[UTMD-108] A Note on Complementarity of Valuation Functions (by Satoru Fujishige, Koji Yokote)

Satoru Fujishige, Koji Yokote

A variety of complementarity notions have been proposed in the economics literature on markets with indivisible goods. For real-valued set functions, these notions are known to be equivalent to supermodularity. We survey these equivalences and extend them to settings in which valuation functions may take the value −∞ and the effective domain is full-dimensional. We also examine the structural changing of demand correspondences according to the changing of price vectors for complementary valuation functions.