Let’s play: Behavioral Game Theory

Picture this scenario: you’ve been locked in an interrogation room for hours, and the police finally layed out their cards on the table. They know you’re guilty and have your partner in crime in the other room. The police needs a confession, and the one to provide it can walk out freely, leaving the other to serve a long sentence in jail. If you both confess, you both go to jail, but for a shorter time. However, if neither does, both go to prision but receive an even shorter sentence. It is up to you to decide. What do you do? 

If you’ve ever been formally introduced to game theory, you know that its answer is that both of you should run to the officers and tell them the truth. This is the economic prediction as it’s the rational thing to do. But would you do it? Most people’s answer is the economists’ favorite response to (almost) every question: it depends. Who is the other person? How much do you trust them? Is it your friend or your 3rd-floor neighbor? Is it your mother? And how long are those sentences? You may hold your ground facing 6 months, but what if you’re looking at 25 years? Are you even truly guilty? Are you willing to trade away your integrity for a shorter sentence?

The conventional game theory looks at the game elements (what are the actions and the payoffs?) for the answer. Behavioral game theory tries to look at all the other questions.

Game Theory vs Behavioral Game Theory

But let’s back away for a second: what even is game theory, and how exactly is behavioral game theory different?

Well, game theory’s main objective is to predict behavior through a systematic, mathematical approach. No need to close the article, this is only the “scary” version of the definition. Thankfully, we are not in a Microeconomics class, so we can use a much more pleasant definition: game theory analyses games. Of course, by “games”, we do not mean football or basketball (although that would be fun) but are instead referring to any interaction between people (the players), where their behavior (actions) determines what they get out of the game (their payoffs). Any economic, political, or social interaction can be rewritten as a game, and thus seen through the lens of game theory. The interrogation room situation we started with is a classic example. It is frequently used as an introduction to the subject. The idea is that each player will look at their possible strategies (if my partner confesses, I can confess/not confess…) and where those strategies will land them (if we both confess, we go to jail…), deciding then what the optimal course of action will be. It’s like playing chess – if, for example, your opponent moves the bishop to B7, and you take your knight to C4, you’re doomed; if instead you move your queen to D6, checkmate! The optimal course of action: queen to D6. 

Game theory does a wonderful job predicting the outcome of such games, but the jump to real life can be tricky. Notice that the optimal course of action was left undefined. “Optimal” depends on what each person wants out of the game, on their preferences. The usual assumption is that players are self-interested to the extreme and completely rational, caring only about getting the best possible outcome for themselves, regardless of what happens to the other player.

This is exactly where behavioral game theory steps into the picture. It has a practical approach to the games, rather than theoretical. Game theory uses logic and mathematics to find out what a rational and self-interested player would do in a game, and then states what people will choose rationally in such a situation. Behavioral Game Theory takes the opposite path. It asks actual people to play the game and observes their behavior. Such experiments make it possible to see how different preferences affect human behavior (how things like altruism or fairness influence people’s decisions) and how that differs from the theoretical predictions. Why would this matter? Well, these preferences can be incorporated in the models, making them closer to the reality we know, and therefore allowing for better predictions of behavior.

Playing the Game

Ultimate Game

The Ultimatum game is an early example of behavioral game theory’s experiments. In this game, one player is given a certain amount of money (say, 10€) and asked to split it with the other player in whatever way they want. The second player then decides whether to accept the offer or to reject it, in which case neither player gets anything.

Conventional game theory’s prediction is that the first player should offer as little as possible (1 cent out of 10€) and pocket the rest, since the second one would have no reason to reject it – after all, 1 cent is better than nothing, right?

Now, picture yourself playing the game. Do you accept such a low offer? Can you think of anyone who would? Do you think this is the right prediction? If not, congratulations! You are a wonderful forecaster of human behavior. In fact, when this experiment was first conducted, the average offer was equivalent to 3.5 €, and offers below 5€ were more likely to be rejected the further down they went. The experiment has been replicated over the years, with high and low amounts to be split, with consistent results.

The preference uncovered here is known as negative reciprocity – being willing to “pay a price” (give up some amount) to punish unfair or inappropriate behavior in others. Upon seeing what they considered as an unfair split (a much too low offer from the first player), most players decided they would rather gain nothing than allow the other person to, in their eyes, treat them unjustly.

Dictator Game

The dictator game is a slight modification of the Ultimatum game: here, the second player has no power to reject the offer. The first player (the dictator) proposes a split of the initial sum, and that is exactly what each one takes home, even if it means that the second player gets nothing at all. Of course, the theoretical prediction is exactly that – the “dictator” will choose to keep the entire 10€ to themselves and won’t offer anything to the second player.

But when the experiment was conducted this was not what happened at all! In fact, around two thirds of people chose to offer the equivalent of 1€ to 5€, keeping the rest.

Those unlikely nice “dictators” were displaying what is known as an altruistic preference. Someone with altruistic preferences is more content with an outcome if the well-being of others increases. That means they play not only with their own outcomes in mind, but also that of others involved in the game, and prefer situations where other people are also benefitted. This behavior can be found in everyday interactions too: when people donate to charities or help someone in need, they are manifesting altruistic preferences.

Gift Exchange Game

Now, for a break from ultimatums and offers, let’s look at the gift-exchange game. This is simply a game made to mimic the interaction between an employer and an employee. First, the “employer” offers the “employee” some amount of money (a “wage”). Then, the employee must perform a task to earn it. Now, what the task is in particular is not so important (it can be anything at all, as long as it is not completely effortless), what is really at stake is how much effort the “employee” puts into completing it.

Game theory’s prediction here is that being offered any amount at all the “employee” would work as little as possible (self-interested as they are). But do you think that happens? Chances are, you’ve had to do some job in your life, and put some amount of effort into it. Do you always do the least possible required? As it turns out, most people didn’t. They responded to more generous “wages” by working harder. They were, in fact, displaying negative reciprocity’s nicer counterpart: positive reciprocity, the willingness to reward generous actions. People presenting this preference respond positively to actions that benefit them: they go an extra mile when they feel that someone has acted in their best interest.

Notice that neither of these experiments challenge the validity of standard game theory. Its systematic and logic process is still sound – games do have optimal courses of action. Its cornerstone assumptions are the ones that fail: behavioral game theory shows that people in general are not merely self-interested, so what is “optimal” varies according to their preferences.  

Behavioral game theory is a great example of what the branch of behavioral economics can do for the economic science. It is not a replacement of traditional game theory, but a way to expand on and improve it: behavior models can arise from practice, not from theory. After all, there’s no better way to figure out someone’s behavior than to observe it.

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Sources: American Economic Association, BehavioralEconomics.com, Blackwell Handbook of Judgment and Decision Making, Behavioural Economics: Introduction to Behavioral Game Theory and Game Experiments.