Pillutla and Murnighan (1996) and Terry Boles and his colleagues (2000) were among several researchers who introduced the variation of giving outside options to responders, or options which they knew they would receive if they rejected an offer. For instance, a responder might reject an offer of $1 if he knows that he has an outside option of receiving $2 when rejecting an offer. With this new twist, researchers can then introduce additional conditions in which offerers know or do not know whether there is an outside option for responders, or what the value of that offer is, or what the range of the offer could be, and so forth. Without getting into all the various permutations, one important result that Boles found was that offerers made lower offers when they knew the size of the outside option, which does not seem to be what fairness would predict (Boles et al. 2000: 247). Furthermore, Boles introduced a wrinkle whereby offerers could send a message with their offer, allowing them to be deceptive about the size of the allocation they had available to them in partial information conditions. The game was repeated with the same participants as offerers and responders for four rounds, and after each round, any deceit that offerers used was revealed to responders. It turned out that offerers were deceptive 13.6% of the time (2000: 247). Boles also discovered that when responders felt deceived, in the next round they were much more likely to reject a new offer, even at the expense of their self-interest. In other words, they wanted to punish the offender for deceiving them (Boles et al. 2000: 249–250).