Game Theory: Winning the Game of Life

Are you the type of person to analyze every second of the interaction you just had with someone for hours on end, or are you normal? Either way, you probably don't think all that hard about every single detail of the decisions you make in social situations. But believe it or not, there's an entire scientific field that applies to social situations and decision-making; we're talking about game theory.

Game theory can be used to analyze both economic and social situations. It's essentially the science of strategy. Just like reality it is trying to model, game theory can get really complicated. And yes, although game theory is relevant to games as we typically understand them, such as poker, most research in game theory focuses on how groups of people interact.

Let's first define what a game is. So what exactly is a game? It sounds like a stupid question—like, who doesn't know what a game is? But games in the field of game theory are a slightly different concept from what you might expect. When it comes to game-theoretic analysis, the game constitutes any interaction between multiple people where each person's payoff is affected by the decision made by others.

Let's apply this definition of a game to a couple of examples. Is Sudoku a game? Well, in the traditional sense, sure. But in game theory, no, Sudoku is not a game. Sudoku is not a game because how you decide to complete the puzzle doesn't affect any other player; there is, after all, only one player in the game—you.

What about Tic-Tac-Toe? Is that a game? Two players can play the game, and each box filled by one of the players affects the other player. Winning requires both players to respond optimally to what the other player is doing. So yes, it is a game. You could also have a situation where two shop owners choose from a finite number of positions where to strategically place their shops for maximum profit. They are each affected by what the other person does since they may be opting for the same market, and there's certainly a win-lose situation here.

Even though placing your shop may not sound like much of a game in the eyes of game theorists, it certainly is. Game theory is the study of games like these, and game theorists try to model games in a way that makes them easy to understand and analyze. I say easy, but a lot of games can end up having pretty similar properties or reoccurring patterns, and more often than not, things can get pretty complicated.

Game theory has two main focuses: cooperative games and non-cooperative games. Most game theory models involve five conditions. It goes something like this: first, each player has two or more choices or sequences of choices; think of these like typical moves in a game, like moving a chess piece. Second, all possible combinations of decisions or plays result in a clear outcome—basically, you can win or lose. Third, it's clear how you can win or lose, and participants will gain or lose something depending on the outcome. Fourth, the players know the rules of the game as well as the payoffs of other players, meaning everyone is aware of what is desirable to the other players as well. Fifth, the players are rational and sensible people. Rational here means strictly that when they're faced with two alternatives, they'll choose the option that provides the greatest benefits.

While players know the rules and their opponents' options, they don't know their opponent's actual decisions in advance. So players must choose options based on assumptions of what their opponents might choose. Some game theory scenarios are zero-sum games, meaning one player's win is another's loss and vice versa. Others, however, allow for mutual gains and losses. These games can involve multiple strategies; you can try to minimize the maximum losses another player can cause and make decisions based on probable outcomes.

This all really just sounds a bit confusing, so here, just let me show you—if life is indeed a game, then the first rule is to be skeptical of other people's suggestions. As we said, if it's a game, someone else is going to be competing, so there's definitely going to be competition and sabotage. Perhaps a straightforward and well-known example is the prisoner's dilemma.

The game goes like this: two criminals are caught red-handed and are arrested. Each has two choices; they can each either stay quiet or testify against their friend. Upon arrest, they are each separated and offered a deal: testify against your friend, and we will let you off the hook easy—with one year in prison, and give the other person 10 years. If both stay quiet, the cops can't really prove the more serious charges, and both criminals would spend only 2 years behind bars.

If they both testify against each other, however, then both would get 5-year prison sentences. At first glance, keeping quiet seems like the best strategy—if they both did this, they would be out after just two years. But right before they're about to testify, one of the two thinks to himself: what if I stay quiet and the other guy rats me out? Without knowing what the other person is actually going to decide, it's a reasonable worry to have.

The smartest solution to this would be to react in a way that is beneficial regardless of what the other person does. A Nash equilibrium is actually a state in which no one person can improve, given what the others are doing. This means you're picking the best response to a particular strategy from your opponent.

A quick analysis of the prisoner's dilemma reveals they would both most likely testify, which is the Nash equilibrium for this problem. This is because, regardless of what the other person does, testifying will lead to a maximum sentence of 5 years—with the potential for a 1-year sentence. Meanwhile, if you don't testify, you could end up with a 10-year term. It's easily the safest thing to do, considering neither party knows what the other is going to do.

Even though both criminals are better off if they just stayed quiet, here the individual incentive wins over group interest. Testifying is a better option because you know that you'll be in trouble if you stay quiet but your friend testifies. But if you can think of that, your friend can too. So, he knows you're likely going to testify, given that it's the safer option for you, and you know he's likely going to testify too for the same reason.

And you know that he knows that you're likely going to testify. You see the loop that's forming? These types of problems are examples of non-cooperative games, which means the two prisoners can't convey their intentions to each other. If they were able to talk to each other, however, we would be in a cooperative setting, and that would affect the likelihood of certain outcomes.

As you can imagine, for example, it'd become much easier for them to agree beforehand that they're both just going to stay quiet. On the contrary, a coordination game is one in which everyone benefits from working together. There's no incentive for either party to cheat since it will result in a worse outcome than if they just cooperated. A good example is driving on the correct side of the road. You win nothing by driving on the wrong side of the road, but sometimes you lose without even playing.

The principal-agent problem is when one person is allowed to make decisions on behalf of another person. In this situation, the first person is likely to prioritize their own interests and pursue their own goals. And well, yeah, that's the basis of modern politics. Game theory can also be applied to biology, though. In fact, its application in the field of biology has allowed biologists to answer a lot of questions about evolution, which is remarkable since game theory was never designed for this.

For example, it's helped scientists explain biological altruism, where an organism acts in a way that is most favorable for the overall species, even if that action is harmful to itself. A bird might warn the rest of the group about the arrival of a predator, doing so risks its own life since it essentially announces itself to the predator. But this trait can later help that bird—assuming it survives, of course—when other birds return the favor and warn it.

These concepts might help you anticipate some of the strategies others might be using to get one over on you. But who really knows what they're thinking? The concept of guessing others' moves is what makes the game so tricky. While each player is likely to be certain about only their own move, they still have to speculate about other players' decisions and, more importantly, other players' conception of every other player's decisions.

Essentially, you are no longer making a decision based on what you think is right; rather, you're anticipating what your opponent thinks is right and simply reacting to it. But then again, your opponent is doing the same exact thing. So, who's really making the decision here? Whose mind is the actual decision being made in?

Let's put it another way: each player must know their own chance of coming out on top, guess everyone else's chance, and also guess what everyone else is guessing about their own chances of winning. Not only this, but you also really need to be able to guess what other players are guessing about your guesses about them. And now look, we're confused again.

Another problem is that although game theory has many benefits, it would be impossible to properly apply it in all situations. There will be times where rationality might not offer the right solutions or a mutual benefit might not be the most ideal outcome. When you come up against these, you have to not only recognize them but then also decide whether using game theory would be the most helpful way to deal with the situation. By then, the moment could already be gone.

The assumption that everyone is going to be rational—a basic premise of game theory—is also a really risky one. Humans can be extremely unpredictable and emotional, and this makes the guessing work near impossible. There's a ton of real-life examples that illustrate the basic concepts of game theory. Apple and Samsung are involved in an endless game of advertising. It's not like either company needs to advertise; besides, advertising can get extremely expensive.

So why not just forego this task altogether and use the money for research and development? If both companies did this, then we'd probably have better phones by now. But sure enough, Apple banks on the possibility of Samsung advertising and gaining an edge over the market, and Samsung does the same. And that possibility soon turns into a certainty—something you and I have all come to accept.

Now, this is an extremely simplistic example that bypasses many other variables, but you see the basic concept. Another good, everyday example can be found in the treatment of public goods and property. If everyone decides to be good citizens and not litter, society benefits as a whole. But you're inevitably going to come up against one or more people who choose to essentially go rogue and behave selfishly by littering.

This leads to society as a whole bearing the cost of cleaning up, all the while making not littering a less worthwhile decision. After all, if the road's already littered, the work to not litter is that much less meaningful. You can probably now see how applicable this is to other situations in life, like every big important decision we're supposed to be fixing. But more on that later.

As interesting as it is, game theory can still only analyze simple situations with well-defined constraints. And you must remember that any model is a subset of reality, no matter how good it is; it's essentially intellectual guesswork. The bottom line? We're all constantly in the game. It's pretty impossible not to be. Our lives are endlessly and unavoidably impacted by the actions and decisions made by others.

So you might as well play the game the best you can. That interaction you spent hours analyzing after the other person has already long forgotten it? Maybe it's not such a bad thing after all. We're just trying to win the game of life, and the reason to win is so that you can be free of it. Game theory is complicated, and I don't think it's something you're consistently aware of. It takes time to truly understand, and there's even more scenarios than just the ones I've mentioned that you'll encounter pretty often.

It has roots in mathematics, statistics, and probability. If you're interested in things like this, then Brilliant is for you. Brilliant is a problem-solving site that helps you think more like a scientist. And if you truly want to understand game theory, they're here to help you with just that. They guide you through problems and topics that are broken down into digestible sections.

They have entire sections of courses on mathematical thinking that cover things like logical reasoning—something you'll need to be talented at if you're a true game theorist. Brilliant exists purely to help you train your skills. If you head to brilliant.org/aperture, you can sign up and start learning today for free. The first 200 of you to do so will also get 20% off a premium subscription, which gives you access to every single course Brilliant has to offer.

Take a look through their stuff; I promise there's something for you. You're supporting yourself and my channel at the same time.