Note: I’m writing this post as the garbage men are finally, after more than one week, starting to collect the bins in the street below my Parisian flat.
Consider a situation where a government is intending and trying to pass an unpopular law. As a sign of protest, part of the population is considering going on strike to make the government give up. Suppose that all collective action problems are solved and that people are able to coordinate to start the strike and for every decision related to it. If people go on strike, the government has the choice between making a step back and renouncing, at least for the time being, passing the law, or persisting. If the government persists, people can stop the strike or continue. This game is repeated many times but because a strike cannot last forever, it can be represented in the following reduced form:
The strategy “Blocking everything” refers to a threat that protesters against the French pension system reform have formulated over the past few weeks. In case the government does not give up its reform, heads of unions were threatening that they would “block the country”. Obviously, such a scenario would be a loss-loss one. The normal form version of this game has two Nash equilibria: one where people go on strike and the government abandons the law, the other where people do nothing and the government persists. Only the latter however is subgame perfect. The threat of blocking everything is not credible. Knowing this, the government’s best response is to persist. Going on strike cannot then be rational.
However, (French) people routinely go on strike. What does it imply for the relevance of the notion of subgame perfection? As my microeconomics students have painfully learned last week, there is something paradoxical with the logic of reasoning underlying subgame perfection. In finite games, we find subgame perfect equilibria by backward induction and we suppose that players are reasoning along the same lines. In the game above, we assume that knowing that protesters will not block the country, the government will persist. But on the equilibrium path, the government will not have to make such a decision. That means that in its reasoning, the government computes its best response assuming that protesters play rationally while it cannot be the case because rational protesters cannot be on strike!
Are subgame perfection and the related concept of sequential rationality useless? Not really. That rather indicates that the analysis is assuming too much information. There is always uncertainty about the characteristics of the players, especially their preferences. What is not featured for instance in my reduced form game are the time preferences of both players, as well as their risk aversion. We should also acknowledge that preferences may eventually reflect non-material considerations such as emotions. Precedents count also. In the French case, strikes have sometimes been successful (as in 2019 and 1995, already with respect to reforms of the pension system). We then enter the domain of games with imperfect information where players’ prior beliefs about other players’ types decisively influence rational decision-making. These priors reflect in part the social and political norms of a country. Apparently, in France, there is a relatively strong prior belief that governments are likely to retreat in the face of massive protests. That didn’t happen this time.