Item Pricing for Combinatorial Public Projects.

We describe and analyze a simple mechanism for the Combinatorial Public Project Problem (Cppp), a prototypical abstract model for decision making by autonomous strategic agents. The problem asks for the selection of k out of m available items, so that the social welfare is maximized. With respect to truthful Mechanism Design, the Cppp has been shown to suffer from limited computationally tractable approximability. Instead, we study a non-truthful Item Bidding mechanism, which elicits the agents' preferences through separate bids on the items and selects the k items with the highest sums of bids. We pair this outcome determination rule with a payment scheme that determines - for each agent - a separate price for each item in the outcome. For expressive classes of the agents' valuation functions, we establish existence of welfare-optimal pure Nash equilibria and strong equilibria. Subsequently, we derive worst-case upper and lower bounds on the approximation of the optimal welfare achieved at strong equilibrium, and at (mixed) BayesNash equilibrium, under an incomplete information setting. The mechanism retains good stability properties and favors an advantage compared to recent related approaches, given its simple per-item bidding and pricing rules, and its comparable performance with respect to welfare approximation.