My rational life as a game theorist

I was on the phone with my mother the other day and she said I should call her more often. As the rational person I am, I made a game out of it. Let me take you through the process of using game theory in everyday decisions, and the possible social cost of being a rational thinker.

Should you use game theory in everyday decisions?

When making a decision in everyday life, most people quickly weigh the pros and cons, whilst other people might just choose the lesser of two evils. This process can lead to a series of undesirable outcomes, and people may end up wishing they could do it all over again to get a different result.

One way to be sure to choose the most rational outcome, is to apply the principles from game theory in your decision making process. Game theory is a mathematical theory that focuses on understanding strategic situations, where the payoff of one person depends on what others do. This way you can be sure that the outcome is a result of a thorough rational process, and you can defend your choice. Game theory can have many applications in everyday life. Spanning from economics, politics and science, game theory can reveal the most efficient to plan your commute, negotiate a price, and even when to leave the toilet seat up. (Zollman, 2013)

What makes this approach differ is that you take your opponents strategies in mind when choosing your own strategy, and choosing a strategy that is the best response to your opponent’s. This assures a rational process, but is it socially optimal? And can social relations be kept alive?

How to use game theory

To apply principles from game theory into your life, you might want to know what a game is. If there are more than one person involved in a choice, it can most likely be seen as a game. Game theory proposes that almost all interaction between people making decisions can be seen as a game or organized through experiment. Wherever decisions overlap each other game theory applies.

This means that you could use math instead of your intuition when making decisions. This is a way to ensure that the decisions that are made are rational, and that the outcome is the best response to any scenario. (Paulas, 2015)

A good way to weigh the options is to map the different payouts in a payoff matrix like the one shown below. Here you can see the different players A and B, and the payoff from their different strategies. Player A’s strategies in the table below are either “up” or “down”, while player B’s strategies are “left” and “right”. The intersection of their strategies show their payoff from the given choices. The payoffs are shown as a pair of values, where the first value is the payoff for player A and the second for player B. By setting up a payoff matrix, you get an overview of the different possible outcomes, and you can make rational choices based on what you think your opponent will do.

Player B

Player A Left Right
Up A(up),B(left) A(up),B(right)
Down A(down),B(left) A(down),B(right)

The parental phone call of guilt

One way to use game theory can be exemplified with what we call the “Mother-son guilt trip dilemma”. The game is based on two players, a mother and her son, who aren’t calling each other as frequently as they feel they should. This results in both players feeling guilty for not calling, but they are also left angry towards the other person not calling as well (Zollman, 2013). This results in four different scenarios which can be displayed in a textual payoff matrix as this:

Son

Mother Son complains Son stays silent
Mother complains Both feel guilty about not calling the other. Both feel guilty for complaining. Son feels guilty about not calling. Mother feels guilty about complaining.
Mother stays silent Mother feels guilty about not calling. Son feels guilty about complaining. Both are annoyed about not calling the other, but neither is made to feel guilty.

(matrix from: Zollman, 2013)

The first player is the mother, who has two choices: Either to complain about her son not calling regularly or to stay silent. The other player is the son, He also has two choices: Either to complain about his mother not calling regularly or to stay silent.

In a scenario where the other player choose to stay silent, you will have the most profit by complain about the other player. This is because by complaining about the other player you gain the moral high ground which will boost your own self esteem.

In a scenario where the other player choose to complain, you will have less to lose by complaining as well. This is to not give the other player the moral high ground.

This makes complaining the dominant strategy because it is each player’s best response to any strategy the other player chooses. (Zollman, 2013)

We can see that this game is similar to the “prisoner’s dilemma” game. A game where two criminals have been caught committing a minor crime. Both criminals are arrested and kept in separate rooms so they can’t communicate with each other. The prisoners are suspected of having done a more serious crime. To get them to confess, the police give them each the offer of freedom in exchange for confessing that the other person did it. If both players end up confessing they both go to jail for the more serious crime. If both players are silent they continue their sentence for the minor crime. A payoff matrix of the game would look like this:

Prisoner B

Prisoner A Silent Confess
Silent -1,-1 -3,0
Confess 0,-3 -2,-2

Prisoner A and B have the same two choices they can make, either to stay silent or to confess.

In a scenario where the other player choose to stay silent, you will have the most profit by choosing to confess. In the other scenario where the other player choose to confess, you will lose less by confessing as well. This makes confessing the dominant strategy for each player which results in them both going to jail.

As we can see from the matrix there is a more profitable solution which is not being played because there is a dominant strategy. The solution for getting this result could be to agree on refraining from confessing on the other player. This could result in both players refraining from confessing on the other to save themselves from a possible retaliation of the other player.

This is a solution that could also be applied to the “mother-son guilt trip dilemma”. Both mother and son then agrees on not guilt tripping the other person when either of them call. (Zollman, 2013)

What has these examples shown?

That when you are in a tough spot, and it is important to find the best course of action, you must compare the different options you have available to you and see wich is better (Paulas, 2015). It is important to work in your own self interest, because any other rational player would do the same. When choosing any other strategies that are not in your own self interest, you might end up being exploited and the other player might earn from your social opted strategy. This can be illustrated with the “Prisoner’s dilemma” game, if you choose to remain silent, since this is the socially optimal outcome, if both choose it, and the other player confesses, he would be released and you would get the highest sentence. If extreme rationality is taken out of the picture, like when the players are related, one might choose a socially better outcome because of this relation.

The biggest lesson to be learned from “prisoner’s dilemma”, in a game theoretical point of view, is that if you end up in a similar situation, where you are offered a deal to reduce your loss at the cost of another player, you should take it. This type of game also teaches us that the only way to reach a socially optimal outcome in a similar game is to change the rules. If both the players agree that they would cooperate, or that they agree to enforce a punishment of some kind against the player that betrays the other. This changes the payoff matrix so that cooperation is the best outcome.

I love you”

My girlfriend dropped the “L-Bomb” the other day, like the rational man I am, I remained silent and changed the topic. “Why?” you ask? Let me illustrate it for you.

If you have been in a relationship you probably have encountered the fearsome “L-Word”. The word that can kill a relationship if said to soon or never at all.

How is this love game played out from a game theory perspective? Well, let’s take a look at the different scenarios that can happen.

Firstly, the players have two choices. Either to say “I love you” to the other person or to stay silent.

The first scenario is if both players say I love you, this results in a payoff of one to both players. The second and third scenario is if one says I love you and the other remains silent. This results in a minus point to the player saying the “L-word” and 0 points to the player who remains silent. The fourth scenario is if both players remain silent, this results in no payoff for either player. (Bhatia, 2016)

In a payoff matrix the game would look like this:

Me

Girlfriend Proclaim Love Stay silent
Proclaim Love 1,1 -1,0
Stay silent 0,-1 0,0

The best scenario here is if both players say “I love you” to each other. This is the only scenario where either player has anything to gain. The dominant strategy however is to remain silent no matter what the other player do, to prevent themselves from losing points.

Another possible solution to this game would be to follow what the other player says. If the other player says I love you, the second player says it aswell. The same count for staying silent.

Conclusion:

One pitfall when using game theory in every decision of your life is the social ramifications of your rational choices. It might not be socially optimal to always have one’s self interest at heart, so social norms might be broken, and this will influence your social life in the long run. This can be shown with the “L-word” game, where the dominant strategy for both players is to avoid dropping the “L-bomb”. In the long run this can ruin a relationship if both players are completely rational and stick to the dominant strategy, hence the bomb association. The same goes for the “mother-son guilt trip dilemma” mentioned earlier. By choosing the dominant strategy of staying silent you will only end up postponing the problem that is ruining the relationship.

What can you take from all of this? When you are making decisions, no matter how banal it seems, do the math and listen to your brain, since going with your intuition often leads to you regretting it. There are of course exceptions to this rule. When social relations are at stake, your gut can outsmart your brain.

PS: Call your mother more often!

By Adrian Borgund and Ruben Skartveit

Resources:

Bhatia S. (2016) What are some real world examples of game theory? [internet] Available from:<https://www.quora.com/What-are-some-real-world-examples-of-game-theory/answer/Srishti-Bhatia-4> (Visited: 18.10.16)

Easley, D. Kleinberg, J. (2010) Networks, Crowds, and Markets. Worldwide: Cambridge University Press.

Paulas, R. (2015) Why You Should Care About Game Theory. [internet] Availible from: <https://psmag.com/why-you-should-care-about-game-theory-d8f2da8dd1a#.vixh7vkxp> (Visited: 18.10.16)

Unibet (no year) Distrust your gut. [internet] available from: <https://www.unibet.co.uk/casino-game-theory/> (visited: 18.10.16)

Zollman, K. (2013) The Next Page: Everyday uses for game theory (such as, when to wash the dishes). [internet] Available from: <http://www.post-gazette.com/opinion/Op-Ed/2013/02/03/The-Next-Page-Everyday-uses-for-game-theory-such-as-when-to-wash-the-dishes/stories/201302030375> (Visited: 18.10.16)

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