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.

Enterprise architecture – the foundation for a strategy

Artikkeli selostaa kokonaisarkkitehtuurin käsitettä ja Kansallinen digitaalinen kirjasto -hankkeen kokonaisarkkitehtuurin laatimista. Kokonaisarkkitehtuuri on tietohallinnon strategisen suunnittelun ja johtamisen väline, mutta sillä on monia käytännöllisempia käyttötarkoituksia esimerkiksi tietojärjestelmien kehittämisessä. Kansallinen digitaalinen kirjasto on opetus- ja kulttuuriministeriön tavoitteena on varmistaa kulttuurin ja tieteen digitaalisten tietovarantojen tehokas ja laadukas hallinta, jakelu ja pitkäaikaissäilytys. Lisäksi hankkeessa edistetään kulttuuriperintö- ja asiakirja-aineistojen digitointia.

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

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.

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.