Global Changes: Facets of Robust Decisions

The aim of this paper is to provide an overview of existing concepts of robustness and to identify promising directions for coping with uncertainty and risks of global changes. Unlike statistical robustness, general decision problems may have rather different facets of robustness. In particular, a key issue is the sensitivity with respect to low-probability catastrophic events. That is, robust decisions in the presence of catastrophic events are fundamentally different from decisions ignoring them. Specifically, proper treatment of extreme catastrophic events requires new sets of feasible decisions, adjusted to risk performance indicators, and new spatial, social and temporal dimensions. The discussion is deliberately kept at a level comprehensible to a broad audience through the use of simple examples that can be extended to rather general models. In fact, these examples often illustrate fragments of models that are being developed at IIASA

Analysis of a Reputation System for Mobile Ad-Hoc Networks with Liars

The application of decentralized reputation systems is a promising approach to ensure cooperation and fairness, as well as to address random failures and malicious attacks in Mobile Ad-Hoc Networks. However, they are potentially vulnerable to liars. With our work, we provide a first step to analyzing robustness of a reputation system based on a deviation test. Using a mean-field approach to our stochastic process model, we show that liars have no impact unless their number exceeds a certain threshold (phase transition). We give precise formulae for the critical values and thus provide guidelines for an optimal choice of parameters.Comment: 17 pages, 6 figure

Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves

We consider how to optimally allocate investments in a portfolio of competing technologies using the standard mean-variance framework of portfolio theory. We assume that technologies follow the empirically observed relationship known as Wright's law, also called a "learning curve" or "experience curve", which postulates that costs drop as cumulative production increases. This introduces a positive feedback between cost and investment that complicates the portfolio problem, leading to multiple local optima, and causing a trade-off between concentrating investments in one project to spur rapid progress vs. diversifying over many projects to hedge against failure. We study the two-technology case and characterize the optimal diversification in terms of progress rates, variability, initial costs, initial experience, risk aversion, discount rate and total demand. The efficient frontier framework is used to visualize technology portfolios and show how feedback results in nonlinear distortions of the feasible set. For the two-period case, in which learning and uncertainty interact with discounting, we compare different scenarios and find that the discount rate plays a critical role

General Stopping Behaviors of Naive and Non-Committed Sophisticated Agents, with Application to Probability Distortion

We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves' behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves' behaviors into account. We then apply the general results to the case when the agents distort probability and the diffusion process is a geometric Brownian motion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We show how the strategic reasoning may turn a naive agent into a sophisticated one. Moreover, we derive stopping strategies of the two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as "never-stopping" or "never-starting"