On the Feedback Solutions of Differential Oligopoly Games with Hyperbolic Demand Curve and Capacity Accumulation

We characterise the subgame perfect equilibrium of a differential market game with hyperbolic inverse demand where firms are quantity-setters and accumulate capacity over time à la Ramsey. The related Hamilton-Jacobi-Bellman are solved in closed form both on infinite and on finite horizon setups and the optimal strategies are determined. Then, we analyse the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand

Analytic solutions for Hamilton-Jacobi-Bellman equations

Closed form solutions are found for a particular class of Hamilton- Jacobi-Bellman equations emerging from a differential game among fims competing over quantities in a simultaneous oligopoly framework. After the derivation of the solutions, a microeconomic example in a non-standard market is presented where feedback equilibrium is calculated with the help of one of the previous formulas

Differential games and applications to counter-terrorism

The application of dynamic games to the study of terrorism has the potential to provide insight for policymakers on the behavior of terrorists and inform them how best response to terror threats. We studied several applications of differential games to counter-terrorism and analyzed the usefulness of each approach. We also discussed possible future research topics

자본 규모가 다른 기업 간 다기간 스타켈버그 게임 모형을 이용한 약탈적 가격책정에 대한 연구

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 이덕주.Amount of capital that market participants have can provide predictive information about occurrence of predation in certain market. Predation or predatory pricing is a firms strategy that a firm with great market power intentionally can utilize to make a situation which is disadvantageous to all market participants through overproduction to get better profit after other several firms getting out of the market, and the market power that enables intentional overproduction and sufficient amount of capital is essential factor for firms which want to implement predatory pricing or predation policy. In this way, presence of market power and sufficient amount of capital can provide some information in predicting the likelihood of occurrence of predation or predatory pricing in certain market. Based on these ideas, we proposed a predatory pricing model by applying the concept of capital variable to multi-period Stackelberg game which is a competitive game model between a firm with great market power and the other. Several characteristics of the proposed predation model were also derived as propositions. Because there were few predation models considering firms capital, this proposed model can be a pragmatic tool for firms with great market power which is finding an alternative-profitable way in competing with its opponents in a certain market, for small companies which consider entering a new market and also for analysts who want to analyze competition structures of some markets between firms especially in terms of predicting the occurrence of predation.기업들이 보유하고 있는 자본의 양은 그 기업들이 속한 시장에서 약탈적 가격책정 상황의 발생 가능성에 대한 예측력 있는 정보를 제공할 수 있다. 특정 시장 참가자가 과잉생산을 통해 모든 시장 참가자들에게 이윤 측면에서 불리한 상황을 의도적으로 형성한 뒤 수익성이 떨어지거나 적자인 상황을 버티지 못하고 시장에서 퇴출되는 시장 참가자가 생기면 제품의 과잉생산이나 약탈가격책정을 중단하고 이전보다 많은 이익을 향유하는 것이 약탈적 가격책정 전략의 핵심이라면, 특정 기업에게 이러한 전략을 가능하게 하는 것은 의도적으로 모든 시장참가자에게 불리한 상황을 발생시키고, 그리고 그 상황에서 견딜 수 있는 능력이 있는가 하는 점이다. 즉, 어떤 기업이 시장지배력이 있는지 그리고 충분한 양의 자본을 보유하고 있는지에 대한 정보는 약탈적 가격책정의 발생 가능성을 예측하는데 좋은 정보가 되며 이는 기존 약탈적 가격책정이 발생한 사례의 분석을 통해서도 확인할 수 있다. 이에 따라 본 논문에서는 시장지배력의 유무에 대한 개념을 포괄하고 있는 슈타켈버그 게임에 부존 자본량이라는 개념을 접목하여 약탈적 가격책정 모델을 구성하였다. 자본량이라는 개념을 토대로 약탈적 가격책정 모델을 구성한 기존의 모델이나 연구가 거의 없는 현 상황에서 본 논문에서 제안하는 모델은 시장 지배력을 이미 가지고 있는 기업이나 어떤 시장에 진입하기를 고민하는 기업 그리고 특정 시장의 구조를 분석하고자 하는 모든 이에게 약탈적 가격책정과 관련된 양질의 정보를 제공할 수 있을 것이다.Chapter 1 Introduction 1 1.1 Background 1 1.2 Research Motivation and Objective 3 1.3 Problem Definition 4 1.4 Organization of the Thesis 5 Chapter 2 Literature Review 6 2.1 Predatory Pricing Model 6 2.2 Capital Accumulation and Differential Game 12 2.3 Antitrust Law 14 Chapter 3 Model 15 3.1 Problem Setting 15 3.2 Modified Model 21 Chapter 4 Analysis 28 4.1 Algorithm 28 4.2 Solution of Modified Model 31 4.3 Numerical Analysis 45 Chapter 5 Conclusion 66 Bibliography 68 국문초록 72Maste

MONETARY POLICY AND BANKING: NON-LINEAR DYNAMIC MODELS EVOLVING AS ADAPTIVE SYSTEMS

Questa tesi presenta cinque capitoli su diversi aspetti della teoria della politica monetaria con un’analisi approfondita degli strumenti a disposizione delle banche centrali (BC) per stabilizzare e correggere gli squilibri nei mercati economici e finanziari globalizzati. I recenti shock provocati dalla recessione del Covid-19 e dalla crisi energetica hanno modificato le interdipendenze tra i principali attori economici, influenzando pesantemente il meccanismo di trasmissione della politica monetaria. L’obiettivo della tesi è indagare l’impatto di tali strumenti monetari in un costrutto teorico che include relazioni non-lineari tra variabili, eterogeneità degli agenti e razionalità limitata, frizioni di mercato e asimmetrie informative. In particolare, le aspettative degli agenti giocano un ruolo cruciale nelle decisioni di politica monetaria e, in questo lavoro, sono ben rappresentate da schemi adattivi che consentono l’apprendimento, l’interazione sociale, l’imitazione e il cambiamento di opinioni. Gli schemi adattivi sono modellati nella forma di sistemi dinamici a tempo discreto e continuo e la loro analisi fornisce nuove intuizioni economiche sul processo evolutivo che porta a situazioni di equilibrio o disequilibrio. Ciò si rivela prezioso in una prospettiva di policy-maker poiché aiuta a comprendere le fragilità intrinseche dei sistemi economici/finanziari, fornendo appropriate misure di policy per mitigarle. Dopo una breve rassegna della letteratura, il capitolo due si concentra sull’identificazione di una regola di Taylor endogena e dinamica per il tasso di interesse a breve termine al fine di ridurre l'inflazione e l'output gap. Lo scopo è quello di mitigare squilibri e shock economici temporanei. I risultati evidenziano il dilemma che le BC si trovano ad affrontare in scenari di trade-off in cui non è possibile raggiungere pienamente entrambi gli obiettivi con un unico strumento a disposizione. Il terzo capitolo fornisce un’analisi approfondita sulla relazione dinamica tra rapporto debito pubblico PIL e tasso di inflazione. Si esamina come diverse politiche monetarie (tasso di interesse, quantitative easing, monetizzazione) e regole fiscali attive possano evitare percorsi insostenibili del debito pubblico e fluttuazioni eccessive dell'inflazione. In scenari di bassa inflazione, il quantitative easing e una modesta monetizzazione finanziaria possono essere utili a stabilizzare l’evoluzione del debito grazie al loro ruolo di contenimento degli spread e di stimolo alla crescita, mentre l’effetto di incremento dell’inflazione è generalmente limitato. Inoltre, la politica basata sui tassi d'interesse da sola non è sufficiente a controllare l'inflazione: la credibilità della BC nel guidare le aspettative di inflazione risulta essere cruciale per controllare l'andamento dei prezzi e raggiungere la stabilità macroeconomica. Una delle novità di questa analisi è la presenza di un livello soglia sia per il rapporto debito/PIL che per l'inflazione, oltre il quale il rapporto debito/PIL diventa insostenibile seguendo un percorso esplosivo. Il quarto capitolo fa luce sui meccanismi attraverso i quali una BC può implementare i rischi legati al cambiamento climatico nelle sue operazioni monetarie non convenzionali (ad esempio, un programma di acquisto di obbligazioni societarie). La cosiddetta politica monetaria verde mira a orientare o a far convergere l'allocazione di attività e garanzie verso i settori industriali a basse emissioni di carbonio. Nel modello sviluppato, questa strategia della BC riduce effettivamente il costo del capitale per le obbligazioni verdi rispetto a quelle convenzionali, favorendo così gli investimenti/tecnologie sostenibili sul mercato...This thesis presents five chapters on different aspects of monetary policy theory with a thorough analysis of the instruments at disposal of central banks (CBs) to stabilize and correct imbalances in globalized economic and financial markets. The recent shocks posed by the Covid-19 recession and energy crisis have changed the interdependencies between key economic actors, heavily affecting the mechanism of transmission of monetary policy. The aim of the thesis is to investigate the impact of such monetary instruments in a theoretical construct that includes non-linear relationships among variables, agents’ heterogeneity and limited rationality, market frictions, and asymmetric information. In particular, the agents’ expectations play a crucial role in monetary policy decisions and, in this work, are well represented by adaptive schemes that allow for learning, social interaction, imitation, and changing beliefs. Adaptive schemes are modeled in the form of discrete or continuous dynamical systems and their analysis provides new economic insights into the evolution process that leads to equilibrium or disequilibrium situations. This turns out to be precious from a policy-maker perspective because it helps to understand the intrinsic fragilities of the economic/financial systems, providing appropriate policy measures to mitigate them. After a brief literature review, chapter two focuses on the identification of an endogenous and dynamic Taylor rule for the short-term interest rate to target inflation and output gaps. The aim is to mitigate temporary economic unbalances and shocks. The results highlight the dilemma faced by the CBs in trade-off scenarios where it is not possible to fully achieve both goals with a unique instrument at their disposal. The third chapter provides an in-depth analysis of the dynamic relationship between the public debt ratio and the inflation rate. It is explored how different monetary policies (interest rate, quantitative easing, monetization) and active fiscal rules can avoid unstainable government debt paths and excessive inflation fluctuations. In low inflation scenarios, quantitative easing and moderate money finance can be helpful in stabilizing debt evolution thanks to their role in containing spreads and stimulating growth, while the effect on inflation rise is generally limited. Furthermore, interest-rate-based policy alone is not sufficient to control inflation: the CB’s credibility in driving inflation expectations results to be crucial to control price developments and achieving macroeconomic stability. One of the novelties of this analysis is the presence of a threshold level for both debt ratio and inflation, beyond which the debt ratio becomes unsustainable following an explosive path. Chapter four sheds light on the mechanisms through which a CB can implement the risks related to climate change in its unconventional monetary operations (e.g. a corporate bonds purchase program). The so-called green monetary policy aims to steer or tilt the allocation of assets and collateral toward low-carbon industries. In the model developed, this CB strategy effectively reduces the cost of capital for green bonds as opposed to conventional bonds, and thus favors sustainable investment/technology in the market. However, there still could be technology trap equilibria in which no investment in green technology occurs in the long-run, even if the non-green investment equilibrium is inefficient. The green monetary policy can help firms to leave these technology traps and the degree of market competition and of market imperfections can contribute to amplifying the effects of this instrument by the transmission channel..

Spatial Economics: Density, Potential, and Flow

Location theory has traditionally considered space as a two-dimensional Euclidean continuum. It has resorted to geometric constructions and emphasized geometric and geographic intuition. More recently, the emergence of linear and mathematical programming methods in regional analysis has favored an abstract indexing of locations. The matrix of spatial relationships has become the matrix of point-pairs. But the intuitive notions of two-dimensional space have been lost in the process. The purpose of this book is to reintroduce the two-dimensional continuum as the natural spatial setting of economic activities and to exploit the idea for all its worth. Economic interaction between agents are viewed as flows, of commodities or persons. These flows are generated by production and consumption activities, which represent the sources and sinks of a flow field. The direction of flow is oriented by principles of cost minimization and/or of profit or utility maximization. In this way neoclassical economics is wedded to the hydrodynamics of flow fields

Advances in Spatial Theory and Dynamics

This book originates from two meetings, set apart in time but closely connected by continuing collaborative efforts between researchers in an international network. The first of these meetings took place at IIASA in October 1984, organized by IIASA's Regional Issues Project under the title "Dynamic Analysis of Spatial Development". About half of the papers in this volume were presented at that meeting. These contributions have been elaborated and revised considerably during the preparation of this volume, and can now be regarded as mature papers embracing the frontiers of spatial and economic dynamics. Another set of contributions was presented during the European Summer Institute in Regional Science held at the University of Umea in June 1986. The Summer Institute was organized by CERUM in collaboration with the Departments of Economics and Geography at the same university. The contributions have been drawn from the sessions on technological change, nonlinear dynamics in spatial networks and infrastructure development. This is reflected in the three parts of the volume (1) Competition, specialization and technological change, (2) Spatial interaction, (3) Urban and regional infrastructure