What a little honesty can do for implementation theory

Moving beyond consequentialism

The vast majority of the implementation literature follows mainstream economic theory by assuming that agents care about outcomes (consequentialism). Of course this is not true; most people care in some measure about how outcomes are achieved, too. They care about the process that brings the outcomes. They are not proud of themselves if they lie in pursuit of wealth or power. (At least I hope this is still true of most people, even if they are graduates of economics programs.)

It seems worthwhile to inject a little caring-about-process into implementation theory to capture such considerations. A few authors have attempted this recently and found out that a truly minimal injection of caring about process has larger results than one would expect.

An aside that promises a future post

A great example of a paper that goes well beyond a minimal injection of process-caring is Pride and Prejudice: The Human Side of Incentive Theory, by Tore Ellingsen and Magnus Johannesson, American Economic Review 2008, 98:3, 990–1008. Since this study limits itself to the principal-agent model and it modifies the outcome-orientation of standard theory drastically, I will discuss it in a separate post. Here I want to discuss a group of related papers that take the smallest possible departure from outcome-orientation in the context of implementation theory.

Four papers on honesty in implementation

Matsushima’s papers

Hitoshi Matsushima comes first with two papers on this topic. In Role of honesty in full implementation, Journal of Economic Theory 2008, 139, 353–359, he introduces a model of an agent who chooses strategies in order to achieve the best payoff as in standard theory, except when faced with a choice between an honest strategy and a dishonest one, such that they each reach outcomes that have the same payoff. In such a situation, the agent plays the honest strategy, defined as the strategy that goes along with the mechanism designer’s—the planner’s—intention.

In detail, an agent has standard, expected-utility, preferences on the alternatives and furthermore suffers a psychological cost, a disutility, from dishonesty. The agent starts life endowed with a signal and is required to make many announcements regarding her signal in the mechanism. Her cost of dishonesty is an increasing function of the proportion of dishonest announcements she makes in the playing of the mechanism game. Apart from this, the model is standard.

Matsushima proves that if a social choice function is Bayesian-incentive compatible (with the dishonesty cost removed from the agents’ utility functions), then it is implementable in iteratively undominated strategies. Further, the mechanism that achieves this implementation is detail-free, meaning that the planner does not need to know details of the agents’ utility functions or prior belief distributions to design the mechanism. In addition, while the mechanism does involve fines that are to be imposed when certain strategies are played, these fines are small. All in all, this is a very impressive result. However, it is not clear in my mind how the planner would know that the social choice function to be implemented is incentive-compatible without the knowledge of the details on utility functions and priors that are not needed for the design of the implementing mechanism.

An answer to this concern is given in the second Matsushima paper I want to discuss, Behavioral aspects of implementation theory, Economics Letters, 100, 2008, 161–164. In this paper any social choice function is implementable in iterative dominance as long as there is aversion to telling lies among the agents. Remarkably, if this aversion is absent, the mechanism of this paper has a large multiplicity of Nash equilibria, a multiplicity that disappears the moment even a slight white-lie aversion comes in and we turn to iteratively undominated equilibrium. The mechanism is entirely detail-free, not even depending on the form of the social choice function.

Both papers use mechanisms with lotteries among alternatives as outcomes. While this allows the designer to sidestep any issues that the discreteness of the set of alternatives raises, it also is subject to the standard criticisms of mechanisms that use lotteries. This criticism points out that such mechanisms depend heavily on the assumption that agents are expected-utility maximizers, and it assumes a very high level of trust in the mechanism operator by the agents.

One last remark on the Matsushima papers: they study social choice functions. Let us now consider two papers that look at social choice correspondences, not functions, and Nash equilibrium as the implementing equilibrium notion, rather than iterative undomination.

Papers on Nash implementation

Dutta and Sen 2009

Bhaskar Dutta and Arunava Sen released a working paper (PDF) entitled Nash Implementation with Partially Honest Individuals on November 9, 2009. They found that even minimal dishonesty aversion, as already described in this post, expands the class of social choice correspondences that are implementable in Nash equilibrium dramatically when there are three or more agents: any social choice correspondence that satisfies No Veto Power is Nash implementable when there exists at least one partially honest individual! This result is spectacular and it stands in stark contrast to Maskin’s classic results that Maskin Monotonicity is a necessary condition for a social choice correspondence to be Nash implementable, and Maskin Monotonicity with No Veto Power are together sufficient. The planner here only needs to know that there is one partially honest agent, not who this agent is.

The paper has additional results for the case of two agents, when it is known that one of them is partially honest and for the case where there is a positive probability that a certain agent would be partially honest. But I think the clearest advance is the extension of Nash implementability so much beyond the walls of the Monotonicity jail.

Lombardi and Yoshihara 2011

The last paper I discuss here is the one that brought Dutta and Sen to my attention (I knew about the Matshushima papers already). It is Partially-honest Nash implementation: Characterization results, by Michele Lombardi and Naoki Yoshihara, February 13, 2011, available in the Munich Personal RePec Archive. This paper gives necessary conditions for Nash implementation with partially honest agents. It also studies the implications of the presence of partially honest individuals for strategy space reduction. The surprise here is that the equivalence between Nash implementation via Maskin’s “canonical” mechanism (which is very demanding in terms of information transmission) and Nash implementation with more information-economical mechanisms (such as Saijo’s strategy-reduction one) breaks down in the presence of partially honest individuals.

This paper is the longest of the four and contains lengthy proofs. It gives the impression of the authors coming into this area and sweeping a lot of cobwebs away from the corners that the seminal works in the nascent partial-honesty implementation area (the previous three papers) did not clean up as they were more concerned with laying foundations.

Musings

I find this trend in implementation theory very refreshing. While it is still at a highly abstract level, it has already set secure foundations for further study. I am eager to see what else can be done with the general idea of adding a degree of honesty to economic agents involved in a mechanism. There are such people around still, even among those super-cynical types with economics degrees! Yet I can see that applied fields like auction theory might resist the trend. Especially for auctions involving corporations, the assumption that the agent, who now is a representative of a corporation, is partially honest, is less appealing than when the agent is an individual playing for herself. But this trend should be fruitful in applications to problems of externalities and public goods, two applied fields that come readily to mind as well-suited for it.

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