An age-structured model for a distributive channel

Negli ultimi anni, modelli con struttura per età sono stati studiati in diversi ambiti, da problemi di approviggionamento a ottimizzazione di coperture vaccinali e controllo di epidemie. Il motivo è che la struttura per età è tra la più semplici da studiare in una popolazione, dato che l'età evolve linearmente col tempo. Questo lavoro di tesi introduce una struttura per età nel lavoro di Buratto e Grosset, 'Advertising & Promotion in a marketing channel'. Nello specifico, il modello è un gioco differenziale a tempo infinito e lineare nello stato, con due giocatori, il produttore e il rivenditore di una certa merce, ognuno dei quali cerca di massimizzare il proprio guadagno; ciascuno di loro agisce tramite il proprio controllo, cioè la pubblicità e la promozione, rispettivamente. Il produttore può decidere di farsi carico di parte delle spese del rivenditore. Si è trovata una soluzione ottimale in senso 'catching up' per due espressioni dei profitti marginali arbitrariamente scelte, e tale soluzione è stata studiata tramite analisi di sensibilità. Nell'ultimo capitolo, il modello è stato modificato, prevedendo la possibilità che le persone nel pubblico interagiscano tra loro, parlando dell'azienda e del prodotto. Per le stesse espressioni dei profitti marginali, è stata trovata una nuova soluzione ottimale in senso 'catching up', ed è stata paragonata alla precedente in termini di guadagno per il produttore. Una ricerca più approfondita è richiesta per introdurre e studiare un meccanismo nella promozione del rivenditore, finalizzato a prevenire la possibilità di un impatto negativo del termine di interazione prima introdotto

Essays in Equilibrium Finance

The first chapter, Open-Loop Equilibria and Perfect Competition in Option Exercise Games , a joint work with Professor Kerry Back, is concerned with the optimal exercise and valuation of growth options within a partial equilibrium setting. A finite number of firms invest irreversibly into production capacities. It is well known (see e.g. Dixit and Pindyck (1994)) that irreversibility creates an option-like feature and it is usually not optimal for a monopolistic firm to exercise its investment option when its option is 'at the money'. But what if there is more than one firm competing for market shares? Competing firms invest earlier in equilibrium. With the number of firms going to infinity, the value of the option of waiting to invest approaches zero. In the limit, investment is undertaken as soon as its net present value reaches zero. Our contribution is to provide a rigorous proof for the statement that the strategies in Grenadier (2002) – properly reinterpreted - form an open-loop equilibrium. As open loop strategies lack subgame perfectness, we further show that perfect competition forms a subgame perfect equilibrium already for two firms. In general equilibrium, the central planner's problem is analogous to the monopolistic problem in partial equilibrium. The planner maximizes utility over all admissible investment paths just as a firm maximizes profits. So it is natural to hypothesize that there also exists an 'option premium of waiting to invest' for a welfare maximizing central planner. But how would a delay reconcile with perfect competition and zero profits for firms? This question is addressed in the second chapter within a stylized general equilibrium model with irreversible investment. While it is true that with a single consumption good there are no relative prices within a particular instant of time, i.e. there are no intra-period prices, prices can still be related on their intertemporal dimension. It are precisely the dynamics of intertemporal prices, i.e. interest rates and future prices, that reconcile investment delays with zero profits in the context of the model. Longer term interest rates and futures on wages contain the expected growth-effect of optimally exercised growth options, rendering current investment opportunities unprofitable whenever a delay is efficient. In this sense, the term-structure of future prices reflects the option premium of waiting and leads to optimal delay in investment. Interestingly, this mechanism is similar to what Keynes termed the 'speculative motive' for money demand and liquidity preference. Thinking about Keynes' theory and the speculative motive in particular, naturally leads to questions linked to liquidity preference, such as “What exactly is a liquidity trap? The third and last chapter attempts to make one first step towards this direction by approaching a more elementary question. It asks: Why do people exchange real goods against a piece of paper that neither provides intrinsic utility nor (unlike in Keynes times) constitutes a claim on a real good such as gold? Why is money a safe asset whose value people (can) rely upon? In the model presented in Chapter 3 money is 'safe': Fiat money has strictly positive value in the unique trembling hand equilibrium. This holds as each bank note is both: a witness for the existence of some agent in the economy with debt, backed by collateral, and the only matter that allows the debtor to settle her debt. Debtors fear to lose the collateral and compete with each other for not defaulting. Hence they compete for money. This creates money demand and thereby ensures positive money value. As not only a single but all debtors in the economy demand money, idiosyncratic shocks to solvency wash out. This makes fiat money a safe asset

Game Theory

The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner

Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.

Special Topics in Information Technology

This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2019-20 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists

Technology Investment: A Game Theoretic Real Options Approach.

The technology investment decision of an individual firm has become a very complex matter in recent years. One reason is the incredibly rapid progress of technological developments in the last decades. Another reason is the existence of and movement towar oligopolistic markets. In this thesis several theoretical technology investment models of the firm are developed and analyzed. To solve these models real options theory and game theory is used. The real options theory makes it possible to explicitly take nto account (and value) the option value of waiting. Game theory is used to incorporate strategic interactions.

Game Theoretic Models for Power Control in Wireless Networks

Τα τελευταία χρόνια, η τεχνολογία των κινητών επικοινωνιών έχει εξελιχθεί ραγδαία εξαιτίας των αυξανόμενων απαιτήσεων των χρηστών, όπως είναι η πρόσβαση σε υπηρεσίες του Διαδικτύου μέσω των ασύρματων έξυπνων κινητών συσκευών καθώς και οι απαιτήσεις σε καλύτερη ποιότητα στις προσφερόμενες υπηρεσίες. Σήμερα, οι συσκεύες αυτές χρησιμοποιούν την τέταρτη γενιά δικτύων (4Gή LTE) καθώς αντικαθιστάτην τρίτη γενιά δικτύων (3G) και προσφέρει στους χρήστες βελτιωμένες υπηρεσίες με υψηλότερες ταχύτητες. Οι ασύρματες έξυπνες κινητές συσκευές (smartphones) έχουν μεγάλη ζήτηση στην αγορά, για το λόγο αυτό γίνεται προσπάθεια να εξελιγχθούν σε επίπεδο ενεργειακής κατανάλωσης, ώστε ο χρήστης να μην χρειάζεται να επαναφορτίζει τη συσκευή του σε τακτά χρονικά διαστήματα. Η θεωρία παιγνίων παρέχει πολύτιμα μαθηματικά εργαλεία όπου μπορούν να χρησιμοποιηθούν για την επίλυση των διαφόρων προβλημάτων που αντιμετώπιζουν τα ασύρματα δίκτυα. Στην παρούσα διπλωματική εργασία μελετάτε το πρόβλημα του ελέγχου ισχύος εκπομπής (powercontrol). Συγκεκριμένα, μελετάμε παιγνιοθεωρητικά μοντέλα για έλεγχο ισχύος εκπομπής σε ασύρματα δίκτυα (CDMA& LTE). Η μελέτη μας επικεντρώνεται στα μη συνεργατικά παίγνια και υποθέτουμε ότι οι χρήστες του δικτύου (αποστολείς, παραλείπτες) είναι εγωιστές και ορθολογιστές. Στη συνέχεια, εισάγουμε αλγορίθμους μάθησης, regretlearningalgorithms, καθώς και την σύνδεση τους με την θεωρία παιγνίων. Τέλος, ερευνάμε τις διάφορες regretlearningτεχνικές εφαρμόζοντάς τες στο πρόβλημα του powercontrolστα ασύρματα δίκτυα επόμενης γενιάς.In recent years, the technology of mobile communications has evolved rapidly due to increasing requirements, such as access to Internet services via mobile phones and requirements better quality services. Nowadays, the devices use the Long Term Evolution (LTE), which called also as 4G networks. The fourth generation (4G) networks replace the third networks generation (3G) and offer to users improved services at higher speeds. Mobile devices to access the Internet, such as smartphones, tablet PCs and netbooks are in high demand in the market for it is an effort to develop in energy consumption level, that the user does not need recharge the device at regular time intervals. Game theory provides valuable mathematical tools that can be used to solve problems of wireless communication networks and can be applied to multiple layers of wireless networks. In this thesis, we study power control issue and consider it at the physical layer of wireless networks. Specifically, we study game theoretic models for power control in wireless communication networks (CDMA & LTE). In the game theory, we have focused in the non-cooperative power control games and assumed that both transmitters and receivers are selfish and rational. In addition, we insert regret learning techniques and their connection with the game theory. Finally, we investigate the regret learning techniques applied to the problem of power control in the next generation networks