Abstract
The current paper derives from a purely set-theoretical approach to the problem of strategic information transmission between an informed sender and an uninformed decision maker. The information provided by the sender is encoded in a multifunction that forces the decision maker to behave according to the preference relation induced by the encoded information. The main purpose of the paper is to study sufficient conditions for an information multifunction to alter an originally given additive preference relation of a decision maker and induce a lexicographic one. In doing so, we build several examples of sets of multifunctions inducing additive and lexicographic preferences.