One thing to note is that no allocation mechanism for more than 2 parties cannot satisfy all 3 of these criteria for general preferences a) Efficient - guarant

One thing to note is that no allocation mechanism for more than 2 parties cannot satisfy all 3 of these criteria for general preferences a) Efficient - guarantees an allocation where making at least one party better off without making anyone else worse off is possible b) Balanced budget - guarantees all prices sum to a fixed number eg the total rent share c) Incentive compatibility - it always a Nash equilibrium for every party to report their true preferences for each good. There is only one allocation mechanism (Vickery-Clarke-Groves) that satisfies the 1st and 3rd criteria and this will generally not also satisfy the 2nd. Reference: https://en.wikipedia.org/wiki/Vickrey%E2%80%93Clarke%E2%80%93Groves_mechanism https://en.wikipedia.org/wiki/Vickrey%E2%80%93Clarke%E2%80%9... Thus, Su and Spliddit's algorithms by definition must be vulnerable to strategic reporting. Example: V=[v1,v2,v3] = preferences for rooms 1,2,3. total rent = 1000 VA = [1000,0,0] VB = [0,1000,0] VC = [0,0,1000] Truth Telling Spliddit Allocation A->1,B->2,C->3 prices = [333,333,333] If C reports [500,500,0] and A,B report truth A->1,B->2,C->3 prices = [500,500,0] TLDR - fair and efficient allocation mechanisms can never avoid vulnerability to gaming for some preferences.