Cheating as a dynamic marketing strategy in monopoly,cartel and duopoly

In 2015 it was discovered that Volkswagen had manipulated the exhaust emissions of its (diesel) cars. Since then, numerous other automotive car manufacturers were strongly suspected to violate against the same emission standards. This paper investigates how and why firms (monopoly, cartel and duopoly) engage in cheating, more precisely, promising attributes that are actually not part of the product. Firms make claims in order to better market their product but risk damaging their future reputation. The upshot of the paper is the stark difference between open loop and Markov perfect oligopolistic equilibrium outcomes. More precisely, the latter mitigates cheating substantially even below the levels attained by monopolies and cartels (unless consumers have a very short memory), which is contrary to the outcome in the limiting static version of the game. Therefore, revealing the true state (e.g., by mandating strict inspections) could force firms to use this information and play in Markov instead of open loop strategies.

     

Reversible stopping (“switching”) implies super contact

This note shows that the second derivative of the value function exists (across a stopping threshold, short “super contact”) if reversibly stopping and entering involves no cost, called “switching”. This holds for discrete (real option) as well as for continuous stochastic control problems and proves particularly suitable in real option set ups since it provides the lacking boundary condition. However, super contact does not hold in dynamic games. A simple example documents the applicability of this condition. This paper was written during my visit of the University of Technology, Sydney (UTS) and I am grateful for the hospitality of and the stimulus at the School of Finance and Economics, in particular to Carl Chiarella. I also acknowledge many helpful discussions with Thomas Dangl on related issues, valuable suggestions from a referee and last but not least encouragement by Josef Kallrath     

Cyclical strategies in two-dimensional optimal control models: Necessary conditions and existence

This paper derives necessary conditions such that cyclical policies may be optimal in concave, two state variable (economic) control problems. These conditions identify four different routes. One major implication is that two of these four conditions may be met by separable models. This possibility has been overlooked so far. Therefore, even separable and structurally very simple models may be characterized by optimal cyclical policies. Indeed, it will be shown that stable limit cycles exist for concave and separable control problems.     

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.     

Pathways to hopf bifurcations in dynamic continuous-time optimization problems

The purpose of this paper is to characterize pathways to Hopf bifurcation in continuous time, concave, two-dimensional optimal control models. It is shown that essentially two pathways exist: control-state interaction and growth. The knowledge of such pathways provides a criterion at the stage of modelling on the potential complexity of optimal trajectories.The author knowledges the many discussions with Professor Gustav Feichtinger.     

Optimal maintenance and scrapping versus the value of back ups

This paper investigates optimal maintenance of equipment under uncertainty and the options of scrapping versus keeping the equipment as a back up (at a cost). This set up is used to analyze three points. The first observation is that the continuous, deterministic and even the unconstrained stochastic problem allow for closed form analytical solutions, realistic constraints require numerical means to solve the corresponding stochastic managerial problem. Second, the possibility to switch at negligible costs between different modes (here running or mothballing the equipment) depending on current states requires a condition in addition to the familiar value matching and smooth pasting conditions, namely continuity of the second derivative of the value function (or super contact). Equipped with these findings the analysis turns to the third point of quantifying numerically the value of keeping equipments as a back-up instead of scrapping.     

Non-cooperative investment in partnerships and their termination

This paper investigates how partners (firms or husband and wife) should invest into an uncertain stock that provides a common good, when to stop investments and when to end their partnership. The assumption of lumpy investments leads to a real option problem which is solved for the cooperative and non-cooperative solutions. Yet despite the analytical solution, numerical means are necessary to investigate economic consequences: strong incentives to free ride under competition even turning one of the options—to stop investment at high stock levels—into one of a negative value; in contrast, divorce remains a positively valued option.     

Social Interactions within a Dynamic Competitive Economy

This paper considers social interactions and investigates how far the properties of moderate social influence and of diminishing returns foster the uniqueness and stability of a dynamic competitive economy. In particular, in contrast to the static framework, it is shown that moderate social influence can neither ensure unique long run outcomes nor rule out other kinds of complexities such as indeterminacy; also, the assumption of diminishing returns for the aggregate economy does not eliminate any of these complexities. Instead, the (derived) property of moderate dynamic social influence, which accounts explicitly for intertemporal spillovers, provides the proper criterion for the (saddlepoint) stable evolution of a competitive economy.