Minimum cost connection networks: Truth-telling and implementation

In the present paper we consider the allocation of costs in connection networks. Agents have connection demands in form of pairs of locations they want to have connected. Connections between locations are costly to build. The problem is to allocate costs of networks satisfying all connection demands. We use a few axioms to characterize allocation rules that truthfully implement cost minimizing networks satisfying all connection demands in a game where: (1) a central planner announces an allocation rule and a cost estimation rule; (2) every agent reports her own connection demand as well as all connection costs; (3) the central planner selects a cost minimizing network satisfying reported connection demands based on the estimated costs; and, (4) the planner allocates the true costs of the selected network. It turns out that an allocation rule satisfies the axioms if and only if relative cost shares are fixed

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

A non-cooperative approach to the folk rule in minimum cost spanning tree problems

This paper deals with the problem of finding a way to distribute the cost of a minimum cost spanning tree problem between the players. A rule that assigns a payoff to each player provides this distribution. An optimistic point of view is considered to devise a cooperative game. Following this optimistic approach, a sequential game provides this construction to define the action sets of the players. The main result states the existence of a unique cost allocation in subgame perfect equilibria. This cost allocation matches the one suggested by the folk rule.The authors thank the support of the Spanish Ministry of Science, Innovation and Universities, the Spanish Ministry of Economy and Competitiveness, the Spanish Agency of Research, co-funded with FEDER funds, under the projects ECO2016-77200-P, ECO2017-82241-R, ECO2017-87245-R, PID2021-128228NB-I00, Consellería d’Innovación, Universitats, Ciencia i Societat Digital, Generalitat Valenciana [grant number AICO/2021/257], and Xunta de Galicia (ED431B 2019/34)

Implementing Efficient Graphs in Connection Networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first property, Pareto Nash Implementation (PNI), requires that the efficient outcome is always implemented in a Nash equilibrium, and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other asymmetric variations, are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominate any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other asymmetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms.Cost-sharing, Implementation, Average Cost, Egalitarian Mechanism.

Implementing Efficient Graphs in Connection Networks

We consider the problem of sharing the cost of a network that meets the connection demands of a set of agents. The agents simultaneously choose paths in the network connecting their demand nodes. A mechanism splits the total cost of the network formed among the participants. We introduce two new properties of implementation. The first prop- erty, Pareto Nash Implementation (PNI), requires that the efficient out- come is always implemented in a Nash equilibrium, and that the efficient outcome Pareto dominates any other Nash equilibrium. The average cost mechanism (AC) and other assymetric variations, are the only rules that meet PNI. These mechanisms are also characterized under Strong Nash Implementation. The second property, Weakly Pareto Nash Implementation (WPNI), requires that the least inefficient equilibrium Pareto dominate any other equilibrium. The egalitarian mechanism (EG), a variation of AC that meets individual rationality, and other assymetric mechanisms are the only rules that meet WPNI and Individual Rationality. PNI and WPNI provide the first economic justification of the Price of Stability (PoS), a seemingly natural measure in the computer science literature but not easily embraced in economics. EG minimizes the PoS across all individually rational mechanisms.ntable SCFs in our environment if we add a few desirable axioms.

Computing with strategic agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 179-189).This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant's best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings - the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices.(cont.) Randomization in truthful mechanism design is undesirable because, in arguing the truthfulness of the mechanism, we employ an underlying assumption that the bidders trust the random coin flips of the auctioneer. Despite conjectures to the contrary, we are able to design a technique to derandomize any multi-unit auction in the limited demand case without losing much of the revenue guarantees. We then consider the limited budget case and provide the first competitive auction for this setting, although our auction is randomized. Next, we consider abandoning truthfulness in order to improve the revenue properties of procurement auctions, or auctions that are used to hire a team of agents to complete a task. We study first-price procurement auctions and their variants and argue that in certain settings the payment is never significantly more than, and sometimes much less than, truthful mechanisms. Then we consider the setting of cost-sharing auctions. In a cost-sharing auction, agents bid to receive some service, such as connectivity to the Internet. A subset of agents is then selected for service and charged prices to approximately recover the cost of servicing them.(cont.) We ask what can be achieved by cost -sharing auctions satisfying a strengthening of truthfulness called group-strategyproofness. Group-strategyproofness requires that even coalitions of agents do not have an incentive to report bids other than their true values in the absence of side-payments. For a particular class of such mechanisms, we develop a novel technique based on the probabilistic method for proving bounds on their revenue and use this technique to derive tight or nearly-tight bounds for several combinatorial optimization games. Our results are quite pessimistic, suggesting that for many problems group-strategyproofness is incompatible with revenue goals. Finally, we study centralized two-sided markets, or markets that form a matching between participants based on preference lists. We consider mechanisms that output matching which are stable with respect to the submitted preferences. A matching is stable if no two participants can jointly benefit by breaking away from the assigned matching to form a pair.(cont.) For such mechanisms, we are able to prove that in a certain probabilistic setting each participant's best strategy is truthfulness with high probability (assuming other participants are truthful as well) even though in such markets in general there are provably no truthful mechanisms.by Nicole Immorlica.Ph.D

Dynamic mechanism design

AbstractIn this paper we address the question of designing truthful mechanisms for solving optimization problems on dynamic graphs with selfish edges. More precisely, we are given a graph G of n nodes, and we assume that each edge of G is owned by a selfish agent. The strategy of an agent consists in revealing to the system–at each time instant–the cost at the actual time for using its edge. Additionally, edges can enter into and exit from G. Among the various possible assumptions which can be made to model how this edge-cost modifications take place, we focus on two settings: (i) the dynamic, in which modifications can happen at any time, and for a given optimization problem on G, the mechanism has to maintain efficiently the output specification and the payment scheme for the agents; (ii) the time-sequenced, in which modifications happens at fixed time steps, and the mechanism has to minimize an objective function which takes into consideration both the quality and the set-up cost of a new solution. In both settings, we investigate the existence of exact and approximate truthful (w.r.t. to suitable equilibrium concepts) mechanisms. In particular, for the dynamic setting, we analyze the minimum spanning tree problem, and we show that if edge costs can only decrease and each agent adopts a myopic best response strategy (i.e., its utility is only measured instantaneously), then there exists an efficient dynamic truthful (in myopic best response equilibrium) mechanism for handling a sequence of k declarations of edge-cost reductions having runtime O((h+k)logn), where h is the overall number of payment changes

Sharing Sequential Values in a Network

Published in Journal of Economic Theory https://doi.org/10.1016/j.jet.2018.08.004</p

Naming and discovery in networks : architecture and economics

In less than three decades, the Internet was transformed from a research network available to the academic community into an international communication infrastructure. Despite its tremendous success, there is a growing consensus in the research community that the Internet has architectural limitations that need to be addressed in a effort to design a future Internet. Among the main technical limitations are the lack of mobility support, and the lack of security and trust. The Internet, and particularly TCP/IP, identifies endpoints using a location/routing identifier, the IP address. Coupling the endpoint identifier to the location identifier hinders mobility and poorly identifies the actual endpoint. On the other hand, the lack of security has been attributed to limitations in both the network and the endpoint. Authentication for example is one of the main concerns in the architecture and is hard to implement partly due to lack of identity support. The general problem that this dissertation is concerned with is that of designing a future Internet. Towards this end, we focus on two specific sub-problems. The first problem is the lack of a framework for thinking about architectures and their design implications. It was obvious after surveying the literature that the majority of the architectural work remains idiosyncratic and descriptions of network architectures are mostly idiomatic. This has led to the overloading of architectural terms, and to the emergence of a large body of network architecture proposals with no clear understanding of their cross similarities, compatibility points, their unique properties, and architectural performance and soundness. On the other hand, the second problem concerns the limitations of traditional naming and discovery schemes in terms of service differentiation and economic incentives. One of the recurring themes in the community is the need to separate an entity\u27s identifier from its locator to enhance mobility and security. Separation of identifier and locator is a widely accepted design principle for a future Internet. Separation however requires a process to translate from the identifier to the locator when discovering a network path to some identified entity. We refer to this process as identifier-based discovery, or simply discovery, and we recognize two limitations that are inherent in the design of traditional discovery schemes. The first limitation is the homogeneity of the service where all entities are assumed to have the same discovery performance requirements. The second limitation is the inherent incentive mismatch as it relates to sharing the cost of discovery. This dissertation addresses both subproblems, the architectural framework as well as the naming and discovery limitations