Franz Wirl

I found the paper stimulating and started my own research. However, I will not pursue the matter further because at least my extension adds little contrary to my ex ante expectations. In fact, despite the extensions for preferences and technology (ho...

Although the possibility of multiple nonlinear equilibria in linear-quadratic differential games is extensively discussed, the literature on models with multiple linear Markov perfect equilibria (LMPEs) is scarce. Indeed, almost all papers confined to a single state (the vast majority of the application of differential games to economic problems) find a unique LMPE. This paper explains this finding and derives conditions for multiplicity based on the analysis of the phase plane in the state and the derivative of the value function. The resulting condition is applied to derive additional pathways different from the (two) known ones. All these examples, more precisely, their underlying pathways or the resulting outcomes, contradict usual assumptions in economic models. However, by extending the state space, we provide an economic setting (learning by doing) that gives rise to multiple LMPEs.

While hundreds of papers study the strategic interactions of oligopolists facing sticky prices only very few treat the in my opinion more important and opposite case of sticky or sluggish demand and supply, e.g., for energy. This point was taken up in Wirl (Int J Ind Organ 28:220–229, 2010) but unfortunately, the computation of the linear Markov perfect equilibrium is wrong. The situation in energy markets following Russia’s invasion of Ukraine adds a topical element to the theoretical analysis. Application to the oil market suggests that the difference between collusion and oligopolistic competition among few (symmetric) players is small for Markov perfect linear eqilibria. This is in stark contrast to the outcome in open loop strategies.

This paper addresses how a Leviathan government taxes income if the earning potential is private information. This complements the normative analyses in the tradition of Mirrlees (1971). Taxes increase with respect to earning (potential and actual since taxation lowers observed earnings). However, accounting for the agent’s private information, average taxes (tax per income) decline for efficient types with zero marginal tax at the top. This conclusion is robust against alternative assumptions: a convex efficiency, i.e., high types are disproportionately more productive; an optimistic prior (i.e., high types are more likely), which, surprisingly, lowers the earnings of all types; and a government concerned about the welfare of its people.

Environmental incentives are characterized by two distinct features: (1) a benefit-cost trade-off; and (2) private information about the trade-off. This suggests a degree of freedom of where to attach the private information, either to the benefit or the costs, as long as these choices imply the same behavior absent incentives (‘observation equivalent’). However, we show that different observation equivalent specifications can lead to different incentives. This is demonstrated for two cases: rainforest protection and contributions to a public good. Therefore, the choice of a private information parameter must be justified against observation equivalent alternatives.

Should oil-rich members of OPEC invest in the oil refinery industry? This is a crucial energy policy question for such economies. We extend theoretical models for a vertical integration strategy within an oil-producing economy, based on a risk-hedging view. The first model highlights the trade-off between return and risk-reduction features of upstream/downstream sectors. The dynamic model demonstrates the volatility of the total budgetary revenue of each sector. Our theory-guided empirical analysis shows that though the average markup in the refining sector is significantly smaller than the profits in the upstream, downstream investment can provide some hedging value. In particular, the more stable and mean-reverting refining margins provide a partial revenue cushion when crude oil prices are low. We discuss the risk-hedging feature of the refinery industry when the crude oil market faces supply versus demand shocks.

Leaders are role models that affect their employees’ efforts. The effect depends on how much an employee identifies with the “boss”. Since this degree of identification is private information of the employee, additional financial incentives must be provided. Therefore, we study a principal-agent problem in which the principal affects the agent’s effort by her own effort and by financial incentives. The resulting principal-agent problem has a few non-standard specifics such as: (i) bilateral externalities as the principal’s effort affects the agent and vice versa and (ii) endogenous reservation utility of the agent. Combined, this leads to non-trivial and interesting contracts.

Leaders are role models that affect their employees' efforts. The effect depends on how much an employee identifies with the "boss" Since this degree of identification is necessarily private information of the employee, additional financial incentives must be provided. Therefore, we study a principal-agent problem in which the principal affects the agent's effort by her own effort and money. The resulting principal-agent problem has a few non-standard specifics such as: (i) bilateral externalities as the principal's effort affects the agent and vice versa and (ii) endogenous reservation utility of the agent. Combined, this leads to non-trivial and interesting contracts.