On Pareto-Optimal and Fair Allocations with Personalized Bi-Valued Utilities

We study the fair division problem of allocating $m$ indivisible goods to $n$ agents with additive personalized bi-valued utilities. Specifically, each agent $i$ assigns one of two positive values $a_i > b_i > 0$ to each good, indicating that agent $i$'s valuation of any good is either $a_i$ or $b_i$. For convenience, we denote the value ratio of agent $i$ as $r_i = a_i / b_i$.