Byzantine Approximate Agreement on Graphs

Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that 1) the output values are in the convex hull of the non-faulty processors\u27 input values, 2) the output values are within distance d of each other. Classically, the values are assumed to be from an m-dimensional Euclidean space, where m >= 1. In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d=0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d >= 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (omega+1)f, where omega is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures

On the Potential Use of Adaptive Control Methods for Improving Adaptive Natural Resource Management

The paradigm of adaptive natural resource management (AM), in which experiments are used to learn about uncertain aspects of natural systems, is gaining prominence as the preferred technique for administration of large-scale environmental projects. To date, however, tools consistent with economic theory have yet to be used to either evaluate AM strategies or improve decision-making in this framework. Adaptive control (AC) techniques provide such an opportunity. This paper demonstrates the conceptual link between AC methods, the alternative treatment of realized information during a planning horizon, and AM practices; shows how the different assumptions about the treatment of observational information can be represented through alternative dynamic programming model structures; and provides a means of valuing alternative treatments of information and augmenting traditional benefit-cost analysis through a decomposition of the value function. The AC approach has considerable potential to help managers prioritize experiments, plan AM programs, simulate potential AM paths, and justify decisions based on an objective valuation framework.adaptive control, adaptive management, dynamic programming, value of experimentation, value of information, Resource /Energy Economics and Policy,

Optimization in non-standard problems. An application to the provision of public inputs

This paper describes a new method for solving non-standard constrained optimization problems for which standard methodologies do not work properly. Our method (the Rational Iterative Multisection -RIM- algorithm) consists of different stages that can be interpreted as different requirements of precision by obtaining the optimal solution. We have performed an application of RIM method to the case of public inputs provision. We prove that the RIM approach and comparable standard methodologies achieve the same results with regular optimization problems while the RIM algorithm takes advantage over them when facing non-standard optimization problems.direct search, constrained optimization, multisection, optimal taxation, public input.

Regular moral hazard economies

That paper formalizes the idea that when the magnitude of the moral hazard phenomenon is not important, the distortions like equilibria multiplicity or equilibrium discontinuity relative to the economic fundamentals disappear. We study a two state of nature insurance model, with a risk neutral principal, a risk averse agent and separable costs. Typically, in such economies, non convexities imply that the set of Pareto optimal allocations is not connected. Surprisingly, we prove that it is never the case under weak and realistic assumptions. That result is in particular valid under simple regularity assumptions on the cost function when the productivity of effort is always positive. We show that such regularity of the moral hazard economy is compatible with remaining strong non convexities.moral hazard ; non convexities ; equilibrium uniqueness

Can stabilization policies be efficient?

This paper makes use of optimal control relaxed problems to prove the absence of optimal trajectory in continuous time models with social increasing returns to scale where indeterminacy occurs. Although an efficient optimal policy does not exist, some chattering stabilization policies can mimic trajectories whose criterion functional approximates the supremum of the relaxed problem. This configuration is closely related to indeterminacy: by contrast, when the steady state is determined, an optimal policy is likely to exist.Increasing returns, Indeterminacy, Stabilization policy, Relaxed problems

Strategic Asset Allocation in Money Management

This article analyzes the dynamic portfolio choice implications of strategic interaction among money managers. The strategic interaction emerges as the managers compete for money flows displaying empirically documented convexities. A manager gets money flows increasing with performance, and hence displays relative performance concerns, if her relative return is above a threshold; otherwise she receives no (or constant) flows and has no relative concerns. We provide a tractable formulation of such strategic interaction between two risk averse managers in a continuous-time setting, and solve for their equilibrium policies in closed-form. When the managers’ risk aversions are considerably different, we do not obtain a Nash equilibrium as the managers cannot agree on who loses (getting no flows) in some states. We obtain equilibria, but multiple, when the managers are similar since they now care only about the total number of losing states. We recover a unique equilibrium, however, when a sufficiently high threshold makes the competition for money flows less intense. The managers’ unique equilibrium policies are driven by chasing and contrarian behaviors when either manager substantially outperforms the opponent, and by gambling behavior when their performances are close to the threshold. Depending on the stock correlation, the direction of gambling for a given manager may differ across stocks, however the two managers always gamble strategically in the opposite direction from each other in each individual stock.Money Managers, Strategic Interaction, Portfolio Choice, Relative Performance, Incentives, Risk Shifting, Fund Flows, Tournaments

Pollution, mortality and optimal environmental policy

We study an overlapping generations economy in which environmental degradation results from economic activity and affects agents' uncertain lifetimes. Life expectancy depends positively on economic activity and negatively on the stock of pollution. This can make the growth-survival relationship convex over some region and lead to two non-trivial steady states, with one a poverty trap. Uniform abatement taxes can cause the poverty trap to widen while increasing incomes at the high steady state. We also study the properties and dynamics of an optimal second-best abatement tax. It is non-homogeneous and increasing in the capital stock, and leads to a variety of dynamic possibilities, including non-existence and multiplicity of steady states, and cycles around some of the steady states, where there were none under exogenous taxes. Thus, optimal taxes can be an independent source of non-linearities

On the mathematical foundations of political economy

Political economy views economic issues through the lens of political organisation. In today's world, it must focus on the roles of markets and of democracy, two concepts which are driving revolutionary changes in the political organisation of both Europe and Asia. There are two main paradigms for the analysis of markets and democracy, both of which have been mathematically advanced over a number of years: the general equilibrium theory of markets, and social choice theory, which examines practical aspects of democracy.' While it is true that political economy has made some limited use of the latter in order to examine political-economic issues of democracy, it has made little use of the former, the theory of market behaviour.general equilibrium; Welfare Theorems; welfare; political economy; mixed economies; political economy agenda; social choice theory; mathematical modelling

Income distribution and Growth: A Critical Survey

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An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)L−1 where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.General equilibrium theory ; Existence of equilibrium ; Increasing returns ; Externalities ; Degree theory