Game Theory and Feelings: The Secret Behind Interactions

In one of our previous blogs, we mentioned that game theory is very important for behavioral economics in general, as it provides a framework where we can explain how interactions happen, and why certain outcomes are dominant. The idea is very simple: by having knowledge of the possible outcomes and the preferences of the other person, taking those into account can lead us to choose from a set of alternative actions. Assigning probabilities to actions can help us to calibrate our choices further.

In short: game theory provides us with the means to model interactions. This is especially useful, as a lot of experiments done by behavioral economists could be interpreted as some sort of game – may that be simultaneous, where choices are made for each person at the same time, or as an action-reaction game.

The Ultimatum Game

One of the more well-known games and experiments is the ultimatum game, created by Güth et. al. (1982). The basic version of the game is pretty simple: there are two players, one sender and one receiver. In the beginning of the game, the sender is given $10, and he needs to decide on how to divide it between himself and the other person. However, there is a twist: the receiver has to accept the offer in question, otherwise nobody will receive anything.

This puts a number of interesting factors into play. First, the sender has to offer an amount that the receiver will surely accept. Ask yourself: playing as the receiver, what would be the minimum amount that you would accept in this case? If your answer is anything greater than $0.01, I’ve got news for you: in economic sense, you are not a rational being. Why? Because you should not care about what the other person receives, you should only consider your own well-being: and as things stand, by only receiving $0.01, you are still better off compared to not receiving anything. In contrast, what you, dear reader, most likely had in mind is a fair division (which does not necessarily mean egalitarian division): maybe you consider that you are entitled to at least $3, and anything below that is just not fair.

This brings us to the second point: by rejecting an offer, you are punishing the other person for being unfair; however, at a cost: the amount of money that you won’t receive. In one interpretation, this means that the “enjoyment” of punishing the other person outweighs the negative utility from not receiving the money offered.

Another aspect which is important to consider is the information the receivers are endowed with – whether they know the amount that is being divided or not. It is somewhat trivial that your perception of the money offered can be altered if you know the budget of the sender. In a behavioural economic sense, this can be interpreted as whether you provide a reference-point to the receiver or not. As we already know from the prospect theory, a negative difference from the reference-point is interpreted as a “loss” by the decision-maker, and since most, or rather, all of us are being dominated by loss-aversion, we want to avoid this. If we tell the receiver that he is being offered $3 out of $10, in his mind he already created a reference-point which is “fair” (let’s say: $4): any negative deviances from that will be instantly rejected. In contrast, by not having any information on the total amount, one can’t really decide whether the offer is fair or not, generous or not, and will likely accept offers which are lower nominally.

Cultural differences are also significant across countries and communities. A great example to this are the findings of Henrich et. al. (2006), which was an enormous project consisting of 17 researchers. Anthropologists, behavioral and social experts conducted ultimatum games, dictator games and public goods games in 15 different small-scale societies. One highlight of their finding was, that in tribal societies, the rate of rejection was smaller than usual, leading the researchers to believe that these societies were “rejection-averse” rather than loss-averse. From interviews, they found out that a lot of senders offered more because they did not want the offer to be rejected – which could have led to conflict in the tribe. In hunter-gatherer societies of Paraguay and Indonesia, senders offered much more than the average, which is due to their lifestyle. Oversharing in these societies is common, because the hunters cannot consume their game privately, so they tend to share it. However, when other members accept these generous offers, it incurs a certain obligation to them to do better in the next hunting party.

You might be inclined to say that if the money in question would be greater, outcomes would differ. Certainly, experiments have been conducted where the stakes were much higher; for instance, a couple of months worth of salaries. These experiments caused the decision-makers to block, because they could not cope with the stress and pressure of the stakes being that high. However, Hoffmann, McCabe and Smith (1996) played the ultimatum game with a budget of $100, and found that the results were remarkably similar to the original experiment. They also found that when people “earned” the role of the sender through competition (for example: by participating in a quiz), their offers tended to be less generous. This was due to a feeling of entitlement from the sender’s side: by being smarter, they felt that they were entitled to earn more money than the receivers. However, and perhaps more interestingly, the receivers were not willing to accede to this sense of entitlement, and the rejection rates were greater as well.

As the saying goes: “It’s the thought that counts”. This can be shown in the case of the ultimatum game as well: Falk, Fehr and Fischbacher (2000, 2002), as well as Andreoni et. al. (2002) showed that intentions do matter. They tested this by modifying the ultimatum game: senders had to choose from two options of distribution. The first one was the same in all conditions: give themselves $8 and offer the receivers $2. The second option varied from the following distributions: offer nothing (selfish option), offer $5 (egalitarian option), and offer $8 (generous option). They found that, for example, the 8/2 offers were rejected 27% of the time in the “2/8 game” and only 9% of the time in the “10/0 game”. The variations in these rejection rates suggest that intention-driven reciprocal behaviour is a major factor behind decision-making. As such, the alternatives did matter: if the sender offered 8/2 instead of 10/0, he was considered to be generous, and was more likely to get the payments. Simultaneously, the unfair 10/0 offers were rejected 90% of the time.

And finally, the last case we want to introduce to you today is “the battle of the sexes”. The situation is simple (and all-too familiar): a wife and a husband want to spend time together, but they have different activities in mind. The wife wants to go to the theatre, while the husband wants to go see a boxing match. If they can come to an agreement, they will both benefit from it – if they agree to go to the theatre, the wife obviously will be happier, but the husband is happy as well, as he gets to spend time with his significant other (and vice versa if they end up going to the boxing match together). If, however, they cannot come to an agreement, both will be worse off due to the absence of each other’s company. Traditional game theory declares that the latter (going to the theater and boxing match alone) would be the outcome in most cases.

However, Rabin (1993) considered an alternative. In the model outlined in his article (which incorporates fairness into decision-theory), economic agents, besides having their own interest, also have social interests and goals. In order to achieve more social acceptance, they are willing to sacrifice their intrinsic, individual well-being and help others. Applying this to the battle of the sexes: suppose that the husband chooses boxing. The wife then concludes that choosing the theatre would hurt both players, and is therefore willing to go to the boxing match.