In Bargaining We Trust

We introduce trustworthy traders in bilateral trading. Trustworthy traders do not misrepresent their private information. We prove that an increase in the levels of trust (probabilities that traders are trustworthy) can reduce the maximum attainable probability of trade among the strategic traders in the set of k-double auctions. In contrast, if the levels of trust increase, then we can construct direct mechanisms with a higher probability of trade among the strategic traders. In fact, there exist ex- post efficient direct mechanisms if the levels of trust are high but k-double auctions are inefficient for all levels of trust. We prove that k-double auctions are constraint- inefficient for generic levels of trust when players have uniform priors.