Game Theory of Trust

By Anmol Srivats

What is trust? A good game theory definition would be “Irrational co-ordination”, where players play strategies that maximise their combined payoffs that may not maximise their individual payoffs.

That sounds a bit wordy, so let me offer an example. Suppose there are two farmers on an island. If they distrust each other, they’ll always be suspicious of the other person stealing from them, so they’ll have to stay up all night and guard their farms. If they trust each other, they can sleep peacefully and have the same outcome. However, both of them have to forgo a profitable opportunity to steal for the benefit of the group.

This sounds like a lovely outcome, however, there are some problems with it. In the previous example, after you were trusted, if you were planning to steal, you can now do so easily. If you were planning not to steal, you can now sleep peacefully. Therefore, it is always a good thing to be trusted, but it can be a good or bad thing to trust. Since being trusted is a universally good thing, everyone has an incentive to appear trustworthy, so it is difficult to figure out when to trust. However, if you don’t trust anyone, you’re not at your best possible outcome (a good night of sleep for a farmer).

I will now re-define trust in a more human way, and link it to the game theory definition. Trust has to do with the sharing of information i.e. honesty. In the farm game, this has to do with the farmers exchanging the information that they don’t plan to rob each other. But again, they might be lying.

An important question to ask is- under what circumstances is honesty always ideal? That’s quite a confusing question, and an easier way to think about it is by looking at circumstances when honesty is not ideal. One time is when one party will exploit the other party for their honesty. The other is when the honesty will be misinterpreted or overreacted to. Therefore, if both parties are well meaning and efficient, honesty is the best policy.

Now you may ask why the party providing the information needs to be well meaning, surely only the listener needs to be.  However, we need to further analyse what exactly constitutes a lie to understand this difference. I would define a lie as deliberately creating a false impression in the listener’s mind, rather than outright stating false facts.

For example, suppose I know you think blue is yellow and yellow is blue, if I’m wearing a blue sweater and say “I’m wearing a blue sweater”, that is a lie, because I know you think that means I’m wearing a yellow sweater. Similarly, it is possible to use true information to create a false impression in the listener’s mind. I could only talk about my good traits and not my flaws, and supposing my listener is adequately naïve, this would make me look like a great human being.

Similarly, if the other party does not have your best interests at heart, honesty may not be the best policy. For example, if you said that when people say the word “cat”, you buy them a pint of Tennents, I would say “I thought I saw a pussy cat” more often than Tweety. Therefore, trust is only ideal when both parties don’t have each other’s best interests at heart.

The second condition is something I like to imagine as efficiency. For example, if I say “my favourite colour is red”, and you irrationally think that means I’m a serial killer, I may be hesitant to tell you regardless of how well meaning you are towards me.

To generalise this further, communication is about signalling- you’re sending a signal to the other party, it can be words, it can be body language, it can be an e-card with a cat on it, but regardless of what it is, it’s a signal. This signal is then interpreted by and reacted to by the other party. Honesty is the act of sending true signals, wherein the interpretation reflects the truth, which means both that you must not be lying (even through facts), and that the other person must not misinterpret the signal. Similarly, the other person’s reaction should be ruinous to you. Under those circumstances, the signal must be mutually beneficial.

Note that this does not mean that both parties need to care about each other deeply. If I am really into cricket, and I ask you to watch the cricket with me, I am signalling that I enjoy cricket and would enjoy watching it with someone, and if you also like cricket, you’ll take up the offer, if not, you won’t. In this case my honesty is good, but that doesn’t mean that I’m going to tell you about my deep-seated fear of kettles.

It ultimately has to do with co-ordination, and the extent of co-ordination in a given circumstance can be calculated by looking at whether the people are well meaning and efficient with regards to signals. In some cases, two rational players should be honest, in others, two irrational players can attain better payoffs by choosing to be well meaning in order to reap the benefits of honesty. The latter case, combined with the efficiency of the former case is what trust is.

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