Binary Mechanism for the Allocation Problem with Single-Dipped Preferences

We consider the problem of fairly allocating a fixed amount of a perfectly divisible resource among agents with single-dipped preferences. In this problem, it is known that any efficient and strategy-proof rule violates several fairness requirements. We alternatively propose a simple and natural mechanism, in which each agent reports only whether he or she wants a resource and the resource is divided equally among agents who want it. We show that any Nash equilibrium allocation of our mechanism belongs to the equal-division core. In addition, we show that our mechanism is Cournot stable. In other words, from any message profile, any path of better-reply must converge to a Nash equilibrium