Service capacity pooling in M/G/1 service systems

International audienceWe study the cost-sharing problem among independent service providers in a service capacity pooling system. The effective improvement of such pooling system can be achieved by reducing the resource idleness in case of congestion. In this paper, we model both the service provider and the cooperative coalition as a single server queue. We attempt to answer the following questions: (i) which coalition strategy should be used; and (ii) which allocation rule should be selected in order to maintain the stability of the coalition? In particular, we consider the service pooling with a fixed service capacity for M/G/1 service systems. The benefit of the pooling system is due to the shortened waiting queue in the overall system. We develop the corresponding cooperative game with transferable utility, and analyze the core allocations. Although it is difficult to express a core allocation explicitly for the game, we prove the non-emptiness of the core. We give a reasonable expression of Equal Profit Method to distribute the cost for our game, and investigate a number of cost allocation rules under three typical situations to evaluate the gain of the service pooling strategy for each service provider. The numerical results show that the cost allocation rule proposed gives a reasonable cost-sharing result considering the contribution of each participant

Pure Nash Equilibria: Hard and Easy Games

We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems

Participatory Approach in Decision Making Processes for Water Resources Management in the Mediterranean Basin

This paper deals with the comparative analysis of different policy options for water resources management in three south-eastern Mediterranean countries. The applied methodology follows a participatory approach throughout its implementation and is supported by the use of three different software packages dealing with water allocation budget, water quality simulation, and Multi Criteria Analysis, respectively. The paper briefly describes the general objectives of the SMART project and then presents the three local case studies, the valuation objectives and the applied methodology - developed as a general replicable framework suitable for implementation in other decision-making processes. All the steps needed for a correct implementation are therefore described. Following the conceptualisation of the problem, the choice of the appropriate indicators as well as the calculation of their weighting and value functions are detailed. The paper concludes with the results of the Multi Criteria and the related Sensitivity Analyses performed, showing how the different policy responses under consideration can be assessed and furthermore compared through case studies thanks to their relative performances. The adopted methodology was found to be an effective operational approach for bridging scientific modelling and policy making by integrating the model outputs in a conceptual framework that can be understood and utilised by non experts, thus showing concrete potential for participatory decision making.Scientific Advice, Policy-Making, Participatory Modelling, Decision Support

Game theoretic optimisation in process and energy systems engineering: A review

Game theory is a framework that has been used by various research fields in order to represent dynamic correlation among stakeholders. Traditionally, research within the process and energy systems engineering community has focused on the development of centralised decision making schemes. In the recent years, decentralised decision-making schemes have attracted increasing attention due to their ability to capture multi-stakeholder dynamics in a more accurate manner. In this article, we survey how centralised and decentralised decision making has been facilitated by game theoretic approaches. We focus on the deployment of such methods in process systems engineering problems and review applications related to supply chain optimisation problems, design and operations, and energy systems optimisation. Finally, we analyse different game structures based on the degree of cooperation and how fairness criteria can be employed to find fair payoff allocations

Mutual information-based group explainers with coalition structure for machine learning model explanations

In this article, we propose and investigate ML group explainers in a general game-theoretic setting with the focus on coalitional game values and games based on the conditional and marginal expectation of an ML model. The conditional game takes into account the joint distribution of the predictors, while the marginal game depends on the structure of the model. The objective of the article is to unify the two points of view under predictor dependencies and to reduce the complexity of group explanations. To achieve this, we propose a feature grouping technique that employs an information-theoretic measure of dependence and design appropriate groups explainers. Furthermore, in the context of coalitional game values with a two-step formulation, we introduce a theoretical scheme that generates recursive coalitional game values under a partition tree structure and investigate the properties of the corresponding group explainers.Comment: 46 pages, 69 figure

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Játékelméleti kutatások = Investigations in Game Theory

A játékelmélet különböző kérdésköreiben végzett kutatásaink eredményeit eddig 9 nemzetközi és 5 hazai folyóiratban, valamint 2 szerkesztett kötetben már megjelent cikkben közöltük (és további 2-4 nemzetközi cikkre számítunk). Eredményeinket több mint 30 nemzetközi, illetve hazai konferencia előadásban is bemutattuk. Legfontosabb eredményeink: • Megmutattuk, hogy a Nash-féle alkuproblémákra ismert implementációs modellek átalakításával megkapható a limit-Nash megoldás is. • Bevezettük a puha korrelált egyensúly fogalmát. Bemutattuk, hogy ez az új korrelált egyensúly több modellben Pareto-értelemben jobb megoldást eredményez, mint más korrelált egyensúlyok. • Megmutattuk, hogy a hozzárendelési piacokon bármelyik szereplő eredményesen tudja manipulálni a ’fair egyensúlyi’, illetve a nukleolusz allokációs mechanizmust, ugyanakkor éles felső korlátokat is megadtunk ennek mértékére. • Karakterizáltuk a stabil halmazokat az egy-eladós hozzárendelési játékokban. • Különféle játékosztályokon megvizsgáltuk a Shapley-érték főbb karakterizációjainak érvényességét. Erre alapozva javasoltuk a Shapley-érték ’mérési eszközként’ való használatát a regressziós modellekben, az általánosított szavazási helyzetekben, illetve a rizikó allokációs problémákban. • Megmutattuk, hogy nincsen univerzális topologikus típustér, a Harsányi-program ilyen típusterekben tehát nem működik. Ugyanakkor matematikailag megalapoztunk egy ilyen jellegű, a mérhető típusterekre vonatkozó pozitív eredményt. | We have investigated various topics in game theory and published so far 9 articles in international journals (and expect to have 2-4 more), 5 articles in domestic journals, 2 papers in an edited volume. We have also presented our results in more than 30 talks at international and domestic conferences. Our main contributions include (but not limited to) the following: • We adjusted various implementation models designed for Nash bargaining problems to obtain the limit-Nash solution as well. • We introduced a new correlation protocol. We demonstrated in several settings that this new (called soft) correlated equilibrium can give Pareto-better outcomes than what other correlated equilibria can. • We showed that in assignment markets each agent can manipulate the ’fair equilibrium’ and the nucleolus allocation mechanisms to his benefit, but established sharp upper bounds to its extent. • We characterized stable sets in assignment games with one-seller. • We examined several characterizations of the Shapley value on various classes of games. Based on these results, we proposed using the Shapley-value as a ’measurement’ tool in regression models, in generalized weighted voting situations, and in risk allocation problems. • We have demonstrated that the Harsányi program does not work in topological type spaces, therefore no universal topological type space exists. We have laid the mathematical foundation of a positive result on measurable type spaces

Collective agency:From philosophical and logical perspectives

People inhabit a vast and intricate social network nowadays. In addition to our own decisions and actions, we confront those of various groups every day. Collective decisions and actions are more complex and bewildering compared to those made by individuals. As members of a collective, we contribute to its decisions, but our contributions may not always align with the outcome. We may also find ourselves excluded from certain groups and passively subjected to their influences without being aware of the source. We are used to being in overlapping groups and may switch identities, supporting or opposing the claims of particular groups. But rarely do we pause to think: What do we talk about when we talk about groups and their decisions?At the heart of this dissertation is the question of collective agency, i.e., in what sense can we treat a group as a rational agent capable of its action. There are two perspectives we take: a philosophical and logical one. The philosophical perspective mainly discusses the ontological and epistemological issues related to collective agency, sorts out the relevant philosophical history, and argues that the combination of a relational view of collective agency and a dispositional view of collective intentionality provides a rational and realistic account. The logical perspective is associated with formal theories of groups, it disregards the psychological content involved in the philosophical perspective, establishes a logical system that is sufficiently formal and objective, and axiomatizes the nature of a collective