Andrea Seidl

Leading bureaucracies to the tipping point: An alternative model of multiple stable equilibrium levels of corruption

Highlights ► We model an alternative explanation for tipping points in societal-level corruption. ► The bureaucracy’s culture of corruption is influenced by an executive’s actions. ► The nonlinear dynamical formulation is solved with Pontryagin’s Principle. ► The solution exhibits state-dependence and so-called Skiba points. ► Policy interpretations are somewhat more optimistic than in Schelling’s (1978) classic model.

Numerical solution of a conspicuous consumption model with constant control delay

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account. This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions. Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case.

Optimal control of a terror queue

The task of covert intelligence agents is to detect and interdict terror plots. Kaplan (2010) treats terror plots as customers and intelligence agents as servers in a queuing model. We extend Kaplan’s insight to a dynamic model that analyzes the inter-temporal trade-off between damage caused by terror attacks and prevention costs to address the question of how many agents to optimally assign to such counter-terror measures. We compare scenarios which differ with respect to the extent of the initial terror threat and study the qualitative robustness of the optimal solution. We show that in general, the optimal number of agents is not simply proportional to the number of undetected plots. We also show that while it is sensible to deploy many agents when terrorists are moderately efficient in their ability to mount attacks, relatively few agents should be deployed if terrorists are inefficient (giving agents many opportunities for detection), or if terrorists are highly efficient (in which case agents become relatively ineffective). Furthermore, we analyze the implications of a policy that constraints the number of successful terror attacks to never increase. We find that the inclusion of a constraint preventing one of the state variables to grow leads to a continuum of steady states, some which are much more costly to society than the more forward-looking optimal policy that temporarily allows the number of terror attacks to increase.

Interaction of pricing, advertising and experience quality: A dynamic analysis

For certain goods or services, the quality of the product can be assessed by customers only after consumption. We determine the optimal time paths for pricing, advertising and quality for a profit-maximizing firm facing demand that is influenced both by this experience quality as well as by advertising. In particular, there may exist two optimal trajectories separated by an indifference threshold in which the firm has the same utility of converging to either of the two long-run steady states. Or, to put it in a nutshell: the optimal mix of marketing instruments may lead to history-dependence. One implication is that there may be a market failure such that a government subsidy could help reach the steady state that is best for the Economy in the sense of having greater sales and a higher quality product.

History-dependence in production-pollution-trade-off models: a multi-stage approach

Multi-stage modeling provides powerful tools to study optimal switches between different technologies. In most of the related literature, however, it is assumed that the number of switches is a-priori fixed. In the present paper we allow for multiple optimally determined switches. Consequently, we are able to locate solution paths that not only lead to different long-run outcomes but also differ in the number of switches along these paths.We present a simple production-pollution model in which a representative firm wants to maximize the profit gained out of production which, however, causes harmful pollution as by-product. The firm has the choice between two different technologies, one which is efficient in production but pollutive, and another one which is less efficient but environmentally friendly.With this two stage-model we focus on the numerical investigation of the conditions determining when and how often it is optimal for the firm to switch between these different technologies. We show that for certain parameters even several switches can be optimal and that the height of the switching costs crucially influences the long-run outcome. In the course of these investigations, we discuss two different economic mechanisms related to the harm due to pollution which lead to the occurrence of multiple equilibria, history-dependence and so-called Skiba points.

Lanchester model for three-way combat

Lanchester (1960) modeled combat situations between two opponents, where mutual attrition occurs continuously in time, by a pair of simple ordinary (linear) differential equations. The aim of the present paper is to extend the model to a conflict consisting of three parties. In particular, Lanchester’s main result, i.e. his Square Law, is adapted to a triple fight. However, here a central factor – besides the initial strengths of the forces – determining the long run outcome is the allocation of each opponent’s efforts between the other two parties. Depending on initial strengths, (the) solution paths are calculated and visualized in appropriate phase portraits. We are able identify regions in the state space where, independent of the force allocation of the opponents, always the same combatant wins, regions, where a combatant can win if its force allocation is wisely chosen, and regions where a combatant cannot win itself but determine the winner by its forces allocation. As such, the present model can be seen as a forerunner of a dynamic game between three opponents.

Optimal language policy for the preservation of a minority language

We develop a dynamic language competition model with dynamic state intervention. Parents choose the language(s) to raise their children based on the communicational value of each language as well as on their emotional attachment to the languages at hand. Languages are thus conceptualized as tools for communication as well as carriers of cultural identity. The model includes a high and a low status language, and children can be brought up as monolinguals or bilinguals. Through investment into language policies, the status of the minority language can be increased. The aim of the intervention is to preserve the minority language in a bilingual subpopulation at low costs. We investigate the dynamic structure of the optimally controlled system as well as the optimal policy, identify stable equilibria and provide numerical case studies.

A Dynamic Analysis of Schelling's Binary Corruption Model: A Competitive Equilibrium Approach

Schelling (in Micromotives and Macrobehavior, Norton, New York, 1978) suggested a simple binary choice model to explain the variation of corruption levels across societies. His basic idea was that the expected profitability of engaging in corruption depends on its prevalence. The key result of the so-called Schelling diagram is the existence of multiple equilibria and a tipping point. The present paper puts Schelling’s essentially static approach into an intertemporal setting. We show how the existence of an unstable interior steady state leads to thresholds such that history alone or history in addition to expectations (or coordination) is necessary to determine the long-run outcome. In contrast to the related literature, which classifies these two cases according to whether the unstable equilibrium is a node or a focus, the actual differentiation is more subtle because even a node can lead to an overlap of solution paths such that the initial conditions alone are insufficient to uniquely determine the competitive equilibrium. Another insight is that a (transiently) cycling competitive equilibrium can dominate the direct and monotonic route to a steady state, even if the direct route is feasible.

Dynamic Perspectives on Managerial Decision Making

This volume collects research papers addressing topical issues in economics and management with a particular focus on dynamic models which allow to analyze and foster the decision making of firms in dynamic complex environments. The scope of the contributions ranges from daily operational challenges firms face to strategic choices in dynamic industry environments and the analysis of optimal growth paths. The volume also highlights recent methodological developments in the areas of dynamic optimization, dynamic games and meta-heuristics, which help to improve our understanding of (optimal) decision making in a fast evolving economy.

Economics of Talent: Dynamics and Multiplicity of Equilibria

The economics of art and science differs from other branches by the small role of material inputs and the large role of given talent and access to markets. E.g., an African violinist lacks the audience ( = market) to appreciate her talent unless it is so large that it transgresses regional constraints; conversely, a European violinist of equal talent may be happy to end up as a member of one of the regional orchestras. This paper draws attention to this second aspect and models dynamic interactions between investments into two stocks, productive capital and access (or bargaining power). It is shown that there exists multiple equilibria. The separation between pursuing an artistic career or quitting depends on both idiosyncracies, individual talent and individual market access (including or depending on market size), which explains the large international variation in the number of people choosing a career in arts as market access is affected by geographic, linguistic, and aesthetic dimensions.