A solution to the two-person implementation problem

We propose strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler (1978) Maskin (1999) according which, in two-person societies, no Pareto efficient rule is Nash-implementable. A mechanism specifies number alternatives that each player vetoes. Each simultaneously casts these vetoes selects randomly one alternative among non-vetoed ones. For strict preferences over under very weak condition for extending lotteries, are deterministic-in-equilibrium. They Nash implement class social choice rules called Pareto-and-veto rules. Moreover, mild richness conditions on domain any Nash-implementable hence implementable through mechanism.