Solution concepts in two-person multicriteria games

In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.

Multicriterion differential games with applications to combat problems

In this paper a theory for two-person zero sum multicriterion differential games is presented. Various solution concepts based upon the notions of Pareto optimality (efficiency), security and equilibrium are defined. These are shown to have interesting applications in the formulation and analysis of two target or combat differential games. The methods for obtaining outcome regions in the state space, feedback strategies for the players and the mode of play has been discussed in the framework of bicriterion zero sum differential games. The treatment is conceptual rather than rigorous.

Weak Ehrenfeucht-Fraïssé Games

In this paper we define a game which is played between two players I and II on two mathematical structures A and B. The players choose elements from both structures in moves, and at the end of the game the player II wins if the chosen structures are isomorphic. Thus the difference of this to the ordinary Ehrenfeucht-Fra¨ıss´e game is that the isomorphism can be arbitrary, whereas in the ordinary EF-game it is determined by the moves of the players. We investigate determinacy of the weak EF-game for different (the length of the game) and its relation to the ordinary EF-game.

Vision based indoor positioning in a retail environment

Modern smart phones often come with a significant amount of computational power and an integrated digital camera making them an ideal platform for intelligents assistants. This work is restricted to retail environments, where users could be provided with for example navigational in- structions to desired products or information about special offers within their close proximity. This kind of applications usually require information about the user's current location in the domain environment, which in our case corresponds to a retail store. We propose a vision based positioning approach that recognizes products the user's mobile phone's camera is currently pointing at. The products are related to locations within the store, which enables us to locate the user by pointing the mobile phone's camera to a group of products. The first step of our method is to extract meaningful features from digital images. We use the Scale- Invariant Feature Transform SIFT algorithm, which extracts features that are highly distinctive in the sense that they can be correctly matched against a large database of features from many images. We collect a comprehensive set of images from all meaningful locations within our domain and extract the SIFT features from each of these images. As the SIFT features are of high dimensionality and thus comparing individual features is infeasible, we apply the Bags of Keypoints method which creates a generic representation, visual category, from all features extracted from images taken from a specific location. A category for an unseen image can be deduced by extracting the corresponding SIFT features and by choosing the category that best fits the extracted features. We have applied the proposed method within a Finnish supermarket. We consider grocery shelves as categories which is a sufficient level of accuracy to help users navigate or to provide useful information about nearby products. We achieve a 40% accuracy which is quite low for commercial applications while significantly outperforming the random guess baseline. Our results suggest that the accuracy of the classification could be increased with a deeper analysis on the domain and by combining existing positioning methods with ours.

Bicriterion differential games with qualitative outcomes

Combat games are studied as bicriterion differential games with qualitative outcomes determined by threshold values on the criterion functions. Survival and capture strategies of the players are defined using the notion of security levels. Closest approach survival strategies (CASS) and minimum risk capture strategies (MRCS) are important strategies for the players identified as solutions to four optimization problems involving security levels. These are used, in combination with the preference orderings of the qualitative outcomes by the players, to delineate the win regions and the secured draw and mutual kill regions for the players. It is shown that the secured draw regions and the secured mutual kill regions for the two players are not necessarily the same. Simple illustrative examples are given.

Solution concepts in continuous-kernel multicriteria games

This paper considers nonzero-sum multicriteria games with continuous kernels. Solution concepts based on the notions of Pareto optimality, equilibrium, and security are extended to these games. Separate necessary and sufficient conditions and existence results are presented for equilibrium, Pareto-optimal response, and Pareto-optimal security strategies of the players.

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

Molecular profiling of indoor microbial communities in moisture damaged and non-damaged buildings

Epidemiological studies have shown an elevation in the incidence of asthma, allergic symptoms and respiratory infections among people living or working in buildings with moisture and mould problems. Microbial growth is suspected to have a key role, since the severity of microbial contamination and symptoms show a positive correlation, while the removal of contaminated materials relieves the symptoms. However, the cause-and-effect relationship has not been well established and knowledge of the causative agents is incomplete. The present consensus of indoor microbes relies on culture-based methods. Microbial cultivation and identification is known to provide qualitatively and quantitatively biased results, which is suspected to be one of the reasons behind the often inconsistent findings between objectively measured microbiological attributes and health. In the present study the indoor microbial communities were assessed using culture-independent, DNA based methods. Fungal and bacterial diversity was determined by amplifying and sequencing the nucITS- and16S-gene regions, correspondingly. In addition, the cell equivalent numbers of 69 mould species or groups were determined by quantitative PCR (qPCR). The results from molecular analyses were compared with results obtained using traditional plate cultivation for fungi. Using DNA-based tools, the indoor microbial diversity was found to be consistently higher and taxonomically wider than viable diversity. The dominant sequence types of fungi, and also of bacteria were mainly affiliated with well-known microbial species. However, in each building they were accompanied by various rare, uncultivable and unknown species. In both moisture-damaged and undamaged buildings the dominant fungal sequence phylotypes were affiliated with the classes Dothideomycetes (mould-like filamentous ascomycetes); Agaricomycetes (mushroom- and polypore-like filamentous basidiomycetes); Urediniomycetes (rust-like basidiomycetes); Tremellomycetes and the family Malasseziales (both yeast-like basidiomycetes). The most probable source for the majority of fungal types was the outdoor environment. In contrast, the dominant bacterial phylotypes in both damaged and undamaged buildings were affiliated with human-associated members within the phyla Actinobacteria and Firmicutes. Indications of elevated fungal diversity within potentially moisture-damage-associated fungal groups were recorded in two of the damaged buildings, while one of the buildings was characterized by an abundance of members of the Penicillium chrysogenum and P. commune species complexes. However, due to the small sample number and strong normal variation firm conclusions concerning the effect of moisture damage on the species diversity could not be made. The fungal communities in dust samples showed seasonal variation, which reflected the seasonal fluctuation of outdoor fungi. Seasonal variation of bacterial communities was less clear but to some extent attributable to the outdoor sources as well. The comparison of methods showed that clone library sequencing was a feasible method for describing the total microbial diversity, indicated a moderate quantitative correlation between sequencing and qPCR results and confirmed that culture based methods give both a qualitative and quantitative underestimate of microbial diversity in the indoor environment. However, certain important indoor fungi such as Penicillium spp. were clearly underrepresented in the sequence material, probably due to their physiological and genetic properties. Species specific qPCR was a more efficient and sensitive method for detecting and quantitating individual species than sequencing, but in order to exploit the full advantage of the method in building investigations more information is needed about the microbial species growing on damaged materials. In the present study, a new method was also developed for enhanced screening of the marker gene clone libraries. The suitability of the screening method to different kinds of microbial environments including biowaste compost material and indoor settled dusts was evaluated. The usability was found to be restricted to environments that support the growth and subsequent dominance of a small number microbial species, such as compost material.

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.

Endemic malaria: an 'indoor' disease in northern Europe

Background: Endemic northern malaria reached 68°N latitude in Europe during the 19th century, where the summer mean temperature only irregularly exceeded 16°C, the lower limit needed for sporogony of Plasmodium vivax. Because of the available historical material and little use of quinine, Finland was suitable for an analysis of endemic malaria and temperature. Methods: Annual malaria death frequencies during 1800–1870 extracted from parish records were analysed against long-term temperature records in Finland, Russia and Sweden. Supporting data from 1750–1799 were used in the interpretation of the results. The life cycle and behaviour of the anopheline mosquitoes were interpreted according to the literature. Results: Malaria frequencies correlated strongly with the mean temperature of June and July of the preceding summer, corresponding to larval development of the vector. Hatching of imagoes peaks in the middle of August, when the temperature most years is too low for the sporogony of Plasmodium. After mating some of the females hibernate in human dwellings. If the female gets gametocytes from infective humans, the development of Plasmodium can only continue indoors, in heated buildings. Conclusion: Northern malaria existed in a cold climate by means of summer dormancy of hypnozoites in humans and indoor transmission of sporozoites throughout the winter by semiactive hibernating mosquitoes. Variable climatic conditions did not affect this relationship. The epidemics, however, were regulated by the population size of the mosquitoes which, in turn, ultimately was controlled by the temperatures of the preceding summer.

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.