Nash Equilibria in the multi-agent project scheduling problem with milestones

Plánovanie projektov zvyčajne zahŕňa viacerých dodávateľov, ktorí majú na starosti rôzne práce v projektovom pláne. Každý dodávateľ má možnosť skrátiť trvanie svojej aktivity z maximálneho až na minimálny časový limit. Projektový manažér je zodpovedný za včasné dodanie projektu. V projektovom pláne stanovuje míľniky s príslušnými termínmi a pokutami za ich nesplnenie. Cieľom práce je nájsť stabilné riešenie s minimálnym časovým trvaním projektu. V stabilnom riešení nemá žiadny dodávateľ záujem zmeniť trvanie svojich aktivít, aby znížil svoje náklady. To pláti za predpokladu, že všetci ostatní dodávatelia nezmenia svoje stratégie. V práci navrhujeme využitie celočíselného lineárneho programovania s podmienkami generovanými v priebehu programu pre výpočet stabilného riešenia s minimálnym časovým trvaním projektu. Analýza výpočtov potvrdzuje efektívnosť nášho riešenia. Taktiež v práci skúmame ukazovatele v anglickej literatúre označované ako price of anarchy a price of stability, aby sme získali lepšiu predstavu o probléme z pohľadu projektového manažéra.Project scheduling often involves multiple contractors, who are in charge of activities in the project plan. They have the power to decrease the duration of their activities from normal duration to the incompressible limit. The project manager is responsible to deliver the project on time. He specifies the milestones with appropriate due dates and penalties in the project plan. The thesis aims to find a stable solution with minimal project duration. In a stable solution, no contractor has the interest to change the duration of his activities to reduce his expenses, since all other contractors do not change their strategies. We propose a mixed integer linear program formulation with lazy constraint generation for its calculation. Computation analysis confirms the effectiveness of our approach. We investigate the values of the price of anarchy and the price of stability to get useful insight for the project manager

Interdependent Scheduling Games

We propose a model of interdependent scheduling games in which each player controls a set of services that they schedule independently. A player is free to schedule his own services at any time; however, each of these services only begins to accrue reward for the player when all predecessor services, which may or may not be controlled by the same player, have been activated. This model, where players have interdependent services, is motivated by the problems faced in planning and coordinating large-scale infrastructures, e.g., restoring electricity and gas to residents after a natural disaster or providing medical care in a crisis when different agencies are responsible for the delivery of staff, equipment, and medicine. We undertake a game-theoretic analysis of this setting and in particular consider the issues of welfare maximization, computing best responses, Nash dynamics, and existence and computation of Nash equilibria.Comment: Accepted to IJCAI 201

Project Games

International audienceWe consider a strategic game called project game where each agent has to choose a project among his own list of available projects. The model includes positive weights expressing the capacity of a given agent to contribute to a given project The realization of a project produces some reward that has to be allocated to the agents. The reward of a realized project is fully allocated to its contributors, according to a simple proportional rule. Existence and computational complexity of pure Nash equilibria is addressed and their efficiency is investigated according to both the utilitarian and the egalitarian social function

On the Manipulability of Maximum Vertex-Weighted Bipartite bb-matching Mechanisms

In this paper, we study the Maximum Vertex-weighted $b$-Matching (MVbM) problem on bipartite graphs in a new game-theoretical environment. In contrast to other game-theoretical settings, we consider the case in which the value of the tasks is public and common to every agent so that the private information of every agent consists of edges connecting them to the set of tasks. In this framework, we study three mechanisms. Two of these mechanisms, namely \MB and \MD, are optimal but not truthful, while the third one, \MG, is truthful but sub-optimal. Albeit these mechanisms are induced by known algorithms, we show \MB and \MD are the best possible mechanisms in terms of Price of Anarchy and Price of Stability, while \MG is the best truthful mechanism in terms of approximated ratio. Furthermore, we characterize the Nash Equilibria of \MB and \MD and retrieve sets of conditions under which \MB acts as a truthful mechanism, which highlights the differences between \MB and \MD. Finally, we extend our results to the case in which agents' capacity is part of their private information.Comment: 10 pages, 0 figure

05011 Abstracts Collection -- Computing and Markets

From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

The Pareto Frontier of Inefficiency in Mechanism Design

We study the trade-off between the Price of Anarchy (PoA) and the Price of Stability (PoS) in mechanism design, in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to the above metrics, and observe that two fundamental mechanisms, namely the First-Price (FP) and the Second-Price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms $\mathcal{SP}_\alpha$ that lie exactly on this frontier. In particular, these mechanisms range smoothly, with respect to parameter $\alpha\geq 1$ across the frontier, between the First-Price ($\mathcal{SP}_1$) and Second-Price ($\mathcal{SP}_\infty$) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether non-truthful mechanisms can provide better makespan guarantees in the equilibrium, compared to truthful ones. We answer this question in the negative, by proving that the Price of Anarchy of all scheduling mechanisms is at least $n$, where $n$ is the number of machines.Comment: To be published in Mathematics of Operations Researc