Now let's examine why group rationality is different from the rationality of individuals. Okay, why Nash Equilibrium is inefficient. Let's try to see the reasons why Nash Equilibrium is often inefficient. Okay, so one of the most important messages of game theory is that group rationality, what is good for society, is different from what is good for each individual. Group rationality is different from rationality of individual players, and Nash equilibrium is quite often not efficient, okay. So let's try to see the reasons why this is true, okay? So this leads us to a puzzle. Okay, so let's consider a simple situation where society consists of two players A and B, Andy and Becky. And here is Andy's payoff and Becky's payoff. And let's consider a very simple situation where the society benefit for the society is just a summation of players' payoffs. Okay, society's payoff is a summation of Andy's payoff and Becky's payoff. So let's say this is Andy's profit, $100. And this is Becky's profit, $300. And the society's benefit is the sum of those two numbers, $400. Okay, a puzzle is the following. Well, game theory shows that individual maximizing those payoffs, is not equal to maximizing total payoff. This is a puzzle because if, you know, Andy is maximizing his payoff, and Becky's also maximizing her payoff, automatically it seems to me that the, society's payoff is automatically maximized. Because society's payoff is just a summation of Andy's payoff and Becky's payoff, okay? Game theory somehow shows that this doesn't happen. Quite often this doesn't happen. So the puzzle is why this simple intuition fails. And there are basically two reasons why Nash equilibrium is different from maximizing society's benefit, okay? The first reason is the following, okay? So, Andy is trying to maximizing his payoff by acting alone, okay? Andy's effort alone cannot create social benefit, okay? The same is true for Becky. Becky's trying to increase her payoff alone. But Becky's effort alone cannot create any social, social benefit. But, if they act together they can create benefit. Now this is one possibility, okay? So this situation is clearly captured by a game we have seen in the second week I suppose. The choice of keyboard of compu-, personal computer. So the choice is in between QWERTY keyboard and optimal keyboard. QWERTY keyboard is what we use now. And the design was inherited from the original mass produced typewriters in the 19th century. So most likely the design of QWERTY, what we use today, is not optimal. But we are stuck with QWERTY because lots of other people are using QWERTY. So if you deviate to another design, it's very inconvenient for you. So if everybody's using QWERTY and you have an incentive to use QWERTY. So, both players using QWERTY is a Nash equilibrium. On the other hand, by the same reasoning, if other people are using the optimal keyboard, I have an incentive to play, or choose optimal keyboard. So the situation where everybody is using optimal keyboard is another Nash equilibrium. And obviously the optimal eq- keyboard equilibrium is much better for the society. But, if you act alone you cannot create any benefit. 'Kay, that's the main characteristics of this coordination game. So in this simple situation society may be trapped in a bad equilibrium. This is one of the reasons why individual se-, the rationality of individual is different from the rationality of society, okay? So this phenomenon is called coordination failure, okay? So, in coordination game individual player fails to create any society's- benefit for the society. They should act together. And in such a situation, often times, society may be trapped in a bad equilibrium. Okay, this is number, reason number 1, about why Nash equilibrium is not best for the society. Okay, second reasoning. Well, in the first reasoning we considered the situation where Andy, alone, cannot create any social benefit. But now let's consider the situation where each player alone can create some social benefit, okay? In this case, Nash equilibrium is inefficient if the benefit you are creating is not coming to you, okay? So you alone can create some social benefit, but benefit is not coming to you, okay? So in such a situation the outcome is often socially inefficient. Okay, so let me go back to this simple diagram, Andy's payoff and Becky's payoff, okay. So the best example to make my point is the famous game of I scratch your back, and you scratch my back, okay? So if we both scratch our backs it, it's better. But let's examine Andy's incentive to scratch Becky's back. Okay, if I, as Andy, scratch your back, it's costly to me. So, Andy's payoff is decreasing, but Becky's payoff is increasing. Altogether, the society's payoff is increasing. But, benefit, social benefit is all coming to Becky, it's not coming to you. Okay, so in this situation, each individual, say Andy, doesn't have any incentive to cooperate. But, if they both cooperate, if I scratch your back and you scratch my back, well, so I'm scra-, Andy is scratching Becky's back. This is the original situation. Andy's payoff is very low but Becky's payoff is very high. But now suppose Becky also scratches Andy's back. Okay, scratching is costly so Becky's payoff decreases a little bit, but Andy's payoff increases. And altogether, compared to the original situation, their payoff increases, okay? So, even though each individual doesn't have any incentive to cooperate, if they cooperate, they may be better off. So if benefit of good behavior doesn't come to you, then rational individual may not take socially desirable behavior. Okay so the previous slides I explained why society maybe trapped in a bad situation. But let me examine the other side of the coin. That is now let's examine why good point is unstable, why good point may not be sustainable. So, let's start with the good point and examine the incentive of each player. Okay, so at the best point maybe you can increase your payoff by taking antisocial behavior, which reduces total payoff to the society. But cost of your bad behavior may be coming to the other players. Okay, you are not paying the cost of your bad behavior. In that case you have an incentive to cheat. Okay, so global warming is a perfect example. So the original situation now is a good point where all countries, country A and B are trying to stop global warming. This is a socially desirable outcome. Okay, but, say country A has an incentive to pollute. Because by polluting, you know, country A can produce lots of products. So the net benefit for- for country A could be positive. But other countries are suffering from pollution. And country B's payoff decreases, and in total the global payoff may be decreasing, okay? So this pollution is antisocial behavior which reduces total benefit to the society. But this country is gaining, and the cost of this antisocial behavior is paid by other countries. And in total, society's payoff may be decreasing. Okay, so if cost of cheating may be paid by- if cost of cheating is paid by other players, you have an incentive to cheat. Okay, rational individual may want to cheat at the best point for society. Okay, so let me summarize the second reason why Nash equilibrium is inefficient. That comes from the effect to other players. Rational individual who maximizes his own payoff ignores the effects to other players, okay? So therefore, rational individual may not take a good behavior that greatly benefits others if it's costly. By the same token, rational individual may take bad behavior that greatly harms other players, if the bad behavior is profitable for him. Okay, so this is probably, the effect to other players ignored, this is one of the most important reasons why maximization of it- each individual payoffs is not equal to maximization of total payoff to the society. Therefore Nash equilibrium is quite often different from best outcome for the society.
