Game theory is the study of strategic interaction between rational agents. The need for understanding interaction arises in many different fields, such as: economics, psychology, philosophy, computer science and biology. The purpose of game theory is to analyse the outcomes and strategies of these interactions, in mathematical models called games. Some of these games have stood out from the rest, e.g. Prisoner's Dilemma, Chicken and Stag Hunt. These games, commonly referred to as the standard games, have attracted interest from many fields of research. In order to understand why these games are interesting and how they differ from each other and other games, many have attempted to sort games into interestingly different classes. In this thesis some already existing classifications are reviewed based on their mathematical structure and how well justified they are. Emphasis is put on mathematical simplicity because it makes the classification more generalisable to larger game spaces. From this review we conclude that none of the classifications captures both of these aspects. We therefore propose a classification of symmetric 2x2 games based on decomposition. We show that our proposed method captures everything that the previous classifications caputure. Our method arguably explains the interesting differences between the games, and we justify this claim by computer experiments. Moreover it has a simple mathematical structure. We also provide some results concerning the size of different game spaces.

Traffic flow predictions are an important part of an Intelligent Transportation System as the ability to forecast accurately the traffic conditions in a transportation system allows for proactive rather than reactive traffic control. Providing accurate real-time traffic predictions is a challenging problem because of the nonlinear and stochastic features of traffic flow. An increasingly widespread deployment of traffic sensors in a growing transportation system produces greater volume of traffic flow data. This results in problems concerning fast, reliable and scalable traffic predictions.The thesis explores the feasibility of increasing the scalability of real-time traffic predictions by partitioning the transportation system into smaller subsections. This is done by using data collected by Trafikverket from traffic sensors in Stockholm and Gothenburg to construct a traffic sensor graph of the transportation system. In addition, three graph partitioning algorithms are designed to divide the traffic sensor graph according to vehicle travel time. Finally, the produced transportation system partitions are used to train multi-layered long shortterm memory recurrent neural networks for traffic density predictions. Four different types of models are produced and evaluated based on root mean squared error, training time and prediction time, i.e. transportation system model, partitioned transportation models, single sensor models, and overlapping partition models.Results of the thesis show that partitioning a transportation system is a viable solution to produce traffic prediction models as the average prediction accuracy for each traffic sensor across the different types of prediction models are comparable. This solution tackles scalability issues that are caused by increased deployment of traffic sensors to the transportation system. This is done by reducing the number of traffic sensors each prediction model is responsible for which results in less complex models with less amount of input data. A more decentralized and effective solution can be achieved since the models can be distributed to the edge of the transportation system, i.e. near the physical location of the traffic sensors, reducing prediction and response time of the models. / Prognoser för trafikflödet är en viktig del av ett intelligent transportsystem, eftersom möjligheten att prognostisera exakt trafiken i ett transportsystem möjliggör proaktiv snarare än reaktiv trafikstyrning. Att tillhandahålla noggrann trafikprognosen i realtid är ett utmanande problem på grund av de olinjära och stokastiska egenskaperna hos trafikflödet. En alltmer utbredd använding av trafiksensorer i ett växande transportsystem ger större volym av trafikflödesdata. Detta leder till problem med snabba, pålitliga och skalbara trafikprognoser.Avhandlingen undersöker möjligheten att öka skalbarheten hos realtidsprognoser genom att dela transportsystemet i mindre underavsnitt. Detta görs genom att använda data som samlats in av Trafikverket från trafiksensorer i Stockholm och Göteborg för att konstruera en trafiksensor graf för transportsystemet. Dessutom är tre grafpartitioneringsalgoritmer utformade för att dela upp trafiksensor grafen enligt fordonets körtid. Slutligen används de producerade transportsystempartitionerna för att träna multi-layered long short memory neurala nät för förspänning av trafiktäthet. Fyra olika typer av modeller producerades och utvärderades baserat på rotvärdes kvadratfel, träningstid och prediktionstid, d.v.s. transportsystemmodell, partitionerade transportmodeller, enkla sensormodeller och överlappande partitionsmodeller.Resultat av avhandlingen visar att partitionering av ett transportsystem är en genomförbar lösning för att producera trafikprognosmodeller, eftersom den genomsnittliga prognoser noggrannheten för varje trafiksensor över de olika typerna av prediktionsmodeller är jämförbar. Denna lösning tar itu med skalbarhetsproblem som orsakas av ökad användning av trafiksensorer till transportsystemet. Detta görs genom att minska antal trafiksensorer varje trafikprognosmodell är ansvarig för. Det resulterar i mindre komplexa modeller med mindre mängd inmatningsdata. En mer decentraliserad och effektiv lösning kan uppnås eftersom modellerna kan distribueras till transportsystemets kant, d.v.s. nära trafiksensorns fysiska läge, vilket minskar prognosoch responstid för modellerna.