Sincere and sophisticated players in an equal-income market

We study the simultaneous direct revelation mechanism associated with each equal-income competitive social choice function in the allocation of objects and money among sincere and strategic agents. Strategic agents take advantage of sincere agents. They non-cooperatively coordinate on the equal-income competitive allocations for the true preferences that are Pareto undominated for them within the set of equal-income competitive allocations. Sincere agents are protected to some extent, however. Their welfare is usually above their maximin payoff.