Emmanouil Pountourakis

Socially stable matchings in the hospitals/residents problem

In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent (or agents) in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings. In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for special cases of the problem.

Optimal Auctions vs. Anonymous Pricing

For selling a single item to agents with independent but non-identically distributed values, the revenue optimal auction is complex. With respect to it, Hartline and Rough garden showed that the approximation factor of the second-price auction with an anonymous reserve is between two and four. We consider the more demanding problem of approximating the revenue of the ex ante relaxation of the auction problem by posting an anonymous price (while supplies last) and prove that their worst-case ratio is e. As a corollary, the upper-bound of anonymous pricing or anonymous reserves versus the optimal auction improves from four to e. We conclude that, up to an e factor, discrimination and simultaneity are unimportant for driving revenue in single-item auctions.

A complete characterization of group-strategyproof mechanisms of cost-sharing

We study the problem of designing group-strategyproof cost-sharing mechanisms. The players report their bids for getting serviced and the mechanism decides a set of players that are going to be serviced and how much each one of them is going to pay. We determine three conditions: Fence Monotonicity, Stability of the allocation and Validity of the tie-breaking rule that are necessary and sufficient for group-strategyproofness, regardless of the cost function. Consequently, Fence Monotonicity characterizes group-strategyproof cost-sharing schemes closing an important open problem. Finally, we use our results to prove that there exist families of cost functions, where any group-strategyproof mechanism has arbitrarily poor budget balance.

Procrastination with Variable Present Bias

Individuals working towards a goal often exhibit time inconsistent behavior, making plans and then failing to follow through. One well-known model of such behavioral anomalies is present-bias discounting: individuals over-weight present costs by a bias factor. This model explains many time-inconsistent behaviors, but can make stark predictions in many settings: individuals either follow the most efficient plan for reaching their goal or procrastinate indefinitely. We propose a modification in which the present-bias parameter can vary over time, drawn independently each step from a fixed distribution. Following Kleinberg and Oren (2014), we use a weighted {\it task graph} to model task planning, and measure the cost of procrastination as the relative expected cost of the chosen path versus the optimal path. We use a novel connection to optimal pricing theory to describe the structure of the worst-case task graph for any present-bias distribution. We then leverage this structure to derive conditions on the bias distribution under which the worst-case ratio is exponential (in time) or constant. We also examine conditions on the task graph that lead to improved procrastination ratios: graphs with a uniformly bounded distance to the goal, and graphs in which the distance to the goal monotonically decreases on any path.

Mechanisms for Hiring a Matroid Base without Money

We consider the problem of designing mechanisms for hiring a matroid base without money. In our model, the elements of a given matroid correspond to agents who might misreport their actual costs that are incurred if they are hired. The goal is to hire a matroid base of minimum total cost. There are no monetary transfers involved. We assume that the reports are binding in the sense that an agent’s cost is equal to the maximum of his declared and actual costs. Our model encompasses a variety of problems as special cases, such as computing a minimum cost spanning tree or finding minimum cost allocation of jobs to machines.

A Complete Characterization of Group-Strategyproof Mechanisms of Cost-Sharing

We study the problem of designing group-strategyproof cost-sharing mechanisms. The players report their bids for getting serviced and the mechanism decides a set of players that are going to be serviced and how much each one of them is going to pay. We determine three conditions: Fence Monotonicity, Stability of the allocation and Validity of the tie-breaking rule that are necessary and sufficient for group-strategyproofness, regardless of the cost function. Consequently, Fence Monotonicity characterizes group-strategyproof cost-sharing schemes closing an important open problem. Finally, we use our results to prove that there exist families of cost functions, where any group-strategyproof mechanism has arbitrarily poor budget balance.

Clustering on k -Edge-Colored Graphs

We study the Max k-colored clustering problem, where, given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e. the edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chromatic degree equal to two and k ≥ 3. Our main result is a constant approximation algorithm for the weighted version of the Max k-colored clustering problem which is based on a rounding of a natural linear programming relaxation. For graphs with chromatic degree equal to two, we improve this ratio by exploiting the relation of our problem with the Max 2-and problem. We also present a reduction to the maximum-weight independent set (IS) problem in bipartite graphs which leads to a polynomial time algorithm for the case of two colors.

Clustering on k -edge-colored graphs

We study the Max k -colored clustering problem, where given an edge-colored graph with k colors, we seek to color the vertices of the graph so as to find a clustering of the vertices maximizing the number (or the weight) of matched edges, i.e.źthe edges having the same color as their extremities. We show that the cardinality problem is NP-hard even for edge-colored bipartite graphs with a chromatic degree equal to two and k ź 3 . Our main result is a constant approximation algorithm for the weighted version of the Max k -colored clustering problem which is based on a rounding of a natural linear programming relaxation. For graphs with chromatic degree equal to two we improve this ratio by exploiting the relation of our problem with the Max 2-and problem. We also present a reduction to the maximum-weight independent set (IS) problem in bipartite graphs which leads to a polynomial time algorithm for the case of two colors.