Combinatorial Agency Of Threshold Functions

We study the combinatorial agency problem introduced by Babaioff, Feldman and Nisan [5] and resolve some open questions posed in their original paper. Our results include a characterization of the transition behavior for the class of threshold functions. This result confirms a conjecture of [5], and generalizes their results for the transition behavior for the OR technology and the AND technology. In addition to establishing a (tight) bound of 2 on the Price of Unaccountability (POU) for the OR technology for the general case of n > 2 agents (the initial paper established this for n = 2, an extended version establishes a bound of 2.5 for the general case), we establish that the POU is unbounded for all other threshold functions (the initial paper established this only for the case of the AND technology). We also obtain characterization results for certain compositions of anonymous technologies and establish an unbounded POU for these cases.