The Pinnacle of Decision Making

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 fish passage goes as follows: Consider a soldier at the front of the battling 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 were to occur, they would all probably realize that they would be better off running away. The seemingly simple yet incredibly reasonable hypothesis is one of the first historical instances of game theory. Flash forward 2,368 years, in 1944, Hungarian-American mathematician John von Neumann 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 game as we understand it. A game, in game theory, is an interaction between multiple people in which each player’s payoff is affected by the decisions of others; namely, any single interaction you’re part of 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:

1. A game needs to include multiple players.
2. The players need to interact with each other.
3. There needs to be a reward.
4. We assume that players act rationally.
5. We assume that players act according to their personal self-interest.

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 potentially imprisonment. The rules are as follows:

1. The players of the game are prisoner A and prisoner B.
2. The players can’t communicate with each other.
3. If A and B each betray each other, each of them serves two years in prison.
4. If A betrays B but B remains silent, A will be set free and B will serve three years in prison, and vice versa.
5. If A and B both remain silent, both of them will only serve one year in prison.

This matrix depicts the different choices of each member and signifies the number of years to serve according to each. Prisoner’s Dilemma exemplifies to a great degree the substrate of human nature. The irrational, self-interest-driven gang member will most probably choose to betray his counterpart, thinking that he will get a better deal. This idiosyncratic choice will most certainly lead to a disaster for both parties, since they will get the worst deal possible. The obvious, mutually beneficial choice here is to keep silent.

The main idea behind this game is to expose the inherent tendency of humans to display a lack of cooperation. In similar games, game theorists usually coin the terms “dominant strategy” and “Nash equilibrium” to distinguish the kind of strategies followed by the players. Those 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.

Those strategies might be great in the case of non-alternatives, but if you’re part of a game with more dominant strategies, which means its player has his own dominant strategy, then they aren’t optimal. In the Prisoner’s Dilemma case, the dominant strategy for each player is to betray. And here is where the term Nash equilibrium comes into play. The term 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 high-level competitive games, like Google vs. Apple or 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 upper left square of the matrix, which means both prisoners need to stay silent. 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 exceptionally in the wonderful movie “A Beautiful Mind.”

Gentlemen, deep breaths. Yes, you might want to stop shuffling your papers for five seconds. I will not buy you gentlemen here. Oh, we’re not here for beer, my friend. Oh, does anyone else feel she should be moving in slow motion? Will she want a large wedding, you think? Should we say swords, gentlemen? Pistols at dawn! Have you remembered nothing? Recall the lessons of Adam Smith, the father of modern economics. In competition, individual ambition serves the common good, exactly.

Every man for himself, gentlemen, and those who strike out are stuck with their friends. I’m not gonna strike out. You can lead a blonde to water, but you can’t make her drink. I don’t think you said that. All right, nobody move! She’s looking over here! She’s looking at Nash! Oh, God! All right, he may have the upper hand now, but wait until he opens his mouth. Adam Smith needs revision. What are you talking about? We’ll go for the blonde. We block each other. Not a single one of us is going to get her. So, then, we go for her friends. But they will all give us the cold shoulder, because nobody likes to be second choice. But what if no one goes for the blonde? We don’t get in each other’s way, and we don’t insult the other girls. That’s the only way we win. That’s the only way we all get laid.

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 to continually scan the market for potential alliances. People who can forge strong alliances will eventually become part of oligopolies and thus dominate their market; the rest will consequently be ostracized. 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 thrive in 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. The sad thing is that after establishing our sovereignty, we overpowered other species and, in most occasions, nature itself. But eventually, we turned ourselves against each other. There are a variety of factors that affect the descent to the point we have reached, but a game theory mindset can work to our advantage.

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. It is interesting to be in the know and discuss and argue about politics and national strategies, but at the end of the day, the trigger is pulled by the respective strategists. What each of us could do instead is to use game theory in our most challenging decisions, in our closest relationships.

Regardless of what decision you have made and how this will impact your future, 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 rationally, 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 often times feels like a game, and usually the winners are those who know how to play. Mindful living.