Now stop the video for 30 seconds and think, would you confess or not? Always keep in mind
that you have NO emotional attachment to the other prisoner, so please don't think "I would
never betray my friend" - that's not the point of the game.
HOW TO WIN AT THE GAME OF LIFE WITH A SCIENTIFIC APPROACH – GAME THEORY
When we find ourselves making important decisions in our daily lives, too often we let our emotions
influence our choices even when we know it is wrong. One of the biggest problems nowadays
is the inability of many people to analyze a problem analytically and rationally, thus
finding themselves making most of their decisions solely trusting their instinct. The problem
here is that making instinct-based decisions should be our last resort, and should be done
in absence of objective information that would allow us to make a rational and calculated
decision. Making decisions on instinct is often a lazy way of acting on something. In
fact, almost all bad decisions, the ones that end up getting us into trouble, are those
made on an emotional, rather than on an analytical basis. Today I am going to talk about Game
Theory, what it is and what it's for, and finally we're going to see in which fields
this approach can help us make the right decisions in everyday life, without letting our emotions
get the better of us. Game theory has in fact a wide range of applications,
including psychology, warfare, politics, economics and business. Despite the progress made in
this field over time, game theory is still a young and developing science.
During the video we will also play a couple of games, I suggest when we get to that point
to pause the video and think about the solution before continuing.
BUT WHAT IS REALLY THE MEANING OF “GAME THEORY”?
Game theory is a theoretical framework for devising social situations between competing
players. In some respects, game theory is the science of strategy, or at least the optimal
decision making of independent, competing actors in a strategic context.
Don't think of a game simply as a “game”, but as a situation you face in everyday life
where you interact with several people and each of those people will have a personal
gain or loss based on the decisions made by the other people.
The key pioneers of game theory were the mathematician John von Neumann and the economist Oskar Morgenstern
in the 1940s. The theory written by the Mathematician John Nash is considered by many to be the
first significant extension of von Neumann and Morgenstern's work.
The centerpiece of game theory is the game, which serves as a model of an interactive
situation between rational players - I repeat "between rational players" because the theory
assumes precisely a certain level of rationality among those who play. The key to game theory
is that one player's gain depends on the strategy implemented by the other players. The game
identifies the identities, preferences, and available strategies of the players and how
these strategies affect the outcome. The actions and choices of all participants in the game
affect the outcome of each. Although there are many types of game theories,
the best known are game theories which we can divide into cooperative and non-cooperative
games. Cooperative game theory is a game between coalitions of players rather than individuals
and questions how groups form and how they distribute gains among players.
Non-cooperative game theory has the sole purpose for each individual to achieve their goals.
The most common non-cooperative game is the strategy game, in which only the strategies
available and the outcomes that will be obtained from a combination of choices are listed.
A simple example of a real-world non-cooperative game is Rock/Paper/Scissors.
Now let's look at a couple of practical games we can use as examples to analyze game theory.
First, let's look at an example of a non-cooperative game called "The Prisoner's Dilemma" - it
is important to understand that the goal of this game is to make the maximum individual
gain from the situation described.
There are two criminals, let's call them Mark and Luke, who have just been arrested for
committing a crime. With the evidence gathered by the police, the Judge would already be
able to sentence them both to 2 years in prison each. However, in order to get a confession,
the police decide to interrogate them separately and offer them some options. Notice that neither
prisoner has the means to communicate with the other before questioning. The police present
each arrestee with 3 offers. Option One: Neither confesses and each spends
2 years in prison. Option Two: If one of them confesses but the
other does not, the one who confesses will be released immediately, but his partner will
be sentenced to 10 years. Third option: If both confess, they will each
receive a five-year prison sentence. Now stop the video for 30 seconds and think,
would you confess or not? Always keep in mind that you have NO emotional attachment to the
other prisoner, so please don't think "I would never betray my friend" - that's not the point
of the game. In theory if this were a cooperative game
neither should confess. Combined they would spend 4 years in prison (2 years each), however
since as previously said there is no emotional bond between the two of them, in theory if
one of them knew that the other doesn’t confess, then he should automatically confess
to be freed immediately. Furthermore, if things go wrong and his partner also confesses he
would end up being sentenced to 5 years instead of 10, which isn't as bad.
So, what is the right choice? Yes, you got it right, the correct choice is to confess,
hoping that the other person will not confess. But if so, if they both confess then the result
will be that they will each be sentenced to 5 years in prison, and this is the final solution
of this example of game theory. If they both play optimally, then they both end up in prison
for 5 years. But why?
According to what is known as the Nash equilibrium both players in this situation will end up
making the best move for them individually but the worst move for them collectively.
A player has found the OPTIMAL STRATEGY - THE DOMINANT STRATEGY when he makes the best choice
for himself regardless of what his opponent does - remember, here we are always talking
about opponents acting rationally. If Mark confesses he could be released immediately
or at worst (in case Luke confesses too) receive a 5 years prison sentence. If he chooses not
to confess in the best-case scenario he would be sentenced to two years, but in the worst
case to 10 years, which is much worse. The best choice here is ALWAYS to confess. And
here we could talk endlessly about how many people judge their choices based purely on
results. Sometimes in life you can make the right choice and get worse results than if
you had made a bad choice, but the results can sometimes be influenced by various random
factors over which we have no control or by irrational behavior, in this case of our opponent,
that is difficult to predict. Our goal in everyday life is to make the choice that in
the long run, on a large sample of occurrences, brings us the best results regardless of how
external agents act. So, what does the prisoner's dilemma teach
us? The prisoner's dilemma shows that simple cooperation
is not always in the best interest. As an example, when purchasing an expensive item
such as a car, bargaining is the preferred course of action from a consumer perspective.
Otherwise, the car dealership might adopt a policy of rigid price negotiation, maximizing
its profits but resulting in consumers overpaying for their vehicles and at the risk of losing
potential customers in the long run. Understanding the relative merits of cooperation rather
than pure individual gain can help you next time you find yourself bargaining for something.
Limits of game theory The biggest problem with game theory is that,
like most other economic models, it is based on the assumption that people are rational
actors who are selfish and maximize utility. The reality though is that this is not always
true - Sometimes, yes, we are selfish, but we are also social beings who cooperate and
care about the welfare of others, often at our expense. Game theory cannot explain the
fact that in some situations we may fall into a Nash equilibrium, and other times we may
not, depending on the social context and who the players are.
Let now see how game theory changes in cooperative games. In these games the goal is the welfare
of the group, not the individual. While in competitive games we use the Nash equilibrium,
in cooperative games there is what we call the Shapley Value which is a concept used
to assign a reward to each player in a coalition, depending on the marginal contribution that
he/she makes to it. Some points of this value: 1. Each player's contribution is determined
by what they would gain or lose if they were removed from the game.
This is also called the Contribution Margin. For example, let’s say you sell ice creams
in a cafe, and you sell 100 ice creams a day. If one day you are sick and the ice cream
shop sells 100 less ice creams because of it, your contribution margin is 100 ice creams.
2. Interchangeable players have the same value. What this means is that if two people bring
the same contribution to the coalition (e.g. they both produce 100 ice creams in a day)
they should be rewarded the same. 3. Players who contribute nothing to the group
should receive nothing in return. If, for example, in the ice-cream shop three people
work hard and sell 100 ice-creams each and the fourth spends all day on his smartphone
instead of working, he should not receive any kind of compensation.
There are exceptions though, if for example one of the members of the group has had an
accident and is injured - this member will not be able to work and therefore the other
members of the coalition may decide to pay him something anyway.
4. The work should be composed in such a way that all coalition members work and produce
for the group equally over a relatively long period of time.
Now let's see how the Shapley's value formula works.
Let's suppose that Mark and Luke, owners of the ice-cream shop we have just talked about,
sell respectively 50 and 100 ice-creams each in a working day. On each ice cream they have
a profit of 1$. Working together, however, they manage to improve the ice-cream selling
process and combined in one day they sell 200 ice creams! Now, if they had not worked
together they would have sold only 150 ice creams in total, 50 Mark and 100 Luke, but
working together they managed to sell 200 ice creams, and today have made a profit of
200 $! How are these earnings distributed, considering that Luke has been much more productive
than Mark? If Mark alone would have sold 50 ice creams
per hour and if we subtract these 50 ice creams from the total of 200 ice creams sold, Luke
would be given credit for 150 ice creams ... mmm a bit 'too much.
If Luke alone would have sold 100 ice-creams per hour and we subtract these 100 ice-creams
from the total of 200 ice-creams sold Marco would be given credit for 100 ice-creams...mmm
here too it seems too much. But then how do we calculate with the Shapley
formula what is right? First we make the sum of the two values that
would have been sold separately (50+100) and divide it by two. The result is 75. This is
what Mark should receive, while Luke, the more productive of the two, would receive
the remainder, that is 200-75=125€. This is an interesting result because at first
glance probably most of us would have split the profit proportionally 1/3 of the total
to Mark and 2/3 of the total to Luke since this was what they sold separately.
This is clearly a very simple example of how this approach can be used in a game, or in
a cooperative situation, but clearly the same can be done in much more complex situations.
So, what can we really learn from Game Theory and how can we use this knowledge in everyday
life? Well, in a competitive situation Game Theory teaches us how to approach the situation
in an intelligent and rational way, while in a cooperative situation Game Theory teaches
us how to be fair to the group that is part of your coalition.
There are countless situations in every single day of our lives in which we find ourselves
making decisions and very often we end up making the wrong decision - only by improving
our analytical skills and our ability to consider the different aspects of a problem without
trivially simplifying it will we be able to consistently make decisions that will be better
in the long run. If you liked the video and don't want to miss
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