Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Denumerable state stochastic games with limiting average payoff

We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.

Determination of rational strategies for players in two-target games

This paper addresses some of the basic issues involved in the determination of rational strategies for players in two-target games. We show that unlike single-target games where the task of role assignment and selection of strategies is conceptually straightforward, in two-target games, many factors like the preference ordering of outcomes by players, the relative configuration of the target sets and secured outcome regions, the uncertainty about the parameters of the game, etc., also influence the rational selection of strategies by players. The importance of these issues is illustrated through appropriate examples.

Migration-Development Nexus in the Malawian Health Sector: European Union Blue Card – circular migration for development?

The European Union has agreed on implementing the Policy Coherence for Development (PCD) principle in all policy sectors that are likely to have a direct impact on developing countries. This is in order to take account of and support the EU development cooperation objectives and the achievement of the internationally agreed Millennium Development Goals. The common EU migration policy and the newly introduced EU Blue Card directive present an example of the implementation of the principle in practice: the directive is not only designed to respond to the occurring EU labour demand by attracting highly skilled third-country professionals, but is also intended to contribute to the development objectives of the migrant-sending developing countries, primarily through the tool of circular migration and the consequent skills transfers. My objective in this study is to assess such twofold role of the EU Blue Card and to explore the idea that migration could be harnessed for the benefit of development in conformity with the notion that the two form a positive nexus. Seeing that the EU Blue Card fails to differentiate the most vulnerable countries and sectors from those that are in a better position to take advantage of the global migration flows, the developmental consequences of the directive must be accounted for even in the most severe settings. Accordingly, my intention is to question whether circular migration, as claimed, could address the problem of brain drain in the Malawian health sector, which has witnessed an excessive outflow of its professionals to the UK during the past decade. In order to assess the applicability, likelihood and relevance of circular migration and consequent skills transfers for development in the Malawian context, a field study of a total of 23 interviews with local health professionals was carried out in autumn 2010. The selected approach not only allows me to introduce a developing country perspective to the on-going discussion at the EU level, but also enables me to assess the development dimension of the EU Blue Card and the intended PCD principle through a local lens. Thus these interviews and local viewpoints are at the very heart of this study. Based on my findings from the field, the propensity of the EU Blue Card to result in circular migration and to address the persisting South-North migratory flows as well as the relevance of skills transfers can be called to question. This is as due to the bias in its twofold role the directive overlooks the importance of the sending country circumstances, which are known to determine any developmental outcomes of migration, and assumes that circular migration alone could bring about immediate benefits. Without initial emphasis on local conditions, however, positive outcomes for vulnerable countries such as Malawi are ever more distant. Indeed it seems as if the EU internal interests in migration policy forbid the fulfilment of the PCD principle and diminish the attempt to harness migration for development to bare rhetoric.

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Provider-Customer Coalitional Games

Efficacy of commercial wireless networks can be substantially enhanced through large-scale cooperation among involved entities such as providers and customers. The success of such cooperation is contingent upon the design of judicious resource allocation strategies that ensure that the individuals' payoffs are commensurate to the resources they offer to the coalition. The resource allocation strategies depend on which entities are decision-makers and whether and how they share their aggregate payoffs. Initially, we consider the scenario where the providers are the only decision-makers and they do not share their payoffs. We formulate the resource allocation problem as a nontransferable payoff coalitional game and show that there exists a cooperation strategy that leaves no incentive for any subset of providers to split from the grand coalition, i.e., the core of the game is nonempty. To compute this cooperation strategy and the corresponding payoffs, we subsequently relate this game and its core to an exchange market setting and its equilibrium, which can be computed by several efficient algorithms. Next, we investigate cooperation when customers are also decision-makers and decide which provider to subscribe to based on whether there is cooperation. We formulate a coalitional game in this setting and show that it has a nonempty core. Finally, we extend the formulations and results to the cases where the payoffs are vectors and can be shared selectively.

Gate Drive Card for High Power Three Phase PWM Converters

Gate driver is an integral part of every power converter, drives the power semiconductor devices and also provides protection for the switches against short-circuit events and over-voltages during shut down. Gate drive card for IGBTs and MOSFETs with basic features can be designed easily by making use of discrete electronic components. Gate driver ICs provides attractive features in a single package, which improves reliability and reduces effort of design engineers. Either case needs one or more isolated power supplies to drive each power semiconductor devices and provide isolation to the control circuitry from the power circuit. The primary emphasis is then to provide simplified and compact isolated power supplies to the gate drive card with the requisite isolation strength and which consumes less space, and for providing thermal protection to the power semiconductor modules for 3-� 3 wire or 4 wire inverters.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

General-sum stochastic games: Verifiability conditions for Nash equilibria

Unlike zero-sum stochastic games, a difficult problem in general-sum stochastic games is to obtain verifiable conditions for Nash equilibria. We show in this paper that by splitting an associated non-linear optimization problem into several sub-problems, characterization of Nash equilibria in a general-sum discounted stochastic games is possible. Using the aforementioned sub-problems, we in fact derive a set of necessary and sufficient verifiable conditions (termed KKT-SP conditions) for a strategy-pair to result in Nash equilibrium. Also, we show that any algorithm which tracks the zero of the gradient of the Lagrangian of every sub-problem provides a Nash strategy-pair. (c) 2012 Elsevier Ltd. All rights reserved.

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.