The complexity of power indices in voting games with incompatible players

We study the complexity of computing the Banzhaf index in weighted voting games with cooperation restricted by an incompatibility graph. With an existing algorithm as a starting point, we use concepts from complexity theory to show that, for some classes of incompatibility graphs, the problem can be solved efficiently, as long as the players have "small" weights. We also show that for some other class of graphs it is unlikely that we can find efficient algorithms to compute the Banzhaf index in the corresponding restricted game. Finally, we discuss the complexity of deciding whether the index of a player is non-zero

An economic analysis of the councils of the United Nations

This thesis consists of three pieces of research focussed on the Councils of the United Nations, predominantly the United Nations Security Council (UNSC). We consider three broad questions: which countries typically get on to the UNSC in its current form; which countries ought to get on to the UNSC; and how well might proposed changes to the UNSC steer it towards such ideals. In order to address the latter two questions it is sensible to begin by investigating how the current system works and if there are any particular characteristics which influence the chances of a country being elected to the UNSC. In Chapter 2 we develop a model to test the significance of a country’s characteristics on their probability of election to the UNSC. Chapter 3 then starts by developing a set of theoretical tests which can be applied to council voting systems, such as the selection of UNSC members from the UN General Assembly. The tests score a voting system based on how well the distribution of power in the council meets the power one would expect under a system where country representatives cast their vote in the council based on the outcomes of country or regional-level referendums. We then apply this, using the implied probabilities of election which are a consequence of the results of Chapter 2, to the UNSC election process. We then finish by applying the tests of Chapter 3, which consider how equitable a proposal is, together with a further test of procedural efficiency, to each of the proposed reforms to the UNSC election process

Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.

Models of Political Economy

Models of Political Economy will introduce students to the basic methodology of political economics. It covers all core theories as well as new developments including: decision theory game theory mechanism design games of asymmetric information. Hannu Nurmi's text will prove to be invaluable to all students who wish to understand this increasingly technical field

Investigation of Game-Theoretic Mechanisms for the Valuation of Energy Resources

Electricity systems are facing the pressure to change in response to the effects of new technology, particularly the proliferation of renewable technologies (such as solar PV systems and wind generation) leading to the retirement of traditional generation technologies that provide stabilising inertia. These changes create an imperative to consider potential future market structures to facilitate the participation of distributed energy resources (DERs; such as EVs and batteries) in grid operation. However, this gives rise to general questions surrounding the ethics of market structures and how they could be fairly applied in future electricity systems. Particularly the most basic question "how should electricity be valued and traded" is fundamentally a moral question without any easy answer. We give a survey of philosophical attitudes around such a question, before presenting a series of ways that these intuitions have been cast into mathematics, including: the Vickrey-Clarke-Groves mechanism, Locational Marginal Pricing, the Shapley Value, and Nash bargaining solution concepts. We compared these different methods, and attempted a new synthesis that brought together the best features of each of them; called the 'Generalised Neyman and Kohlberg Value' or the GNK-value for short. The GNK value was developed as a novel bargaining solution concept for many player non-cooperative transferable utility generalised games, and thus it was intrinsically flexible in its application to various aspects of powersystems. We demonstrated the features of the GNK-value against the other mathematical solutions in the context of trading the immediate consumption/generation of power on small sized networks under linear-DC approximation, before extending the computation to larger networks. The GNK value proved to be difficult to compute for large networks but was shown to be approximable for larger networks with a series of sampling techniques and a proxy method. The GNK value was ethically compared to other mechanisms with the unfortunate discovery that it allowed for participants to be left worse-off for participating, violating the ethical notion of 'euvoluntary exchange' and 'individual rationality'; but was offered as an interesting innovation in the space of transferable utility generalised games notwithstanding. For sampling the GNK value, there was a range of new and different techniques developed for stratified random sampling which iteratively minimise newly derived concentration inequalities on the error of the sampling. These techniques were developed to assist in the computation of the GNK value to larger networks, and they were evaluated in the context of sampling synthetic data, and in computation of the Shapley Value of cooperative game theory. These new sampling techniques were demonstrated to be comparable to the more orthodox Neyman sampling method despite not having access to stratum variances

On the Combination of Game-Theoretic Learning and Multi Model Adaptive Filters

This paper casts coordination of a team of robots within the framework of game theoretic learning algorithms. In particular a novel variant of fictitious play is proposed, by considering multi-model adaptive filters as a method to estimate other players’ strategies. The proposed algorithm can be used as a coordination mechanism between players when they should take decisions under uncertainty. Each player chooses an action after taking into account the actions of the other players and also the uncertainty. Uncertainty can occur either in terms of noisy observations or various types of other players. In addition, in contrast to other game-theoretic and heuristic algorithms for distributed optimisation, it is not necessary to find the optimal parameters a priori. Various parameter values can be used initially as inputs to different models. Therefore, the resulting decisions will be aggregate results of all the parameter values. Simulations are used to test the performance of the proposed methodology against other game-theoretic learning algorithms.</p