Reverse production systems are often comprised of several tiers with independent members competing at each tier. This research develops and designs a decision-making process for decentralized reverse production systems where each participant in the network determines its decisions in a self-interested way. This dissertation includes three major parts. The first part develops a prototype model for a decentralized reverse production system with two tiers, collectors and processors, focusing on the coordination of transactions of recycled items between these two tiers. The collectors determine the individual material flow allocation mechanisms, based on predictions of the range of prices from the processors, that relate the flow amount to the overall vector of acquisition prices that will be offered by the processors to all the collectors. The processors compete for the flow from the collectors and reach an equilibrium state where no entity is willing to change its decisions. In the second part, we extend the prototype model for a general multi-tiered recycling network comprised of the upstream boundary tier, several intermediate tiers, and the downstream boundary tier where each of the tiers has multiple independent entities. Recycled items flow from the top tier to the downstream tier, but acquisition prices are set from the downstream tier back to the upstream tier. Finally the third part provides a comparison of centralized and decentralized models for reverse production systems and addresses several numerical insights of different system subsidy schemes.

The dissertation deals with the interplay of fiscal and monetary policy in face of uncertainty about the estimation of the true output gap. Theoretical framework of the dissertation set this interplay of monetary and fiscal policy into the realm of game theory, in particularly non-cooperative games of the Nash and Stackelberg equilibrium, respectively. The theoretical framework continued with a description of various methods used for estimation of potential output and output gap, with a special emphasis on methods used in both the Czech National Bank and Czech Ministry of Finance. In the applied part of the dissertation, I studied the interplay of monetary and fiscal policy in the case of Czech economy facing an uncertainty about the estimation of the true output gap. I studied the impact of this interplay on major macroeconomic variables and I tried to determine, which of these two policies plays the role of a leader and which plays the role of a follower in the case of Czech economic environment.

Cette thèse présente de nouvelles techniques pour les Constraint Games.La manière de résoudre un Constraint Game est repensée en terme de propagation de contraintes.Les préférences des joueurs sont maintenant considérées comme des contraintes globales permettant une intégration transparente dans les solveurs de contraintes ainsi que d'améliorer l'efficacité du framework.Notre nouveau solveur ConGA est diffusé en open source.Celui-ci est plus rapide que les travaux connexes et est capable de trouver tous les équilibres de Nash, et cela même dans des jeux avec 200 joueurs voir 2000 pour certains jeux graphiques.Grâce à cette perspective, le framework a pu être utilisé pour résoudre un problème de routage dans le domaine des télécommunications. Les aspects centralisé et décentralisé ont été étudiés.La comparaison de ces derniers est très importante pour évaluer la qualité de service dans les applications multi-utilisateurs. L'évaluation de cette dernière peut être très coûteuse, c'est pourquoi nous proposons plusieurs techniques permettant d'améliorer la résolution de ce problème et ainsi d'améliorer la résolution du problème. / This thesis revisits the Constraint games framework by rethinking their solving technique in terms of constraint propagation.Players preferences are considered as global constraints making transparently the integration in constraints solvers.It yields not only a more elegant but also a more efficient framework.We release our new solver ConGA in open source.Our new complete solver is faster than previous state-of-the-art and is able to find all pure Nash equilibrium for some problems with 200 players or even with 2000 players in graphical games.This new perspective enables us to tackle real-worlds Telecommunication problems.This problem is solved with a centralized perspective and a decentralized one.The comparison of the two last approaches is really important to evaluate the quality of service in multi-users application, but computationally consuming.That is why, we propose new techniques in order to improve the resolution process.

In this thesis we consider a set of mobile users that employ cloud-based computation offloading. In computation offloading, user energy consumption can be decreased by uploading and executing jobs on a remote server, rather than processing the jobs locally. In order to execute jobs in the cloud however, the user uploads must occur over a base station channel which is shared by all of the uploading users. Since the job completion times are subject to hard deadline constraints, this restricts the feasible set of jobs that can be remotely processed, and may constrain the users ability to reduce energy usage. The system is modelled as a competitive game in which each user is interested in minimizing its own energy consumption. The game is subject to the real-time constraints imposed by the job execution deadlines, user specific channel bit rates, and the competition over the shared communication channel. The thesis shows that for a variety of parameters, a game where each user independently sets its offloading decisions always has a pure Nash equilibrium, and a Gauss-Seidel method for determining this equilibrium is introduced. Results are presented which illustrate that the system always converges to a Nash equilibrium using the Gauss-Seidel method. Data is also presented which show the number of Nash equilibria that are found, the number of iterations required, and the quality of the solutions. We find that the solutions perform well compared to a lower bound on total energy performance. / Thesis / Master of Applied Science (MASc)

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Increasing dynamics in power systems on account of renewable integration, electric vehicle penetration and rising demands have resulted in the exploration of energy storage for potential solutions. Recent technology- and industry-driven developments have led to a drastic decrease in costs of these storages, further advocating their usage. This thesis compiles the author's research on optimal integration of energy storage. Unpredictability is modelled using random variables favouring the need of stochastic optimization algorithms such as Lyapunov optimization and stochastic approximation. Moreover, consumer interactions in a competitive environment implore the need of topics from game theory. The concept of Nash equilibrium is introduced and methods to identify such equilibrium points are laid down. Utilizing these notions, two research contributions are made. Firstly, a strategy for controlling heterogeneous energy storage units operating at different timescales is put forth. They strategy is consequently employed optimally for arbitrage in an electricity market consisting of day-ahead and real-time pricing. Secondly, energy storages owned by consumers connected to different nodes of a power distribution grid are coordinated in a competitive market. A generalized Nash equilibrium problem is formulated for their participation in arbitrage and energy balancing, which is then solved using a novel emph{weighted} Lyapunov approach. In both cases, we design real-time algorithms with provable suboptimality guarantees in terms of the original centralized and equilibrium problems. The algorithms are tested on realistic scenarios comprising of actual data from electricity markets corroborating the analytical findings. / Master of Science

This dissertation consists of three chapters on the topic of differential games and resource economics. The first chapter extends the envelope theorem to the class of discounted infinite horizon differential games that posses locally differentiable Nash equilibria. The theorems cover both the open-loop and feedback information structures, and are applied to a simple analytically solvable linear-quadratic game. The results show that the conventional interpretation of the costate variable as the shadow value of the state variable along the equilibrium path is only valid for feedback Nash equilibria, but not for open-loop Nash equilibria. The specific linear-quadratic structure provides some extra insights on the theorem. For example, the costate variable is shown to uniformly overestimate the shadow value of the state variable in the open-loop case, but the growth rate of the costate variable are the same as the shadow value under open-loop and feedback information structures. Chapter two investigates the qualitative properties of symmetric open-loop Nash equilibria for a ubiquitous class of discounted infinite horizon differential games. The results show that the specific functional forms and the value of parameters used in the game are crucial in determining the local asymptotic stability of steady state, the steady state comparative statics, and the local comparative dynamics. Several sufficient conditions are provided to identify a local saddle point type of steady state. An important steady state policy implication from the model is that functional forms and parameter values are not only quantitatively important to differentiate policy tools, but they are also qualitatively important. Chapter three shifts the interests to the lottery mechanism for rationing public resources. It characterizes the optimal pricing strategies of lotteries for a welfare-maximization agency. The optimal prices are shown to be positive for a wide range of individual private value distributions, suggesting that the sub-optimal pricing may result in a significant efficiency loss and that the earlier studies under zero-pricing may need to be re-examined. In addition, I identify the revenue and welfare equivalency propositions across lottery institutions. Finally, the numerical simulations strongly support the findings.

Tato práce se zabývá současnými trendy v aplikaci teorie her k tvorbě ekonomických modelů, které se následně využívají při ekonomickém rozhodování s podporou prostředků informatiky. Práce se zejména opírá o poznatky teorie statických a dynamických her a her s dokonalými a nedokonalými informacemi. Zkoumány jsou modely týkající se sdílení zdrojů, aukcí a managementu. Pro každý z popsaných modelů je prezentována konkrétní aplikace.

The present work seeks to incorporate a popular descriptive, empirically grounded model of human preference under risk, prospect theory, into the equilibrium theory of noncooperative games. Three primary, candidate definitions are systematically identified on the basis of classical characterizations of Nash Equilibrium; in addition, three equilibrium subtypes are defined for each primary definition, in order to enable modeling of players' reference points as exogenous and fixed, slowly and myopically adaptive, highly flexible and non-myopically adaptive. Each primary equilibrium concept was analyzed both theoretically and empirically; for the theoretical analyses, prospect theory, game theory, and computational complexity theory were all summoned to analysis. In chapter 1, the reader is provided with background on each of these theoretical underpinnings of the current work, the scope of the project is described, and its conclusions briefly summarized. In chapters 2 and 3, each of the three equilibrium concepts is analyzed theoretically, with emphasis placed on issues of classical interest (e.g. existence, dominance, rationalizability) and computational complexity (i.e, assessing how difficult each concept is to apply in algorithmic practice, with particular focus on comparison to classical Nash Equilibrium). This theoretical analysis leads us to discard the first of our three equilibrium concepts as unacceptable. In chapter 4, our remaining two equilibrium concepts are compared empirically, using average-level data originally aggregated from a number of studies by Camerer and Selten and Chmura; the results suggest that PT preferences may improve on the descriptive validity of NE, and pose some interesting questions about the nature of the PT weighting function (2003, Ch. 3). Chapter 5 concludes, systematically summarizes theoretical and empirical differences and similarities between the three equilibrium concepts, and offers some thoughts on future work.