In their very successful theory of institutions, rules, and equilibria, Hindriks and Guala (Reference Hindriks and Guala2014) unify three approaches to the study of institutions: an equilibrium theory attributed to Lewis (Reference Lewis1969); the rule-based theory of North (Reference North1990); and Searle's (Reference Searle1995) constitutive-rules theory.

The synthesis of the first two theories into what they call the rules-in-equilibrium approach is not new (Greif and Kingston, Reference Greif, Kingston, Schofield and Caballero2011) but they offer a fresh and instructive exposition. Their main purpose is to reconcile the constitutive-rules theory with the rules-in-equilibrium approach. A translation of the language of the former into the language of the latter is proposed, which seems very reasonable to me. However, a better assessment of the relative status of the three theories would have been helpful. Everybody knows the verse:

To understand this flea ecology one needs to take account of the fleas of all sizes, but the role of the smaller fleas cannot be understood without appreciating that they ride upon the back of larger fleas. I see equilibrium as the big flea in Hindriks and Guala's ecology. On its back rides North's theory of rules. If Hindriks and Guala are right, Searle's theory about the grammar of rules is either a companion or a subordinate flea to North’s.

Such a prioritization matters because an institution needs to be in some kind of equilibrium to survive, and survival is fundamental. Rules are necessary but subsidiary (Binmore, Reference Binmore2010). As Hindriks and Guala explain, rules are needed because players unknowingly operating an equilibrium in a game of which they are unaware need rules to follow if an equilibrium is to be sustained.

The players will not usually understand why the institutional rules that govern their behavior hold together. Otherwise they would not invent rationalizations of the type that Searle seeks to capture. But social analysts need to look deeper if we are to escape from the kind of work that continues to proliferate in those parts of political economy and constitutional economics in which large conclusions are drawn from simple mechanism-design models that have been put together with little or no thought as to why anybody should obey the rules that supposedly constrain a citizen's behavior. In a constitutional setting, there is nobody outside the system to enforce the rules. The only viable rules are therefore those that enforce themselves because they call for equilibrium play in an underlying game of life whose rules are enforced by Nature herself. In brief, the answer to the classical question of who guards the guardians is that they must guard each other.

How do we model the game of life? For the sake of simplicity, Hindriks and Guala confine their attention to simple coordination games but the underlying game appropriate to the study of political institutions will usually be at least as complex as a repeated game (Guala, Reference Guala2012). How are such games to be studied? There are two approaches: rational and evolutionary. I think Lewis (Reference Lewis1969) led us astray by focusing on the rationality option,Footnote ¹ which led him to the indefensible claim that workable conventions need to be common knowledge (Binmore, Reference Binmore2008).Footnote ² It is evolutionary game theory that matters when studying institutions (Young, Reference Young2001). To argue otherwise is to neglect the role of history – to side with Thomas Paine rather than Edmund Burke.

What kind of equilibrium? The orthodox answer is Nash equilibrium – the weakest notion which ensures that the outcome be the end-product of an evolutionary process (usually cultural in an institutional context). Hindriks and Guala muddy the waters a bit here by using Maynard Smith's (Reference Maynard Smith1982) Hawk–Dove game as an example. Like most biologists, Maynard Smith talks about evolutionary stable strategies (ESS) rather than Nash equilibria. This is fine in symmetric games with only two strategies like the Hawk–Dove game, but simple evolutionary processes can easily converge on Nash equilibria that are not ESS in games with more than two strategies (Hofbauer and Sigmund, Reference Hofbauer and Sigmund1998). Worse still, a repeated game lacks any pure ESS at all.Footnote ³

In rational game theory, it is sometimes proposed that Nash equilibria be replaced by correlated equilibria. A correlated equilibrium of a game G is just a Nash equilibrium of a new game H constructed from G by appending an opening move in which Nature sends correlated signals to each player on which they can condition their choice of strategy in G. In endorsing the correlated equilibrium concept, Hendriks and Guala use Maynard Smith's example of the bourgeois Hawk–Dove Game that begins with Nature telling each player who is the ‘owner’ of the resource in dispute in the original Hawk–Dove game.

I have devoted a good part of my life to studying fairness as a coordinating device (Binmore, Reference Binmore2005). I therefore agree very much with the emphasis Hendriks and Guala give to correlation, but I feel that correlation devices are so important that their structure needs to be laid on the table rather than hidden from view in the abstract definition of an equilibrium concept. That is to say, I think we need to talk about Nash equilibria of the game H rather than correlated equilibria of G. One is then forced to be completely explicit about the coordinating device that opens the game H. The danger in restricting attention to correlated equilibria of G in rational game theory is that one may inadvertently invent ways for the players to get along together that are hopelessly impractical or historically impossible.Footnote ⁴ In evolutionary game theory, the situation is worse since evolutionary processes in H can be much more flexible than in G because of the possibility of evolutionary drift off the equilibrium path (Samuelson, Reference Samuelson1997).