The Power of Subgame Perfection, French Politics Edition
Compared to other social sciences, economics has two really large comparative advantages, one empirical and the other theoretical. The former is relatively recent, or at least has significantly increased over the last couple of decades. It is the ability to conduct powerful quantitative studies measuring all kinds of mechanisms accounting for a large range of phenomena, economic or not. Economics is now predominantly an applied and experimental science, even though complex micro- (especially in the field of information economics, i.e., mechanism and market designs) and macroeconomic modeling work is still undergoing. Rather than its ability to produce complex models, economics’ second comparative advantage is rather that it provides simple and very effective concepts and thinking tools to achieve a better understanding of our social reality and the underlying mechanisms at work.[1]
I’m fairly incompetent to discuss the former comparative advantage in more detail (which makes me wonder if I’m still a real economist!), so let me illustrate quickly the second one, taking the case of the concept of subgame perfection, which we owe to the game theorist Reinhard Selten. Subgame perfection can be viewed as a straightforward extension of the rationality assumption in games (i.e., players always play the best response given their belief about others’ strategic play) where strategic interactions are sequential. I would be ready to contend that this concept figures among the most powerful ones in the economist’s toolbox (with the concepts of opportunity costs and comparative advantages by the way). Here is a simple illustration.
Consider a group G of n players competing for some resource R. Suppose that R can be divided at least by n so that all players can theoretically have some share of R. A subgroup C decides to form a coalition, based on the assumption (which we assume to be true) that together they will obtain a greater share of R than if they compete separately. Denote s_i the share obtained by any player i and s_C the share of the coalition obtained by summing up the shares obtained by its members at this allocative stage. Once the resource has been allocated, the members of C can either decide to pool their shares together or to keep their shares for themselves. All the players belonging to C understand that pooling will be to the advantage of no one but one member of the coalition, player m. As it happens, m, who is the only member of the coalition who would have had a chance p to obtain a greater share of R by not entering in C than by entering without the shares being pooled after, is also the one at the initiative of the formation of C. Was this a rational decision?
This game has a risky component (the probability p that m has a bigger share by not entering in C than by entering and the subsequently won shares are not pooled) so the answer is not straightforward. But what is straightforward however is that it was common knowledge from the start that the other members of C would not agree to pool the shares they have won at the allocative stage. Given this, m rational decision (whether to form and enter C) is entirely dependent on his assessment p. Asking for pooling the resources after the allocative stage is strategically inept and denotes a lack of understanding of the idea of subgame perfection… or reveals m’s belief that the other members of the coalition are not rational!
My French readers will no doubt have recognized here a simple (and maybe uncharitable) model of the political situation of the so-called NUPES coalition following the French legislative elections. Player m, Mélenchon, has called his partners in the coalition to form a unique political group at the Assemblée Nationale, which would presumably have served the interests of his party. Unsurprisingly, this call has been firmly rejected by the other members of the coalition. Now, this simple theoretical model permits to make some conjectures about Mélenchon’s rationality or belief regarding his friends’ rationality.
[1] These two comparative advantages have been exploited notably in popular books written for a wide audience. Think for instance of Dubner and Levitt’s Freakonomics for the empirical and quantitative side, and of Tim Harford’s The Logic of Life for the theoretical side.