A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

General clas of inhomogeneous perfect-fluid solutions

We present a general class of solutions to Einstein's field equations with two spacelike commuting Killing vectors by assuming the separation of variables of the metric components. The solutions can be interpreted as inhomogeneous cosmological models. We show that the singularity structure of the solutions varies depending on the different particular choices of the parameters and metric functions. There exist solutions with a universal big-bang singularity, solutions with timelike singularities in the Weyl tensor only, solutions with singularities in both the Ricci and the Weyl tensors, and also singularity-free solutions. We prove that the singularity-free solutions have a well-defined cylindrical symmetry and that they are generalizations of other singularity-free solutions obtained recently.

Petrou type-D perfect-fluid solutions in generalized Kerr-Schild form.

Generalized KerrSchild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

Product Perfect Codes and Steganography

A new coding technique to be used in steganography is evaluated. The performanceof this new technique is computed and comparisons with the well-known theoreticalupper bound, Hamming upper bound and basic LSB are established.

Delegation and information sharing in oligopoly

Information sharing in oligopoly has been analyzed by assuming that firms behave as a sole economic agent. In this paper I assume that ownership and management are separated. Managers are allowed to falsely report their costs to owners and rivals. Under such circumstances, if owners want to achieve information sharing they must use managerial contracts that implement truthful cost reporting by managers as a dominant strategy. I show that, contrary to the classical result, without the inclusion of message-dependent payments in managerial contracts there will be no information sharing. On the other hand, with the inclusion of such publicly observable payments and credible ex-ante commitment by owners not to modify these payments, there will be perfect information sharing without the need for third parties. Keywords: Information sharing, Delegation, Managerial contracts. JEL classification numbers: D21, D82, L13, L21

Efficient bidding with externalities

We implement a family of efficient proposals to share benefits generated in environments with externalities. These proposals extend the Shapley value to games with externalities and are parametrized through the method by which the externalities are averaged. We construct two slightly different mechanisms: one for environments with negative externalities and the other for positive externalities. We show that the subgame perfect equilibrium outcomes of these mechanisms coincide with the sharing proposals.

Forming efficient networks

In this paper, we suggest a simple sequential mechanism whose subgame perfect equilibria give rise to efficient networks. Moreover, the payoffs received by the agents coincide with their Shapley value in an appropriately defined cooperative game.

Information-sharing implications of horizontal mergers

We analyze the effects of uncertainty and private information on horizontal mergers. Firms face uncertain demands or costs and receive private signals. They may decide to merge sharing their private information. If the uncertainty parameters are independent and the signals are perfect, uncertainty generates an informational advantage only to the merging firms, increasing merger incentives and decreasing free-riding effects. Thus, mergers become more profitable and stable. These results generalize to the case of correlated parameters if the correlation is not very severe, and for perfect correlation if the firms receive noisy signals. From the normative point of view, mergers are socially less harmful compared to deterministic markets and may even be welfare enhancing. If the signals are, instead, publicly observed, uncertainty does not necessarily give more incentives to merge, and mergers are not always less socially harmful.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

Sequential formation of coalitions through bilateral agreements

We study a sequential protocol of endogenous coalition formation based on a process of bilateral agreements among the players. We apply the game to a Cournot environment with linear demand and constant average costs. We show that the final outcome of any Subgame Perfect Equilibrium of the game is the grand coalition, provided the initial number of firms is high enough and they are sufficiently patient.

Mediation incomplete information bargaining with filtered communication

We analyze a continuous-time bilateral double auction in the presence of two-sided incomplete information and a smallest money unit. A distinguishing feature of our model is that intermediate concessions are not observable by the adversary: they are only communicated to a passive auctioneer. An alternative interpretation is that of mediated bargaining. We show that an equilibrium using only the extreme agreements always exists and display the necessary and sufficient condition for the existence of (perfect Bayesian) equilibra which yield intermediate agreements. For the symmetric case with uniform type distribution we numerically calculate the equilibria. We find that the equilibrium which does not use compromise agreements is the least efficient, however, the rest of the equilibria yield the lower social welfare the higher number of compromise agreements are used.

Income taxation with habit formation and consumption externalities

We analyze the dynamic behavior and the welfare properties of the equilibrium path of a growth model where both habits and consumption externalities affect the utility of consumers. We discuss the effects of flat rate income taxes and characterize the optimal income taxation policy. We show that, when consumption externalities and habit adjusted consumption are not perfect substitutes, a counter-cyclical income tax rate allows the competitive equilibrium to replicate the efficient path. Our analysis highlights the crucial role played by complementarities between externalities and habits in order to generate an inefficient dynamic equilibrium.

Bidding for the surplus: realizing efficient outcomes in general economic environments

In this paper, we consider two classes of economic environments. In the first type, agents are faced with the task of providing local public goods that will benefit some or all of them. In the second type, economic activity takes place via formation of links. Agents need both to both form a network and decide how to share the output generated. For both scenarios, we suggest a bidding mechanism whereby agents bid for the right to decide upon the organization of the economic activity. The subgame perfect equilibria of this game generate efficient outcomes.