Equilibrium in Combinatorial Public Projects

We study simple item bidding mechanisms for the combinatorial public project problem and explore their efficiency guarantees in various well-known solution concepts. We first study sequential mechanisms where each agent, in sequence, reports her valuation for every item in a predefined order on the agents determined by the mechanism. We show that if agents’ valuations are unit-demand any subgame perfect equilibrium of a sequential mechanism achieves the optimal social welfare. For the simultaneous bidding equivalent of the above auction we show that for any class of bidder valuations, all Strong Nash Equilibria achieve at least a O(logn) factor of the optimal social welfare. For Pure Nash Equilibria we show that the worst-case loss in efficiency is proportional to the number of agents. For public projects in which only one item is selected we show constructively that there always exists a Pure Nash Equilibrium that guarantees at least 1 2 (1 − 1 n ) of the optimum. We also show efficiency bounds for Correlated Equilibria and Bayes-Nash Equilibria, via the recently introduced smooth mechanism framework [26].