Who benefits from price indexation?

We consider two products traded in two duopoly markets, where competition is assumed a la Hotelling. Firms A and B are operating in Market 1, while Firm B is also competing in Market 2 with Firm C. Prices in Market 2 are pegged linearly to the average price in Market 1. We show that price indexation has anticompetitive consequences that always benefit Firm A, and that benefit Firm B operating in both markets if the size of the reference market is large enough.Hotelling, prices, indexation

A Dynamic Programming Approach for Pricing Options Embedded in Bonds

The aim of this paper is to price options embedded in bonds in a Dynamic Programming (DP) framework, the focus being on call and put options with advance notice. The pricing of interest rate derivatives was usually done via trees or finite differences. Trees are not really very efficient as they deform crudely the dynamic of the underlying asset(s), here the short term risk-free interest rate. They can be interpreted as elementary DP procedures with fixed grid sizes. For a long time, finite differences presented poor accuracy because of the discontinuities of the bond's value that may arise at decision dates. Recently, remedies were given by d'Halluin et al (2001) via techniques related to flux limiters. DP does not suffer from discontinuities that may arise at decision dates and does not require a time discretization. It may also be implemented in discrete-time models. Results show efficiency and robustness. Suggestions to combine DP and finite differences are also formulatedDynamic Programming, Stochastic Processes, Options Embedded in Bonds, American Options

Resolution of Financial Distress under Chapter 11

We develop a contingent claims model of a firm in financial distress with a formal account for renegotiations under the Chapter 11 bankruptcy procedure. Shareholders and two classes of creditors (senior and junior) alternatively propose a reorganization plan subject to a vote. The bankruptcy judge can intervene in any renegotiation round to impose a plan. The multiple-stage bargaining process is solved in a non-cooperative game theory setting. The calibrated model yields liquidation rate, Chapter 11 duration and percentage of deviations from the Absolute Priority Rule that are consistent with empirical evidence.Credit risk, Chapter 11, Game theory, Dynamic programming

Dynamic Models for International Environmental Agreements

In this paper we develop a model to analyze, in a dynamic framework, how countries join international environmental agreements (IEAs). In the model, where countries suffer from the same environmental damage as a result of the total global emissions, a non-signatory country decides its emissions by maximizing its own welfare, whereas a signatory country decides its emissions by maximizing the aggregate welfare of all signatory countries. Signatory countries are assumed to be able to punish the non-signatories at a cost. When countries decide on their pollution emissions they account for the evolution of the pollution over time. Moreover, we propose a mechanism to describe how countries reach a stable IEA. The model is able to capture situations with partial cooperation in an IEA stable over time. It also captures situations where all countries participate in a stable agreement, or situations where no stable agreement is feasible. When more than one possibility coexists, the long-term outcome of the game depends on the initial conditions (i.e. the size of the initial group of signatory countries and the pollution level).International Environmental Agreements, Non-Cooperative Dynamic Game, Coalition Stability

Game Theoretic Analysis of Negotiations under Bankruptcy

We extend the contingent claims framework for the levered firm in explicitly modeling the resolution of financial distress under formal bankruptcy as a non-cooperative game between claimants under the supervision of the bankruptcy judge. The identity of the class of claimants proposing the first reorganization plan is found to be a key determinant of the likelihood of liquidation and of the renegotiated value of claims. Our quantitative results confirm the economic intuition that a bankruptcy design must trade-off the initial priority of claims with the viability of reorganized firms.Bankruptcy procedure, game theory, dynamic programming

Cooperating firms in inventive and absorptive research

We consider a duopoly competing in quantity, where firms can invest in both innovative and absorptive R&D to reduce their unit production cost, and where they benefit from free R&D spillovers between them. We analyze the case where firms act non cooperatively and the case where they cooperate by forming a research joint venture. We show that, in both modes of play, there exists a unique symmetric solution. We find that the investment in innovative R&D is always higher than in absorptive R&D. We also find that the value of the learning parameter has almost no impact on innovative R&D, firms profits, consumer's surplus and social welfare. Finally, differences in investment in absorptive research and social welfare under the two regimes are in opposite directions according to the importance of the free spillover.Innovative R&D; Absorptive R&D; Learning Parameter; Spillover; Research Joint Venture

Resolution of Financial Distress under Chapter 11

We develop a contingent claims model of a firm in financial distress with a formal account for renegotiations under the Chapter 11 bankruptcy procedure. Shareholders and two classes of creditors (senior and junior) alternatively propose a reorganization plan subject to a vote. The bankruptcy judge can intervene in any renegotiation round to impose a plan. The multiple-stage bargaining process is solved in a non-cooperative game theory setting. The calibrated model yields liquidation rate, Chapter 11 duration and percentage of deviations from the Absolute Priority Rule that are consistent with empirical evidence

Game Theoretic Analysis of Negotiations under Bankruptcy

We extend the contingent claims framework for the levered firm in explicitly modeling the resolution of financial distress under formal bankruptcy as a non-cooperative game between claimants under the supervision of the bankruptcy judge. The identity of the class of claimants proposing the first reorganization plan is found to be a key determinant of the likelihood of liquidation and of the renegotiated value of claims. Our quantitative results confirm the economic intuition that a bankruptcy design must trade-off the initial priority of claims with the viability of reorganized firms

LQG Risk-Sensitive Mean Field Games with a Major Agent: A Variational Approach

Risk sensitivity plays an important role in the study of finance and economics as risk-neutral models cannot capture and justify all economic behaviors observed in reality. Risk-sensitive mean field game theory was developed recently for systems where there exists a large number of indistinguishable, asymptotically negligible and heterogeneous risk-sensitive players, who are coupled via the empirical distribution of state across population. In this work, we extend the theory of Linear Quadratic Gaussian risk-sensitive mean-field games to the setup where there exists one major agent as well as a large number of minor agents. The major agent has a significant impact on each minor agent and its impact does not collapse with the increase in the number of minor agents. Each agent is subject to linear dynamics with an exponential-of-integral quadratic cost functional. Moreover, all agents interact via the average state of minor agents (so-called empirical mean field) and the major agent's state. We develop a variational analysis approach to derive the best response strategies of agents in the limiting case where the number of agents goes to infinity. We establish that the set of obtained best-response strategies yields a Nash equilibrium in the limiting case and an $\varepsilon$-Nash equilibrium in the finite player case. We conclude the paper with an illustrative example

Birds of a Feather: Teams as a Screening Mechanism

This paper studies the informational content of elective teams in a dynamic principal/multiple-agents framework with adverse selection. Two agents with different employment histories are paid their conditional expected marginal product. They observe their types (good or bad), and choose between working together or separately. We characterize the distributions on agents' types, nature and wages such that teams are formed exclusively by good-type agents, with and without side payments. As employment records matter when idiosyncratic contributions are difficult to isolate, a good-type agent prefers not to jeopardize his reputation by teaming up with a bad-type agent. Cet article étudie le contenu informationel des équipes facultatives, dans le cadre d'un modèle dynamique de principal-agent avec sélection adverse. Deux agents ayant des historiques d'emploi différents reçoivent leur produit marginal espéré conditionnel. Ils observent leurs types (bon ou mauvais) et doivent décider s'ils veulent travailler ensemble ou séparément. Nous caractérisons la distribution sur les types, les chocs de la nature et les salaires pour lesquelles des équipes sont formées exclusivement par deux agents de bon type, avec ou sans paiements latéraux. Parce que les dossiers d'emploi sont valorisés lorsque les contributions individuelles sont difficiles à évaluer, un agent de bon type refuse de mettre en péril sa réputation en formant une équipe avec un agent de mauvais type.