Global Nash convergence of Foster and Young's regret testing

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about the game. In fact, players' actions are based only on their own past payoffs and, in a variant of the strategy, players need not even know that their payoffs are determined through other players' actions. The procedure works for general finite games and is based on appropriate modifications of a simple stochastic learningrule introduced by Foster and Young.

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs up to level li about the state of nature coincide, weobtain quotient type spaces that are typically smaller than the original ones, preserve basic topologicalproperties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash(li; l-i)-equilibria capture players inability to distinguish types belonging to the same equivalence class.The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustratethe constructions.

Contagion and efficiency in gross and net interbank payment systems

The increased fragility of the banking industry has generatedgrowing concern about the risks associated with the paymentsystems. Although in most industrial countries differentinterbank payment systems coexist, little is really knownabout their propierties in terms of risk and efficiency. Wetackle this question by comparing the two main types ofpayment systems, gross and net, in a framework whereuncertainty arises from several sources: the time ofconsumption, the location of consumption and the return oninvestment. Payments across locations can be made either bydirectly transferrring liquidity or by transferring claimsagainst the bank in the other location. The two mechanism areinterpreted as the gross and net settlement systems ininterbank payments. We characterize the equilibria in the twosystems and identify the trade-off in terms of safety andefficiency.

Information acquisition and entry

Before firms decide whether to enter a new market or not, they havethe opportunity to buy information about several variables that might affectthe profitability of this market. Our model differs from the existing literatureon endogenous information acquisition in two respects: (1) there is uncertaintyabout more than one variable, and (2) information is acquired secretly. Whenthe cost of acquiring information is small, entry decisions will be as ifthere was perfect information. Equilibria where each firm acquires only asmall amount of information are more robust than the socially undesirableequilibria where all firms gather all information. Examples illustrate theimportance of assumptions (1) and (2).

Competing engines of growth: Innovation and standardization

We study a dynamic general equilibrium model where innovation takes theform of the introduction of new goods whose production requires skilled workers.Innovation is followed by a costly process of standardization, whereby these newgoods are adapted to be produced using unskilled labor. Our framework highlightsa number of novel results. First, standardization is both an engine of growth anda potential barrier to it. As a result, growth is an inverse U-shaped function ofthe standardization rate (and of competition). Second, we characterize the growthand welfare maximizing speed of standardization. We show how optimal protection of intellectual property rights affecting the cost of standardization vary withthe skill-endowment, the elasticity of substitution between goods and other parameters. Third, we show that, depending on how competition between innovatingand standardizing firms is modelled and on parameter values, a new type of multiplicity of equilibria may arise. Finally, we study the implications of our model forthe skill-premium and we illustrate novel reasons for linking North-South trade tointellectual property rights protection.

Recontracting and competition

We characterize the set of Walrasian allocations of an economy as theset of allocations which can be supported by abstract equilibria that satisfy a recontracting condition which reflects the idea that agents can freely trade with each other. An alternative (and weaker) recontracting condition characterizesthe core. The results are extended to production economies by extending thedefinition of the recontracting condition to include the possibility of agentsto recontract with firms. However, no optimization requirement is imposed onfirms. In pure exchange economies, an abstract equilibrium is a feasible allocation and a list of choice sets, one for each agent, that satisfy thefollowing conditions: an agent's choice set is a subset of the commodity space that includes his endowment; and each agent's equilibrium bundle isa maximal element in his choice set, with respect to his preferences. Therecontracting condition requires that any agent can buy bundles from any other agent's choice set by offering the other agent a bundle he prefers tohis equilibrium bundle.

Noise and aggregation of information in large markets

We study a novel class of noisy rational expectations equilibria in markets with largenumber of agents. We show that, as long as noise increases with the number of agents inthe economy, the limiting competitive equilibrium is well-defined and leads to non-trivialinformation acquisition, perfect information aggregation, and partially revealing prices,even if per capita noise tends to zero. We find that in such equilibrium risk sharing and price revelation play dierent roles than in the standard limiting economy in which per capita noise is not negligible. We apply our model to study information sales by a monopolist, information acquisition in multi-asset markets, and derivatives trading. Thelimiting equilibria are shown to be perfectly competitive, even when a strategic solutionconcept is used.

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.

The magmatic to hydrothermal evolution of the intrusive Mont Saint-Hilaire Complex: Insights into the late-stage evolution of peralkaline rocks

The Cretaceous Mont Saint-Hilaire complex (Quebec, Canada) comprises three major rock units that were emplaced in the following sequence: (I) gabbros; (II) diorites; (III) diverse partly agpaitic foid syenites. The major element compositions of the rock-forming minerals, age-corrected Nd and oxygen isotope data for mineral separates and trace element data of Fe-Mg silicates from the various lithologies imply a common source for all units. The distribution of the rare earth elements in clinopyroxene from the gabbros indicates an ocean island basalt type composition for the parental magma. Gabbros record temperatures of 1200 to 800 degrees C, variable silica activities between 0 center dot 7 and 0 center dot 3, and f(O2) values between -0 center dot 5 and +0 center dot 7 (log delta FMQ, where FMQ is fayalite-magnetite-quartz). The diorites crystallized under uniform a(SiO2) (a(SiO2) = 0 center dot 4-0 center dot 5) and more reduced f(O2) conditions (log delta FMQ similar to-1) between similar to 1100 and similar to 800 degrees C. Phase equilibria in various foid syenites indicate that silica activities decrease from 0 center dot 6-0 center dot 3 at similar to 1000 degrees C to < 0 center dot 3 at similar to 550 degrees C. Release of an aqueous fluid during the transition to the hydrothermal stage caused a(SiO2) to drop to very low values, which results from reduced SiO(2) solubilities in aqueous fluids compared with silicate melts. During the hydrothermal stage, high water activities stabilized zeolite-group minerals. Fluid inclusions record a complex post-magmatic history, which includes trapping of an aqueous fluid that unmixed from the restitic foid syenitic magma. Cogenetic aqueous and carbonic fluid inclusions reflect heterogeneous trapping of coexisting immiscible external fluids in the latest evolutionary stage. The O and C isotope characteristics of fluid-inclusion hosted CO(2) and late-stage carbonates imply that the surrounding limestones were the source of the external fluids. The mineral-rich syenitic rocks at Mont Saint-Hilaire evolved as follows: first, alkalis, high field strength and large ion lithophile elements were pre-enriched in the (late) magmatic and subsequent hydrothermal stages; second, percolation of external fluids in equilibrium with the carbonate host-rocks and mixing processes with internal fluids as well as fluid-rock interaction governed dissolution of pre-existing minerals, element transport and precipitation of mineral assemblages determined by locally variable parameters. It is this hydrothermal interplay between internal and external fluids that is responsible for the mineral wealth found at Mont Saint-Hilaire.

Geochemistry and stable isotope composition of fresh alkaline porphyry copper tailings: Implications on sources and mobility of elements during transport and early stages of deposition

Prevention of acid mine drainage (AMD) in sulfide-containing tailings requires the identification of the geochemical processes and element pathways in the early stages of tailing deposition. However, analyses of recently deposited tailings in active tailings impoundments are scarce because mineralogical changes occur near the detection limits of many assays. This study shows that a detailed geochemical study which includes stable isotopes of water (delta H-2, delta O-18), dissolved sulfates (delta S-34, delta O-18) and hydrochernical parameter (pH, Eh, DOC, major and trace elements) from tailings samples taken at different depths in rainy and dry seasons allows the understanding of weathering (oxidation, dissolution, sorption, and desorption), water and element pathways, and mixing processes in active tailings impoundments. Fresh alkaline tailings (pH 9.2-10.2) from the Cu-Mo porphyry deposit in El Teniente, Chile had low carbonate (0.8-1.1 Wt-% CaCO3 equivalent) and sulfide concentrations (0.8-1.3 wt.%, mainly as pyrite). In the alkaline tailings water, Mo and Cu (up to 3.9 mg/L Mo and 0.016 mg/L Cu) were mobile as MoO42- and Cu (OH)(2)(0). During the flotation, tailings water reached equilibrium with gypsum (up to 738 mg/L Ca and 1765 mg/ L SO4). The delta S-34 VS. delta O-18 covariations of dissolved sulfate (2.3 to 4.5% delta S-34 and 4.1 to 6.0 % delta O-18) revealed the sulfate sources: the dissolution of primary sulfates (12.0 to 13.2%. delta S-34, 7.4 to 10.9%.delta O-18) and oxidation of primary sulfides (-6.7 to 1.7%. delta S-34). Sedimented tailings in the tailings impoundment can be divided into three layers with different water sources, element pathways, and geochemical processes. The deeper sediments (> 1 m depth) were infiltrated by catchment water, which partly replaced the original tailings water, especially during the winter season. This may have resulted in the change from alkaline to near-neutral pH and towards lower concentrations of most dissolved elements. The neutral pH and high DOC (up to 99.4 mg/L C) of the catchment water mobilized Cu (up to 0.25 mg/L) due to formation of organic Cu complexes; and Zn (up to 130 mg/L) due to dissolution of Zn oxides and desorption). At I m depth, tailings pore water obtained during the winter season was chemically and isotopically similar to fresh tailings water (pH 9.8-10.6, 26.7-35.5 mg/L Cl, 2.3-6.0 mg/L Mo). During the summer, a vadose zone evolved locally and temporarily up to 1.2 m depth. resulting in a higher concentration of dissolved solids in the pore water due to evaporation. During periodical new deposition of fresh tailings, the geochemistry of the surface layer was geochemically similar to fresh tailings. In periods without deposition, sulfide oxidation was suggested by decreasing pH (7.7-9.5), enrichment of MoO42- and SO42-, and changes in the isotopic composition of dissolved sulfates. Further enrichment for Na, K, Cl, SO4, Mg, Cu, and Mo (up to 23.8 mg/L Mo) resulted from capillary transport towards the surface followed by evaporation and the precipitation of highly soluble efflorescent salts (e.g., mirabilite, syngenite) at the tailing surface during summer. (C) 2008 Elsevier B.V. All rights reserved.

Adaptive learning in models with lagged variables

In this work I study the stability of the dynamics generated by adaptivelearning processes in intertemporal economies with lagged variables. Iprove that determinacy of the steady state is a necessary condition for the convergence of the learning dynamics and I show that the reciprocal is not true characterizing the economies where convergence holds. In the case of existence of cycles I show that there is not, in general, a relationship between determinacy and convergence of the learning process to the cycle. I also analyze the expectational stability of these equilibria.

Recursive contracts

We obtain a recursive formulation for a general class of contractingproblems involving incentive constraints. Under these constraints,the corresponding maximization (sup) problems fails to have arecursive solution. Our approach consists of studying the Lagrangian.We show that, under standard assumptions, the solution to theLagrangian is characterized by a recursive saddle point (infsup)functional equation, analogous to Bellman's equation. Our approachapplies to a large class of contractual problems. As examples, westudy the optimal policy in a model with intertemporal participationconstraints (which arise in models of default) and intertemporalcompetitive constraints (which arise in Ramsey equilibria).

Finite horizon bargaining and the consistent field

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

Financial intermediation and equity investment with costly monitoring

This paper studies the efficiency of equilibria in a productive OLG economy where the process of financial intermediation is characterized by costly state verification. Both competitive equilibria and Constrained Pareto Optimal allocations are characterized. It is shown that market outcomes can be socially inefficient, even when a weaker notion than Pareto optimality is considered.

A simple adaptive procedure leading to correlated equilibrium

We propose a simple adaptive procedure for playing a game. In thisprocedure, players depart from their current play with probabilities thatare proportional to measures of regret for not having used other strategies(these measures are updated every period). It is shown that our adaptiveprocedure guaranties that with probability one, the sample distributionsof play converge to the set of correlated equilibria of the game. Tocompute these regret measures, a player needs to know his payoff functionand the history of play. We also offer a variation where every playerknows only his own realized payoff history (but not his payoff function).