REU Project

We provide a comprehensive landscape of possibilities and impossibilities for NOM fair division across both goods and chores. For additive valuations, we design NOM mechanisms that guarantee EF1 for any number of agents, and MMS for two agents. When items are unit-demand valuations, we show that NOM mechanisms can simultaneously achieve EF1, EFX, and MMS. To capture complementary items in real-world environment, we analyze k-minded valuations, proving a stark dichotomy: while EF1 and EFX remain achievable by NOM mechanisms (under mild agent-count conditions for chores), guaranteeing MMS is fundamentally impossible for both goods and chores. Our results establish sharp boundaries on what cognitive relaxations of strategyproofness can achieve in fair division.