The design and implementation of mechanisms and institutions are an extremely important element of social decision making. These ideas and thought-experiments encompass our democratic electoral process, public goods provision and market design. This is a brief look into the work of Leonid Hurwicz (with a particular focus on his prize lecture).
Leonid Hurwicz originated both mechanism design and incentive compatibility. The 2007 Nobel Prize in Economics was jointly awarded to Leonid Hurwicz, Eric Maskin and Roger Myserson for “having laid the foundations of mechanism design theory.”
Leo’s Nobel Prize Lecture (But Who Will Guard the Guardians) is a fantastic introduction to mechanism design, and deserves a brief overview (if not a whole re-examination). Hurwicz begins with a brief foray into the history of guardianship, citing Juvenal, Plato and Socrates with their question of how to guard the guardians. That is, how can we be sure the guardians aren’t acting in their own self-interest? Do they need their own guardians? If there is no one who can be trusted, then we reach an infinite regress of monitoring (a worrying thought).
Hurwicz then develops the idea of the implementation of institutions. After all, if institutions are impossible or extremely costly to implement, “…even the most attractive mechanism remains a utopia.”
When working in a game-theoretic framework, there are a number of assumptions imposed. Hurwicz questions some of these: particularly the idea of truth. Do all players play within the rules of the game, or do they undertake illegal strategies? Do all players reveal their preferences fully? Further, when we begin to question these assumptions “… then there is no doubt that enforcement is a valid question to pose, even in Nash equilibria.”
Hurwicz proposes a re-formulation of the rules of a game as ‘game-forms’ or ‘mechanisms’. This has a number of distinct differences to the regular game-theoretical approach.
Introduce: the outcome function. This associates a physical outcome with a given point in the domain. This ‘mechanism’ is not affected by changes in preferences but the payoff functions are. Therefore, we can directly influence the mechanism, but the payoff functions may only be changed indirectly through changes in the mechanism. The outcome is a physical fact, yet the payoff is this fact + preferences.
Introduce: true strategy domain. If everyone in society plays along by the rules of the game, then all goes to plan. Yet, what if people violate? This was not taken into account previously. Where we have violation, we have the need for enforcement. To take this into account, what we need to do is extend our focus. Hurwicz includes the entire set of feasible actions (both legal and illegal) and creates the true strategy domain. Now we have two feasible and disjoint subsets: legal strategies and illegal strategies. Although we want people to play the legal game, they have the option to not.
From this perspective, we may move back to enforcement. In this new situation, what is successful enforcement? Firstly, Hurwicz holds that if the legal game rules are being successfully enforced, what we are ensuring if that illegal strategies are less attractive than legal ones. That is, illegal strategies are dominated by legal ones. This is incentive compatability.
Yet, we need to adopt a weaker concept of successful enforcement, and delve deeper into the implementation idea. After a discussion of the definition of implementation, Hurwicz concludes the section with “implementation is successful if the equilibrium outcomes correspond to those of the desired game, i.e., those envisaged by the legislation.” From this, Nash equilibria are neither self-enforcing, nor self-implementing.
If we do need to enforce and implement, Hurwicz provides some optimism. Firstly, introducing the term Intervenors. They are guardians “who are in sympathy with the rules”. If we assume these individuals exist, even if they are rare, we have the chance to successfully enforce rules. Secondly, our elective, democratic society introduces a type of ‘guardianship loop’ – giving supervisors (politicians) the incentive to make sure we are reaching the relevant goals.Thirdly, he provides an argument that even without intervenors, our rational self-interested behaviours may result in the legal outcomes we desire. Finally:
“… it may be possible to create systems in which rational self-interest, due to a variety of rewards and punishments, leads, or may lead, to legal and ethical behavior.”
This is by no means an extensive look into the work of Hurwicz. For a more detailed look, see this by Myerson (Nobel co-winner), and this is a more broad look into the 2007 prize (by Matthew Jackson, of Stanford).