When It’s Rational to be Irrational
Link: https://www.sciencenews.org/article/travelers-dilemma-when-its-smart-be-dumb
So far, we have seen many examples where game theory gives us a accurate framework with which to reason about a set of choices. But even though game theory helps us determine equilibrium strategies and the most profitable actions to take when faced with choices, for many real life situations it does not accurately predict people’s thought processes. One such situation is modeled by the “Traveler’s Dilemma”.
Formulated by Kaushik Basu of Cornell University in 1994, the Traveler’s Dilemma is a setup with a counterintuitive Nash Equilibrium, similar to that of the famed Prisoner’s Dilemma. The typical scenario is where two passengers are asked to appraise the value of identical antiques of theirs (possibly just “souvenir” antiques) that the airlines had lost. The passengers are to name a whole dollar value between $2 and $100, without conferring about it beforehand. If both passengers name the same dollar value, they will both be reimbursed that amount. Otherwise, they will be reimbursed with the lower of the two values. Additionally, the person with the lower value statement receives a $2 reward, while the other person gets a $2 demerit. The apparent best action to take in this case is to choose $100, which the other person would also certainly do. One of the travelers can take advantage of this certain outcome by claiming $99 instead, giving her a $2 reward, and the other person a $2 demerit. But why wouldn’t the other person have the exact same thought? After some time, you realize that, assuming that both travelers are perfectly selfish and rational, game theory predicts that the Nash Equilibrium is where both people write down $2. Then, it is impossible for either person to be guaranteed any higher payoffs.
As the ScienceNews article explains, experiments show that people in reality tend not to follow the Nash Equilibrium plan of declaring the smallest possible appraisal value. Clearly, this is not surprising. What is interesting is that, in this case, irrationality makes people richer. So how would we fix our model to account for the way people actually think? An important detail is how people adopt certain strategies depending on their situation. People change their strategies depending on the persona they expect the other person to take. This means people have to be playing randomly, instead of sticking to the most rational plans. And playing randomly, at least in this situation, actually increases your expected payoffs.
Although this seems to suggest that analyzing cases of this nature with game theory is not useful, coming to a conclusion like this shows us that game theory must consider when it is rational to make irrational decisions, and take other people’s characters and expectations into account. Even if game theory does not always provide us with socially popular decisions, understanding where it lacks insight can be crucial to building more precise models of reality.