Pelaamiskokemukset ja pelaamisen yksilöllisten merkitysten yhteys flow n kokemiseen

The main goal of this study was to explore experiences induced by playing digital games (i.e. meaning of playing). In addition, the study aimed at structuring the larger entities of gaming experience. This was done by using theory-driven and data grounded approaches. Previously gaming experiences have not been explored as a whole. The consideration of gaming experiences on the basis of psychological theories and studies has also been rare. The secondary goal of this study was to clarify, whether the individual meanings of playing are connected with flow experience in an occasional gaming situation. Flow is an enjoyable experience and usually activities that induce flow are gladly repeated. Previously, flow has been proved to be an essential concept in the context of playing, but the relations between meanings of playing and flow have not been studied. The relations between gender and gaming experiences were examined throughout the study, as well as the relationship between gaming frequency and experiences. The study was divided into two sections, of which the first was composed according to the main goals. Its data was gathered by using an Internet questionnaire. The other section covered the themes that were formulated on the basis of the secondary aims. In that section, the participants played a driving game for 40 minutes and then filled in a questionnaire, which measured flow related experiences. In both sections, the participants were mainly young Finnish adults. All the participants in the second section (n = 60) had already participated in the first section (n = 267). Both qualitative and quantitative research techniques were used in the study. In the first section, freely described gaming experiences were classified according to the grounded theory. After that, the most common categories were further classified into the basic structures of gaming experience, some according to the existing theories of experience structure and some according to the data (i.e. grounded theory). In the other section flow constructs were measured and used as grouping variables in a cluster analysis. Three meaningful groups were compared regarding the meanings of gaming that were explored in the first section. The descriptions of gaming experiences were classified into four main categories, which were conceptions of the gaming process, emotions, motivations and focused attention. All the theory-driven categories were found in the data. This frame of reference can be utilized in future when reliability and validity of already existing methods for measuring gaming experiences are considered or new methods will be developed. The connection between the individual relevance of gaming and flow was minor. However, as the scope was specified to relations between primary meanings of playing and flow, it was noticed that attributing enjoyment to gaming did not lead to the strongest flow-experiences. This implies that the issue should be studied more in future. As a whole this study proves that gamer-related research from numerous vantage points can benefit from concentrating on gaming experiences.

Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

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.

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