Lying about the price? Ultimatum bargaining with messages and imperfectly observed offers

We introduce the taxicab game, related to the ultimatum game and Gehrig et al.'s (2007) yes/no game. The proposer makes an offer, and simultaneously sends a cheap talk message indicating (possibly falsely) the amount of the offer. The responder observes the message with certainty and the offer with probability p before accepting or rejecting the offer. We investigate versions with p = 0 and p = 0.5 along with the ultimatum game as a baseline. Intuition and a model comprising both standard economic agents and others who dislike inequity, lies and lying provide clear predictions that our experimental results support. As the likelihood increases of offers being seen, the offers themselves increase, messages over-state them less, and responders are more likely to accept (even when the offer is unseen). Also, responders are more likely to accept after truthful messages than after lies or when no message is sent.