The Cost of Stability in Coalitional Games

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the \emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particular coalition structure). This payment is conditional on players not deviating from their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the \emph{cost of stability (CoS)} as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.Comment: 20 pages; will be presented at SAGT'0

On the Complexity of Core, Kernel, and Bargaining Set

Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single out the most desirable outcomes in terms of appropriate notions of worth distributions, which are usually called solution concepts. Motivated by the fact that decisions taken by realistic players cannot involve unbounded resources, recent computer science literature reconsidered the definition of such concepts by advocating the relevance of assessing the amount of resources needed for their computation in terms of their computational complexity. By following this avenue of research, the paper provides a complete picture of the complexity issues arising with three prominent solution concepts for coalitional games with transferable utility, namely, the core, the kernel, and the bargaining set, whenever the game worth-function is represented in some reasonable compact form (otherwise, if the worths of all coalitions are explicitly listed, the input sizes are so large that complexity problems are---artificially---trivial). The starting investigation point is the setting of graph games, about which various open questions were stated in the literature. The paper gives an answer to these questions, and in addition provides new insights on the setting, by characterizing the computational complexity of the three concepts in some relevant generalizations and specializations.Comment: 30 pages, 6 figure

Initial State Stabilities and Inverse Engineering in Conflict Resolution

Two original contributions are made which extend the Graph Model for Conflict Resolution: one is a new family of solution concepts, while the other is a novel methodological approach. In addition to theoretical contributions, applications to complex energy problems are demonstrated; in particular, the consideration of the ongoing Trans Mountain Expansion Project is the first of its kind. The family of solution concepts, called initial state stabilities, is designed to complement existing solution concepts within the Graph Model framework by modelling both risk-averse and risk-seeking decision-makers. The comparison which underpins these concepts examines the consequences of moving from a given starting state to those of remaining in that state. The types of individuals modelled by these stability concepts represent a new class of decision-makers which, up until now, had not been considered in the Graph Model paradigm. The innovative methodology presented is designed to "inverse engineer" decision-makers’ preferences based on their observable behaviour. The algorithms underlying the inverse engineering methodology are based on the most commonly used stability concepts in the Graph Model for Conflict Resolution and function by reducing the set of possible preference rankings for each decision-maker. The reduction is based on observable moves and counter-moves made by decision-makers. This procedure assists stakeholders in optimizing their own decision-making process based on information gathered about their opponents and can also be used to improve the modelling of strategic interactions. In addition to providing decision-makers and analysts with up-to-date preference information about opponents, the methodology is also equipped with an ADVICE function which enriches the decision-making process by providing important information regarding potential moves. Decision-makers who use the methods introduced in this thesis are provided with the expected value of each of their possible moves, with the probability of the opponent’s next response, and with the opponent reachable states. This insightful data helps establish an accurate picture of the conflict situation and in so doing, aids stakeholders in making strategic decisions. The applicability of this methodology is demonstrated through the study of the conflict surrounding the Trans Mountain Expansion Project in British Columbia, Canada

Risk Hedging Strategies in New Energy Markets

In recent years, two typical developments have been witnessed in the energy market. On the one hand, the penetration of renewable generations has gradually replaced parts of the traditional ways to generate energy. The intermittent nature of renewable generation can lead to energy supply uncertainty, which might exacerbate the imbalance between energy supply and demand. As a result, the problem of energy price risks might occur. On the other hand, with the introduction of distributed energy resources (DERs), new categories of markets besides traditional wholesale and retail markets are emerging. The main benefits of the penetration of DERs are threefold. First, DERs can increase power system reliability. Second, the cost of transmission can be reduced. Third, end users can directly participate in some of these new types of markets according to their energy demand, excess energy, and cost function without third-party intervention. However, energy market participants might encounter various types of uncertainties. Therefore, it is necessary to develop proper risk-hedging strategies for different energy market participants in emerging new markets. Thus, we propose risk-hedging strategies that can be used to guide various market participants to hedge risks and enhance utilities in the new energy market. These participants can be categorized into the supply side and demand side. Regarding the wide range of hedging tools analyzed in this thesis, four main types of hedging strategies are developed, including the application of ESS, financial tools, DR management, and pricing strategy. Several benchmark test systems have been applied to demonstrate the effectiveness of the proposed risk-hedging strategies. Comparative studies of existing risk hedging approaches in the literature, where applicable, have also been conducted. The real applicability of the proposed approach has been verified by simulation results