Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Budget Feasible Mechanisms

We study a novel class of mechanism design problems in which the outcomes are constrained by the payments. This basic class of mechanism design problems captures many common economic situations, and yet it has not been studied, to our knowledge, in the past. We focus on the case of procurement auctions in which sellers have private costs, and the auctioneer aims to maximize a utility function on subsets of items, under the constraint that the sum of the payments provided by the mechanism does not exceed a given budget. Standard mechanism design ideas such as the VCG mechanism and its variants are not applicable here. We show that, for general functions, the budget constraint can render mechanisms arbitrarily bad in terms of the utility of the buyer. However, our main result shows that for the important class of submodular functions, a bounded approximation ratio is achievable. Better approximation results are obtained for subclasses of the submodular functions. We explore the space of budget feasible mechanisms in other domains and give a characterization under more restricted conditions

The Strategy-Proof Provision of Public Goods under Congestion and Crowding Preferences

We examine the strategy-proof provision of excludable public goods when agents care not only about the level of provision of a public good, but also the number of consumers. We show that on such domains strategy- proof and efficient social choice functions satisfying an outsider independence condition must be rigid in that they must always assign a fixed number of consumers, regardless of individual desires to participate. The fixed number depends on the attitudes of agents regarding group size - being small when congestion effects dominate (individuals prefer to have fewer other consumers) and large when cost sharing effects dominate (agents prefer to have more consumers). A hierarchical rule selects which consumers participate and a variation of a generalized median rule to selects the level of the public good. Under heterogeneity in agents' views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.Public Goods, Congestion, Club Goods, Strategy-Proof

Characterizing Optimal Adword Auctions

We present a number of models for the adword auctions used for pricing advertising slots on search engines such as Google, Yahoo! etc. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for this auction with a multi-dimensional type-space that are {\em not} affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity $O(n^2m^2)$ and $O(n^2m^3)$ respectively, where $n$ is number of bidders and $m$ is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The numerical results suggest that customized rank-based allocation rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c) Decision Sciences Seminar, Fuqua School of Business, Duke Universit

Characterizations of the cumulative offer process

In the matching with contracts setting, we provide two new axiomatic characterizations of the "cumulative offer process" (COP) in the domain of hospital choices satisfying "unilateral substitutes" and "irrelevance of rejected contracts." We say that a mechanism is truncation-proof if no doctor can ever benefit from truncating his preferences. Our first result shows that the COP is the unique stable and truncation-proof mechanism. Next, we say that a mechanism is invariant to lower tail preferences change if any doctor's assignment does not depend on his preferences over worse contracts. Our second characterization shows that a mechanism is stable and invariant to lower tail preferences change if and only if it is the COP

Greedy Allocations and Equitable Matchings

I provide a novel approach to characterizing the set of interim realizable allocations, in the spirit of Matthews (1984) and Border (1991). The approach allows me to identify precisely why exact characterizations are difficult to obtain in some settings. The main results of the paper then show how to adapt the approach in order to obtain approximate characterizations of the interim realizable set in such settings. As an application, I study multi-item allocation problems when agents have capacity constraints. I identify necessary conditions for interim realizability, and show that these conditions are sufficient for realizability when the interim allocation in question is scaled by 1/2. I then characterize a subset of the realizable polytope which contains all such scaled allocations. This polytope is generated by a majorization relationship between the scaled interim allocations and allocations induced by a certain ``greedy algorithm''. I use these results to study mechanism design with equity concerns and model ambiguity. I also relate optimal mechanisms to the commonly used deferred acceptance and serial dictatorship matching algorithms. For example, I provide conditions on the principal's objective such that by carefully choosing school priorities and running deferred acceptance, the principal can guarantee at least half of the optimal (full information) payoff

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a very well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Although Serial Dictatorship is a purely combinatorial mechanism, our analysis uses linear programming; a linear program expresses its greedy nature as well as the structure of the input, and finds the input instance that enforces the mechanism have its worst-case performance. Bounding the objective of the linear program using duality arguments allows us to compute tight bounds on the approximation ratio. Among other results, we prove that Serial Dictatorship has approximation ratio $g/(g-2)$ when the capacities are multiplied by any integer $g \geq 3$. Our results suggest that even a limited augmentation of the resources can have wondrous effects on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation