Relationship Week #1: Adding Relationship Value in a Game Theory Example

November 15, 2005 - Get free updates of new posts here

I decided that not enough cubicle dwellers or college students knew about relationship making and all the fun things that go along with it. So this ENTIRE week is devoted to creating good friendships and fun things about it. I will never use the N word at all or possibly try to avoid it as much as possible. So let’s begin with an article from Shivani Sopory about relationships and adding value through a game theory example. Yes, I am lucky to have much smarter than me friends:)

Game Theory Explaining Relationships by Shivani Sopory

What is a relationship?

It’s a connection between people, right? It can be business, pleasure, personal…and the list goes on. Everyday we are presented with opportunities to build relationships and to keep those connections. And…well, I don’t know about everybody else, but I find it damn hard to make some of those connections last. So, sitting in game theory class, I decided to use something my professor was saying to some use (for once in my college career).

**Just a disclaimer, this post takes a serious turn for a little bit**

What is the general idea?
Using the fundamentals of game theory, a player will always maximize his payoff given the strategy of the other player. So, how does a person maximize their payoff in a repeated game without the other player defaulting (choosing not to cooperate).

Setting up the game:
In a typical game, if both players make themselves vulnerable (choose to cooperate) they get the maximum collective payoff, however, if one defaults and the other cooperates, the player that defaults gets a much larger individual payoff, and the other loses out badly. If both default, they choose not to be vulnerable to one another and because they protect themselves, the outcome is not bad, but it’s not optimal either.

So, what happens when you make this game into a repeated game?
This can be represented by a contract it’s a relationship that binds two groups but there is definite end date to this relationship. What usually happens in this type of situation is that the two parties cooperate until the end of the relationship when the parties choose to default, resulting in a lower benefit for both of them. A player will default because they assume the other person will continue to cooperate in which case the player will receive a much larger individual payoff, but the other person will be left with nothing.

So then, how can a person make it so that a relationship continues to have the maximum benefit?

1) Make the game appear to be infinite. One way to do this is to provide no end date to a contract. This gives incentives for both parties to continue the relationship at the highest communal benefit in other words, it keeps you from getting screwed over.

2) Threaten/give the appearance of punishment if the other person defaults. A punishment can be anything that would provide a lower payoff to the other party, so things like a fine, or bad publicity, or threatening to never work with the other party in the future. This works because a person will chose to cooperate if the costs of defaulting are too high. It doesn’t work so well though, because the threat has to be credible, and it’s hard to convince other people that you will actually follow through on your threats.

3) Only work with “patient” people. Patient people are people that will value the long-term benefit over the short-term benefit. People who are short-term in their thinking will take the earliest opportunity to default if it results in more benefit for them initially.

4) Add Value (this is my personal favorite) CHANGE THE GAME! If you continuously change the benefits of the game, or add benefits to the game so that both parties have no reason to default on a relationship, and the relationship will continue with maximum benefits. Adding value can be cheap but still effective. For a restaurant, food is great, but food with a smile is even better; the smile adds value. If you are working on a project with somebody else, but you notice something that can be fixed outside of the project, give suggestions. It doesn’t cost anything to give extra advice, but it shows the other party that you have more to offer. By doing this, you increased both of your payoffs and you have the changed the game to your benefit.

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5 responses to “Relationship Week #1: Adding Relationship Value in a Game Theory Example

  1. Teale Reply

    Very helpful advice, Shivani. But for those of us who are outside of the formal business world, how can we take your advice? Last time I checked, my friendships generally don’t have expiration dates, and I’m not really in the market for business partnerships, but I am interested in keeping the relationships I do have… How does your theory address my concern?

    Also, I’m a bit confused by your prefered method of extending a relationship. You seem to think that rewarding the other player for cooperating will help to prolong a relationship, but from what I understand, it will sacrifice quality of relationship for quantity of relationship, since you will have to sacrifice something yourself in order to give your partner incentive for cooperation. With the whole principle of diminishing returns, it seems like the cost of maintaining the relationship will eventually reduce its rewards to the point that they would have been had the other player defaulted in the first place. But I want my relationships to last forever and everyone to be happy.

  2. Shivani Reply

    Good points, Teale…THANKS FOR POSTING!! I like hearing what people have to say.

    To address your first point…friendships can still follow this same theory. I think most people do this without thinking about it, though. For instance, when you meet somebody, you don’t put a time restriction on your friendship…like you don’t tell your new found friend that they have till Friday to prove that they are a good friend. So, inherently, you’re making a friendship potentially infinite.

    Another way to look at this is with, what I call, friends with a purpose. These are friends that you make for a certain purpose (I know this sounds bad, but everybody does it to a certain extent). An example of this is when you are in a class and you don’t know anybody, so you start talking to the person next to you and the two of you share notes, etc…they become your new best friend in that class. Chances are, when that class is over, you’ll never talk to that person again unless they show up in another class.

    So, how to fix this problem using these strategies? Well, you can invite the person out for coffee or the next time your friends are throwing a party, invite the person to that. This takes the relationship outside of the classroom…it adds benefits and gives the potential for an infinite relationship.

    As for your second point…that’s a good point. I think whenever you have a friendship or a business relationship of some sort, you have to weigh the costs and benefits. You don’t want to add so much value to the other person’s payoff to the point that it is too costly to yourself. I think another thing that I am assuming is if you add benefit to the other player, they will choose to reciprocate because your friendship has now become more valuable to them…so they will add benefit to your payoff to keep you around.

  3. Tram Reply

    For someone who’s thought long and hard about relationships and gone through hours of trying to figure out whether or not to end certain relationships or keep them going, I’ve realized that the people that I actually want to be in a relationship with are the ones I never have to question. That being said, Shivani, you’re a dork for thinking too much and you shouldn’t stress out that tubby little head of yours.

    Here’s a shout out to Teale for posting something 500 times more intelligent than what I’ve just posted.