Supermodular utility representations

Abstract

Many problems in decision theory and game theory involve choice problems over lattices and invoke the assumption of supermodularity of utility functions. In the context of choice over finite lattices, it is well-known that existence of supermodular representations is equivalent to existence of quasisupermodular ones for monotone preferences. In particular, strictly monotone preferences admit a supermodular representation. This paper revisits the axiomatic foundations of supermodularity of utility functions representing preferences over finite lattices, and develops an axiomatic foundation in the context of choice over lotteries over outcomes in arbitrary lattices.