Plato, in two of his texts, the Laches and the Symposium,
explains how Socrates recalls an episode from the famous battle of Delium
in 424 BC between the Athenians and the Boeotians. The synopsis of his passage goes as follows:
Consider a soldier, at the front of the Boeotian line, having the following realization:
If our defense is successful, I still risk the chance of dying. If our defense is unsuccessful,
I will almost certainly die. Based on this reasoning, it seems that the
best alternative for the soldier is to run away regardless of who is going to win the battle.
Now imagine if all soldiers were to exhibit this very reasoning at the same time. If such an event
would occur, they would all probably realize that they would be better off running away.
This seemingly simple yet incredibly reasonable hypothesis
is one of the first historical instances of game theory.
Flash forward 2368 years in 1944, Hungarian-American mathematician
John von Neuman published a book titled “Theory of Games and Economic Behavior.”
This foundational work contains the method for finding mutually consistent solutions
for two-person zero-sum games.
This great book introduced game theory as a concept, thus extending its application to fields
like economics, politics, and sports, and leading to the expansion of the array of scientists that
showed interest in it. One of those scientists was the legendary John Nash who won the Nobel Memorial
Prize in Economic Sciences in 1994 and popularized the idea of Game Theory as we know it today.
Something very fundamental about game theory is that it doesn’t get its name from the preconceived
notion of a game as we understand it. A game in game theory is any interaction
between multiple people in which each person’s payoff is affected by the decisions of others.
Namely, any interaction you are part of, under certain circumstances,
can be analyzed with game theory in order to produce the most beneficial outcome.
But before we get into the mechanics, let’s lay out the main principles:
A skeptical person would automatically assume that these rules can’t be applied to real life,
since most people operate in a strictly emotional and irrational manner.
Stay with me for a second.
Let’s dive a bit deeper and you will open your eyes to probably the most important
decision-making theory ever conceived.
Prisoner’s Dilemma is the most widely
mentioned game in game theory. The basic premise is how to establish a mutually beneficial strategy
between two members of a gang that got arrested and face potential imprisonment.
The rules are as follows:
This matrix depicts the different choices
and each number signifies the number of years to serve according to each choice.
Since both members can’t interact with each other,
the obvious, mutually beneficial choice here is to betray.
Choosing to remain silent constitutes a high-risk choice,
since the other party could betray and the party that remained silent will serve 3 years in prison.
Betraying sounds a bit cruel, but, in this specific game, it is optimal.
Stay with me and I will explain in a bit how this strategy can actually change.
Game theorists usually coin the terms dominant strategy and Nash equilibrium to distinguish
the kind of strategies followed by the players. These two terms are usually used together and form
the basis upon which game theory is founded. Dominant strategy refers to strategies that are
better than other strategies for one player, no matter how the opponent may play. In the
prisoner’s dilemma case, the dominant strategy for each player is to betray.
The term Nash equilibrium is used since John Nash explained the essentiality
of equilibrium in his landmark work – Equilibrium points in N-Person Games.
In essence, what he proposed, is that, even in high-level competitive games,
like Google vs Apple, USA vs Russia, there exists an “equilibrium” where
no side would benefit by changing its course. At this equilibrium, each side knows its adversary
very well and sticks to its strategy. For instance, in the prisoner’s dilemma,
the Nash Equilibrium is the bottom right square of the matrix - both prisoners to betray.
What makes Nash’s theory of equilibrium so special, is that
it presupposes that in each game there is at least one point of equilibrium and
all players will be better off trying to find it and form their strategy around it.
This momentous revelation helped people in disciplines like politics, war, economics,
business and social theory understand the world better and form better strategies.
The inception of Nash equilibrium was portrayed falsely in the wonderful movie “A beautiful mind.”
While this scene wants to point out the importance of cooperation,
it is not an example of a Nash equilibrium.
A Nash equilibrium is only reached when all players adopt a strategy where
no single player, by changing his or her strategy, can obtain a better outcome.
In the example shown in the movie, that’s not the case. Assuming that everyone prefers the blonde,
any one of the guys could independently change strategy by going for her.
Therefore, if no one else goes after her, she could accept him and he could be the only one
ending up with her. Hence, the proposed strategy is not a Nash equilibrium. A Nash equilibrium is
really only obtained when all the men follow the strategy of going after the blonde.
According to Wikipedia, researchers found out that
if two players play prisoner's dilemma more than once in succession and they remember
previous actions of their opponent and change their strategy accordingly, greedy strategies
tended to do very poorly in the long run while more altruistic strategies did better.
The researchers used this to show a possible mechanism for the evolution
of altruistic behavior from mechanisms that are initially purely selfish, by natural selection.
The essence of Game theory is that it looks at strategic decision-making and
offers insight into the dynamics of human rivalry.
Apparently, even if people or companies rationally follow their own self-interest,
the best outcome is hard to reach when they can’t or don’t cooperate.
Therefore, the best strategy is for one to continually scan the “market” for potential
alliances and keep playing games so that one can understand them well.
That’s what I love about game theory. It approaches the “game of life” from its most
axiomatic principle, that of evolution.
Evolution equals adaptation and therefore life is an omnipresent game of adaptation.
Humans always compete at first. But, given the right circumstances, humans will choose
cooperation because it is the main strategy that helped us survive and thrive after
years of adversity and struggle to compete against different forces of nature.
I always believed that change and equilibrium start at the micro level.
And that is something we fail to grasp because we are usually consumed by events at the macro.
What each of us could do is to use game theory in our most challenging decisions and
in our closest relationships. Regardless of the circumstance, try to think like a game theorist.
Ponder questions like: Are the actors in the situation rational?
Are we able to reach Nash equilibrium?
Do they act according to their self-interest?
Do they understand the rules of the game?
Is their dominant strategy really that dominant? If you see that most game theory parameters
aren’t met, you know that you have to change your approach. You either need
to also act irrationally, which is something I wouldn’t suggest, or you need to step away
and find better players or games. The choice is always yours.
Life oftentimes feels like a game. And we make the game better,
by learning how to play.