Game theory in a highly complex and radically uncertain world –
Game theory in a highly complex and radically uncertain world Are we – as economics textbooks posit – cold, rational calculators calculating our optimal utility trajectory by taking into account what others will do optimally? Or are we grappling with a complex reality, striving to use “satisfactory” (satisfactory + sufficient) rules of thumb? Moreover, we may behave *as if* were we rational even when we only used approximate heuristics? Or are our behavioral and cognitive biases so strong and pervasive that conclusions based on rationality totally fail to explain what is happening in financial markets or the economy as a whole?
This is not a trivial debate, and such questions have sparked countless academic papers and squabbles between “classical” and “behavioral” economists over the past 40 years.
The “Mean-Field Games” (MFG) are the latest vintage of models based on the rational optimization of utility. Game theory includes interactions between agents in the optimization program: what others do will affect my gain, and what I do will affect what others do.
The idea of Lasry & Lions is when all agents are rational and have common knowledge. The theory is considerably simplified in the limit where the number of agents becomes very large, so that the interactions between agents are captured by an “average field”: the average (local) decision of the others.
One application of MFG is the description of the movement of crowds. For example, how will the crowd flow when they have to rush out of a lecture hall with two exit doors? Solving the corresponding MFG equations generates “optimal” flow patterns, which minimize everyone’s exit time, assuming that the others themselves behave rationally.
Is this a good description of crowd behavior? Here is the content of a very beautiful paper:
The authors compare the result of a controlled experiment. Where an intruder (say a car) attempts to drive through a crowded square. People have to move to make way for the car. MFG makes accurate predictions for the flow pattern, which match empirical observations. Naive behavioral models, which assume agents are short-sighted to avoid getting run over. As a result, fare much worse. The authors conclude that pedestrians behave more like players than grains of sand.
Is this a justification that the rational team is right after all? I think the story is more complicated, perhaps in an interesting way. Yes, when the car is moving slow enough, we humans can act like we’re optimizing our future path. In addition, find a compromise between speed and promiscuity. But when the level of uncertainty or danger is high (fast moving car), I suspect people will behave much less rationally. Describing simple, repeated games using anticipatory rational agents might do the trick. But as soon as the game is complex and the uncertainty is high. My hunch is that rationality isn’t even the right starting point.
Alas, we live in a very complex and radically uncertain world.