the converse here in that sense there is a converse payoffs achievable okay so now these so once again I will emphasize this direct communication as an aspect because we will now move to indirect communication okay so once again what is what are we assuming about the direct communication about communication here is that the strategy is designed in such a way that it requires all players to witness the outcome of the experiment okay and then based on the outcome they have to take the choose their choose their actions all right now the so observe now you may think that okay what is the big deal about observing the outcome of the outcome of the experiment but it turns out that if players are allowed to communicate indirectly then they can actually do more all right so let us actually calculate the payoff for just for for completeness sake so what is the payoff that they can get here in this example they can 3 and 3 no half of half this and half this they can get 3 and 3 right so the payoff that they can get is this leads to the payoff 3 comma 3 for the players now can players do better than 3 comma 3 and that is what I will show you that it is actually possible to do better than 3 comma 3 okay by by allowing mediation I mean you can the half is not important as I said it is like you can take any convex from yeah yeah yeah because each of these terms right does an inequality oh you mean this you mean it would not be 3 comma 3 anymore right yeah yeah yeah yeah so but I this is I will just give you an example I mean this is so so actually we I will eventually we will draw a figure in which all of the and all the regions are indicated so that that is the the 3 is not that important that is actually the highest the better payoff that they can get okay so because of symmetry that you will you will see that they can in fact get do better through indirect communication it would still be it would be still achievable under this under this kind of communication under direct communication no problem yeah that would still be achievable under under direct communication so the set of payoffs achievable through direct under direct communication is the convex hull of all all the set of all Nash equilibria of the loop okay okay so now here is just now as I said this this requires them to witness the experiment witness the outcome of the experiment now if you let us now generalize this a little bit and what I will do is I will allow for mediation okay now mediation may look like initially may look like I am allow bringing in one more player you know mediator into the picture but what you will see is actually that there is that mediation is in fact just another form of indirect communication between the players okay so this was direct communication where players are where all you know players are witnessing everything together you can once you allow for indirect communication you have you you are basically you have the you can actually achieve more all right so now let us let us bring in so first let us bring in mediation so how does mediation how would mediation work so suppose you have a mediator okay now what the mediator would do is mediator would announce announces that he is going to be using a correlated strategy okay mediator announces a correlated strategy strategy mu which is a probability distribution on the set of all action but now here is what he would do the mediator only communicates confidentially with each player okay there is communication only there is no common experiment that he can that all players witness he communicates confidentially with each player means that he will tell each player a recommended action right so the mediator so he for example he will tell player 1 you play x1 he will also tell player 2 confidentially that you play y2 okay players would know that that the recommendations are being generated from a certain correlated strategy this correlated strategy mu all right but they do not know what has been recommended to the other player they just know that the recommendations have been generated through this they know their own recommendation all right but they do not know what has been recommended to the other player this is clear this is the role of a mediator this is indirect communication okay so here is an example so suppose a mediator recommends this so with probability one third he says you play your first Nash equilibrium x1 x2 with probability one third you play y I am going to give you y1 y2 and with probability one third remember there was this another payoff here 4 4 payoff yeah so with another probability one third I am going to recommend you y1 x2 the as I said the mode of communication is this that you have a mediator who talks confidentially to the players okay so this is this is your echo to player 1 this is a echo to player 2 each player only hears his own record he knows that and each player knows that the recommendation has been generated through this probability distribution mu is this clear okay now what this does is basically what is happening behind the scenes is not known to the players players do not get to know what happened in the experiment they just know what you they they just know that what part they need to play respectively right they just know that okay mediator has told me to play this I will that that is what I need to and that is what has been that is all he knows the player knows okay he does not know you know whether tales came whether heads came you know whatever whether eyes game or whatever yeah yes yes yes yeah so this is a trusted mediator okay so the mean you will later see that the mediator is actually just is not really another player it is just a it is just a sort of a thought device okay so eventually what we will do is we will reduce this to a game of indirect communication between the players itself okay so so for the moments are so that is why I assume that the you know mediator is some some software that they have that is generating these recommendations and they have all trust they all trust that software so the framework is like this that the mediator just recommends something to these individual players and now the because players do not know what is happening behind the scenes right they each have partial information about what has actually happened okay they only know what has been recommended to them okay so I will give you an example you know a lot of platforms we use today are actually of this nature right so when Google Maps tells you that you know take this route you just know that you Google Maps has told you to take this route maybe there is another person who wants to go from the same origin to the same destination and Google map has said you know take some other route okay or let us say in finance broker tells you you know buy this who knows maybe to some other client he is telling is telling something else he is saying do not buy this buy the or buy that buy something else or he may be saying he will sell this right so all of these actually form all of these platforms that we use are actually what they are actually doing is doing this kind of mediated communication we only know what has been recommended we have a general impression of what kind what you know how the recommendations are being generated now if the platform is actually doing what it should be doing okay then it should it should be some if the platform for the platform to let us say be successful what do what do you expect to have what should how should it produce its recommendations so for example why would I want to keep you know why would I want to keep using Google Maps or rather why would I want to follow the route given by Google Maps so it should if I deviate from Google what has been recommended to me by Google Maps it should give me a higher travel time right I do not care what has been recommended to the others what I only know is somehow Google Maps is figuring out its set of recommendations in such a way that if I stick to my each if I if each guy sticks to his recommendation right then the rather for each guy it is optimal to stick to his own recommendation assuming the other guys stick to it okay so I will come to this remember this point so the essentially what is what is going on with a mediator is some sort of this sort of partial information sharing need to know basis you each player is just told what his own recommendation is and based on that he needs to now he needs to now take an action so but for a strategy to be implementable through a mediation like this what should satisfy it should satisfy a basic obedience requirement that it should be it should be in my interest to obey the recommendations given by Google Maps assuming the others also are obeying all right so let us come to we will come to this in a bit more detail so here is then the strategy that this mediator announces okay now what does this mean let us let us understand this a little so so let us see how this strategy would work so suppose the mediator says x1 is the recommendation to player 1 now what does player 1 know from this recommendation he knows that player 2 has been recommended x2 with probability 1 since he has been player 1 has been recommended x1 he knows that this mediators mediators coin toss has resulted in this right because that is the only way he gets to he gets a recommendation x1 so he knows that player 2 has been recommended x2 now if player 2 is playing x2 is it optimal for player 1 to continue to play x1 yes all right so if player 1 here is x1 it means that implies that player 2 has been recommended x2 so as I said this player this mediator forgot to write this maintains partial information okay now suppose the player 1 hears y1 as a recommendation now if he hears y1 what has what does that mean what can he say if he hears y1 then he means that either this has come about or this has come about but because the players do not get to witness the experiment itself he does not know which one he just knows that one of these two has come about but from there what he can say is that well player player 2 has been recommended y2 with probability half or it is that he has been recommended x2 with probability half okay so there is a 50 percent chance that he is that player 2 has been recommended y2 and 50 percent chance that he has been recommended x2 that player 2 has been recommended x2 okay then player 1 knows that 2 has been has been recommended y2 with probability half or x2 with probability half right now look at the payoff now now suppose if you if player 2 is then going to be recommended x2 with probability half and y2 with probability half then what is the then you have half of this plus half of this as the payoff that player 1 sees right so so what is the payoff he is going to get from x1 he is going to get 2.5 what is the payoff he is going to get from y1 he is also going to get 2.5 so both x1 and y1 given are giving him 2.5 he is been recommended y1 so it is in his interest to to play y1 okay so in other words he has no rather let us put it this way he has no incentive to deviate from the recommendation okay so no incentive to deviate from the recommendation and a symmetric thing holds for player 2 as well now with this now what is the payoff that they can get can you calculate this is of course again symmetric yeah they get 3 3 and one third so earlier they were getting 3 3 as the symmetric one this is they are get they get 3 and one third okay so the so what has happened here the the way this has worked is this mediator has maintained a kind of confidentiality need to know whatever you want to call it and through that implemented this strategy now I will tell you you can see why confidentiality is actually important here so suppose okay suppose now here if you look at what player the case with player 2 okay player 2 has been recommended x2 here okay he is also been recommended x2 here now if player 1 knows okay suppose this was the outcome okay let us say this this thing was the outcome then player 1 would get outcome of the experiment of the coin toss mediator tosses the coin it turns out to be this this is the outcome so he will tell player 1 y1 and he will tell player 2 y2 now when player if the outcome of the coin tosses revealed to the player then player 1 when he sees y1 he knows that player 2 has been recommended x2 if the outcome is also revealed then he knows that he is been recommended x1 and player 2 has been recommended sorry he has been recommended y1 and player 2 has been recommended x2 okay now if player 2 has been recommended x2 is y1 the best response to that no y1 is not the the best response, X1 is the best response. X1 actually is strictly better than Y1. So player 1 sticks to playing Y1 only because he is not been told what the outcome of the coin toss actually is. It is because player 1 is just knows this. It could be a Y2, it could be this with probability half or this with probability half. And as a result of that player 1 agrees to play Y1. If there is this too much information then player 1 would not agree to play Y1 in this case. So this is where mediated versus unmediated makes a difference. See the direct communication that I was telling you is essentially where the players can observe the experiment itself. Whereas here there is no observation of the experiment. They just observe the action that has been recommended to them. And there is a vast difference between the two. So here basically the mediator is saying Tumam Khau, Gutliy Ahmad Ginoz do not worry about what is happening behind the scenes. You have been told is just do that. So this is obviously a much more general strategy because now there is also a possibility of partial information which is built in as a part of the definition of the strategy. So with direct unmediated communication such a strategy cannot possibly be played because players have to witness the experiment when they are communicating directly. So you ask me what is the definition of direct communication. Direct communication is where the sample is actually directly observed. Whereas here function of the sample is observed which is the recommended action. Is this clear? So now let us come back to the Google Maps example. So Google Maps is doing something like this.  They are suggesting other articles etc. etc. What all of them are doing is something like that. If Zomato tells everybody to go and eat in a particular restaurant, everyone will go there and crowd the restaurant and nobody will actually get a great experience. So the kind of optimal thing for Zomato to do is actually spread around its recommendations also. Thinking of various things and so on. So actually then this kind of puts into this thing. If you think of mediator not as a fictitious entity but in fact as a real player then you can actually think of things like what are the feasible recommendations, what recommendations maximized if mediators revenue, the platform revenue etc. etc. All bunch of other kind of questions can be thought about in this.