Behavioral game theory extends standard (analytical) game theory by taking into account how players feel about the payoffs other players receive, limits in strategic thinking, the influence of context, as well as the effects of learning . Games are usually about cooperation or fairness.
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.