## Jean-François Laslier*, Matias Núñez and Remzi Sanver

This article was originally published in the September 2020 edition of the 5 papers…in 5 minutes.

How can we help two people, or two intelligent entities, to come to a decision when their interests diverge partially? Customs and laws propose criteria to decide whether an outcome is “fair”, “good”, “equitable”, or “just”. But these criteria are not solutions when the parties to the negotiations exaggerate their needs, bluff, minimize certain elements, and generally make strategic use of the possibilities offered by the procedures in place. **“Implementation theory” offers to define collective decision-making procedures – or mechanisms – that can be used for a wide range of problems**. These mechanisms must be independent of the actors’ preferences because the negotiations require a certain strategic freedom for the agents. Their actions must not reveal their preferences. However, it is permissible to aim for a procedure that is sufficiently astute that the clear interest of an intelligent actor will always lead her to behave “sincerely”.

**In this article, Laslier, Núñez and Sanver propose a veto mechanism that could respond to an existing theoretical gap similar to the Prisoner’s dilemma** [1]. This mechanism is the following: an adjudicator lists all logically possible outcomes (including the worst). All outcomes envisaged by one of the players must be put on the list. Each player is given the right to exercise her veto on a certain number of the outcomes. If, for example, there are 17 possible outcomes, then each player has 8 vetoes. Thus, the rule is as follows: simultaneously, each player indicates 8 possible outcomes that she rejects. There remains therefore at least one admissible outcome. If there is only one, that one is chosen. If there are several, lots are drawn from them.

For an uneven number of alternatives, each player is given the same rights; if there is an even number, then a (small) asymmetry will be required. The veto mechanism is this: the players exercise their veto over distinct alternatives so that, in the end, one and only one is left available and the drawing of lots is not necessary. **The authors also show that the mechanism resolves the problem identified by Hurwicz and Schmeidler** because any alternative chosen in an equilibrium is optimal in Pareto’s sense.

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(1) Leonid Hurwicz and David Schmeidler, in 1978, posed the problem of the two-player implementation, demonstrating that for every procedure there are circumstances in which the players can block each other in a sub-optimal situation in the sense of the prisoner’s’ dilemma: there is a best solution for the two, but given what the other does, each is right to do what she does … In technical terms, there is no mechanism for which the Nash equilibria are always Pareto-optimal.

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**References**

*Original title of the article*: A solution to the two-person implementation problem

*Published in*: PSE Working Paper, 2020

*Available at*: https://hal-pse.archives-ouvertes.fr/halshs-02173504

* PSE Member

*Credits* : Shutterstock, Rudall 30