A large class of sequential decision making problems under uncertainty with multiple competing decision makers/agents can be modeled as stochastic games. Stochastic games having Markov properties are called Markov games or competitive Markov decision processes. This dissertation presents an approach to solve non cooperative stochastic games, in which each decision maker makes her/his own decision independently and each has an individual payoff function. In stochastic games, the environment is nonstationary and each agent's payoff is affected by joint decisions of all agents, which results in the conflict of interest among the decision makers. In this research, the theory of Markov decision processes (MDPs) is combined with the game theory to analyze the structure of Nash equilibrium for stochastic games. In particular, the Laurent series expansion technique is used to extend the results of discounted reward stochastic games to average reward stochastic games. As a result, auxiliary matrix games are developed that have equivalent equilibrium points and values to a class of stochastic games that are irreducible and have average reward performance metric. R-learning is a well known machine learning algorithm that deals with average reward MDPs. The R-learning algorithm is extended to develop a Nash-R reinforcement learning algorithm for obtaining the equivalent auxiliary matrices. A convergence analysis of the Nash-R algorithm is developed from the study of the asymptotic behavior of its two time scale stochastic approximation scheme, and the stability of the associated ordinary differential equations (ODEs). The Nash-R learning algorithm is tested and then benchmarked with MDP based learning methods using a well known grid game. Subsequently, a real life application of stochastic games in deregulated power market is explored. According to the current literature, Cournot, Bertrand, and Supply Function Equilibrium (SFEs) are the three primary equilibrium models that are used to evaluate the power market designs. SFE is more realistic for pool type power markets. However, for a complicated power system, the convex assumption for optimization problems is violated in most cases, which makes the problems more difficult to solve. The SFE concept in adopted in this research, and the generators' behaviors are modeled as a stochastic game instead of one shot game. The power market is considered to have features such as multi-settlement (bilateral, day-ahead market, spot markets and transmission congestion contracts), and demand elasticity. Such a market consisting of multiple competing suppliers (generators) is modeled as a competitive Markov decision processes and is studied using the Nash-R algorithm.

Doctor of Philosophy (PhD) / This thesis examines the growing debate around the concept of social capital. The concept has been heralded by many as a means of uniting the social sciences, particularly economics and sociology, and of overcoming ideological divisions between left and right. However, critics argue that the concept is poorly theorised and provides little insight. More radical critics have claimed the concept may be a neo-liberal ‘Trojan horse’, a mechanism by which the atomistic thinking of neoclassical economics colonises social theory. I examine these more radical claims by exploring the origins of the concept of social capital within rational choice economics. I argue that we should differentiate between two types of potential colonisation. The first is a form of methodological colonisation, whereby overly abstract, reductionist and rationalist approaches (which I term modernist) are extended into social theory. The second is a form of ideological colonisation, whereby a normative commitment to individualism and the market is extended into social theory. I argue that the concept of social capital has been the product of a trend within rational choice economics away from the extremes of modernism. In this sense the concept represents an attempt to bring economics and social theory closer together, and a willingness on the part of rational choice theorists to take more seriously the techniques and insights of the other social sciences. However, I argue that this trend away from modernism has often been associated with a reaffirmation of rational choice theorists’ normative commitment to individualism and the market. In particular, I argue the concept of social capital has been strongly influenced by elements of the Austrian economic tradition, and forms part of a spontaneous order explanation of economic and social systems. I then apply these insights to the Australian social capital debate. I argue that initially the Australian social capital debate continued an earlier debate over economic rationalism and the merits of market-orientated economic reform. I argue that participants from both sides of the economic rationalism debate used the concept of social capital to move away from modernism, but continued to disagree over the role of individualism. Finally, I argue that confusion between moving away from modernism, and moving away from market ideology, has led some Third Way theorists to misconstrue the concept as a means to overcome ideology.

<p>Whist is one of the most played card games of the world. Though there have been many studies made in the field of game theory, whist is still somewhat of an unchartered territory. In this thesis some methods to obtain an optimal strategy for whist are discussed. </p><p>Whist belongs to a group of games called logical games. For this group there exists algorithms which result in an optimal strategy. Two algorithms where examined. The minmax algorithm and the alphbeta algorithm. these algorithms could be adapted to whist </p><p>It is possible that there are methods that use the properties of the cards better the the former algorithms to get an optimal result. A few such methods will also be discussed. </p><p>The practical result of the theoretical investigation was a game where the adapted algorithms were implemented. </p>

<p>According to the Leniency programme that was implemented in Sweden in 2002, a company participating in a cartel can escape administrative fines if it exposes the cartel to the Swedish Competition Authority and cooperates with the Authority during its investigation. Whether cartels should be criminalized, or not, has been debated in the Swedish Parliament in recent years. If cartels are turned into a felony, the leaders of the companies involved risk being held personally responsible.</p><p>This essay discusses how the incitements for unveiling cartels take form, drawing on game-theoretical models. The essay, in addition, analyses how the incitement-structure would change if cartels would become a felony, compared to the current legislation, in the form of the Leniency programme.</p><p>The conclusions that the author arrives at are that the incitements to expose cartels would increase if fines were to increase. The incitements would furthermore increase if the company feared that someone within the organization could expose the cartel to the Competition Authority. Turning cartels into a felony would on the contrary decrease the incitements for unveiling the cartel. The key task for the Competition Authority, as regards to cartels, should hence be to create uncertainty for firms participating in cartels and increase the security of employees if and when exposing their employer as a participant in a cartel.</p> / <p>År 2002 skrevs Leniencyprogrammen in i svensk konkurrenslagstiftning. Ett företag som ingår i ett kartellsamarbete kan i enlighet med programmen undslippa konkurrensskadeavgift ifall företaget avslöjar kartellen och samarbetar med konkurrensverket. Under senare år har en debatt kring huruvida karteller bör kriminaliseras eller inte förts i Riksdagen. En kriminalisering skulle innebära personligt straffansvar för bland annat företagsledare.</p><p>Uppsatsens syfte är att med spelteoretiska modeller och resonemang kartlägga och analysera hur incitamentsstrukturen för avslöjandet av karteller kan tänkas se ut. Vidare syftar uppsatsen till att föra en diskussion kring hur incitamentsstrukturen kan tänkas förändras om nuvarande lagstiftning ändras till att medföra en kriminalisering av karteller.</p><p>Slutsatser som kan dras av uppsatsens analys är att incitamenten för avslöjande med nuvarande lagstiftning skulle öka om konkurrensskadeavgifterna höjs. En kriminalisering skulle minska incitamenten för avslöjande, jämfört med nuvarande lagstiftning. Incitamenten för företagen att avslöja karteller ökar om företagen befarar att någon inom organisationen har för avsikt att avslöja kartellen till konkurrensverket. Konkurrensverkets viktigaste uppgift vad gäller kartellbekämpning torde därmed bli att skapa osäkerheter för företagen på flera områden för att öka misstron mellan aktörerna samt att arbeta för att öka anställdas incitament att avslöja sin arbetsgivares inblandning i kartellsamarbeten.</p>

Future wireless communications expect to experience a spectrum shortage problem. One practical solution is spectrum sharing. This thesis studies precoding strategies to allocate communication resources for spectrum sharing in multi-user wireless systems from a game-theoretic perspective. The approaches for the precoding games are developed under different constraints. It is shown that the precoding game with spectral mask constraints can be formulated as a convex optimization problem and a dual decomposition based algorithm can be exploited to solve it. However, the problem is non-convex if users also have total power constraints. This study shows that an efficient sub-optimal solution can be derived by allocating the bottleneck resource in the system. The sub-optimal solution is proved to be efficient and can even achieve an identical performance to that of the optimal solution in certain cases, but with significantly reduced complexity. / Communications

This paper studies the problem of multi-period pricing for perishable products in a competitive (oligopolistic) market. We study non cooperative Nash equilibrium policies for sellers. At the beginning of the time horizon, the total inventories are given and additional production is not an available option. The analysis for periodic production-review models, where production decisions can be made at the end of each period at some production cost after incurring holding or backorder costs, does not extend to this model. Using results from game theory and variational inequalities we study the existence and uniqueness of equilibrium policies. We also study convergence results for an algorithm that computes the equilibrium policies. The model in this paper can be used in a number of application areas including the airline, service and retail industries. We illustrate our results through some numerical examples. / Singapore-MIT Alliance (SMA)

Thesis (M.A.)--Ohio University, June, 2005. / Title from PDF t.p. Includes bibliographical references (p. 132-140)

The problem of relating inter-agent and intra-agent behavioral specifications is investigated. These two views are complimentary, in that the former is closer to scenario-based user requirements whereas the latter is design-oriented. We use a graphical, user-friendly and very simple language as inter-agent specification language: Live Sequence Charts (LSC). LSC is presented and its properties are investigated: it is highly succinct, but inexpressive. There are essentially two ways to relate inter-agent and intra-agent specifications: (i) by checking that an intra-agent specification is correct with respect to some LSC specification and (ii) by automatically building an intra-agent specification from an LSC specification. Several variants of these problems exist: closed/open systems and centralized/distributed systems. We give inefficient but optimal algorithms solving all problems, besides synthesis of open distributed systems, which we show is undecidable. All the problems considered are difficult, even for a very restricted subset of LSCs, without alternatives, interleaving, conditions nor loops. We investigate the cost of extending the language with control flow constructs, conditions, real-time and symbolic instances. An implementation of the algorithms is proposed. The applicability of the language is illustrated on a real-world case study.

La théorie des jeux est un outils standard quand il s'agit de l'étude des systèmes réactifs. Ceci est une conséquence de la variété des modèles de jeux tant au niveau de l'interaction des joueurs qu'au niveau de l'information que chaque joueur possède. Dans cette thèse, on étudie le problème de la valeur pour des jeux où les joueurs possèdent une information parfaite, information partiel et aucune information. Dans le cas où les joueurs possèdent une information parfaite sur l'état du jeu, on étudie le problème de la valeur pour des jeux dont les objectifs sont des combinaisons booléennes d'objectifs qualitatifs et quantitatifs. Pour les jeux stochastiques à un joueur, on montre que les valeurs sont calculables en temps polynomiale et on montre que les stratégies optimales peuvent être implementées avec une mémoire finie. On montre aussi que notre construction pour la conjonction de parité et de la moyenne positive peut être étendue au cadre des jeux stochastiques à deux joueurs. Dans le cas où les joueurs ont une information partielle, on étudie le problème de la valeur pour la condition d'accessibilité. On montre que le calcul de l'ensemble des états à valeur 1 est un problème indécidable, on introduit une sous classe pour laquelle ce problème est décidable. Le problème de la valeur 1 pour cette sous classe est PSPACE-complet dans le cas de joueur aveugle et dans EXPTIME dans le cas de joueur avec observations partielles.

A trade-off between seed size and seed number is central in seed ecology, and has been suggested to be related to a trade-off between competition and colonization, as well as to a trade-off between stress tolerance and fecundity. Large seeds endure hazards during establishment, such as shading, drought, litter coverage and competition from other plants, better than do small seeds, due to a larger amount of stored resources in the seed. Small seeds, however, are numerous and small-seeded species are therefore more fecund. Moreover, a pattern with small-seeded species being associated with open habitats and large-seeded species being associated with closed habitats has been reported in the literature. In this thesis I assess effects of seed size on recruitment, and how relationships between seed size and recruitment may relate to habitat conditions. Seed sowing experiments were performed in the field to assess inter- and intra-specific relationships between seed size and recruitment in open and closed habitats (Paper I and II). Seed removal experiments were performed in the field to assess what effects seed predation may have on a relationship between seed size and recruitment (Paper III). A garden experiment was performed based on contests between larger-seeded and smaller-seeded species, in order to examine different models on co-existence of multiple seed size strategies. The results showed that there was a weak positive relationship between seed size and recruitment in the field, and that this relationship was only weakly and inconclusively related to habitat (Paper I and II). Seed removal was negatively related to seed size in closed habitats and unrelated to seed size in open habitats (Paper III). This indicates that any positive relationship between seed size and recruitment may be an effect of higher seed removal in small-seeded species. However, when grown under controlled conditions in a garden experiment, there was a clear advantage of larger-seeded species over smaller-seeded species (Paper IV). This advantage was unaffected by seed density, indicating that there was no competitive advantage of the larger-seeded species. Instead, indirect evidence suggests that larger-seeded species exhibit higher tolerance to stress. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Accepted.</p><p> </p>