Achieving the maximum size for exchange problems with dichotomous preferences

We consider an exchange problem with dichotomous preferences, and agents endowed with acceptable (unacceptable) objects can exchange their endowments with other acceptable (unacceptable) objects in order to achieve the “maximum size” of the problem, that is, the maximum number of agents who obtain acceptable objects. We observe that the priority mechanisms appeared in the literature before are not fully incentive-compatible—agents may pretend that their endowments are acceptable to themselves to get better results. We construct a new class of mechanisms called “endowment-respecting priority mechanisms” to solve this problem. Our mechanisms are dominant strategy incentive-compatible, individually rational, and always achieve the maximum size.