Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity of fair allocations. We study the problem of finding an allocation that is Pareto-optimal. While it is easy to find an efficient allocation when the underlying graph is a path or a star, the problem is NP-hard for many other graph topologies, even for trees of bounded pathwidth or of maximum degree 3. We show that on a path, there are instances where no Pareto-optimal allocation satisfies envy-freeness up to one good, and that it is NP-hard to decide whether such an allocation exists, even for binary valuations. We also show that, for a path, it is NP-hard to find a Pareto-optimal allocation that satisfies maximin share, but show that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.Comment: 21 pages, full version of paper at AAAI-201

Monopolistic Provision of Excludable Public Goods under Private Information

This paper characterizes the optimal contract designed by a profit-maximizing monopolist, who can provide an indivisible and excludable public good to a group of n potential consumers, whose valuations are private information. The analysis takes distribution costs and congestion effects into account. The second-best allocation rule, which is welfare-maximizing under the constraint of non-negative profits, is characterized. Properties of the optimal mechanism in the case of many potential consumers are analyzed and it is shown that in this case the monopolist can use simple posted-price contracts. Finally, implications for public intervention are discussed.

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer setting bid and ask prices nearly equal to Walrasian equilibrium prices. In the model agents trade either through the intermediary or privately. Buyers (sellers) choosing to trade through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as potential gains. Agents trading privately capture all of the gains to trade, but risk costly delay in finding a partner. We show that when the cost of delay is small, the intermediary sets bid and ask prices nearly equal to Walrasian equilibrium prices. As the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. If the possibility of trading through the intermediary is removed, and therefore all trade takes place in the private trading market, then prices are not close to Walrasian equilibrium prices even as the cost of delay vanishes