Peter M. Kort

We study optimal management of the standard shallow lake model with special attention to the damage caused by the accumulated phosphorus in the water of the lake. The occurrence of a tipping point leads to a stronger increase in the damage after moving from the low-damage to the high-damage regime, because of the loss of ecosystem services. We modify the standard quadratic damage function by introducing a jump in marginal damage when moving from the low-damage to the high-damage regime. Connecting the lower and the higher marginal damage functions yields a continuous piecewise linear marginal damage function with a strong increase around the jump. In addition to the well-known oligotrophic and eutrophic steady states, we find that a third steady state can occur, separated by two Skiba points. This implies that a corridor or a basin of attraction arises between these two Skiba points where optimal management of the lake stabilizes the amount of phosphorus somewhere in the middle instead of either moving to the low-damage or to the high-damage regime, as is the result in the standard knife-edge case with one Skiba point.

Modeling Cooperative and Noncooperative Incentives in Investment Projects: A Novel Approach Using Cooperative Game Theory and Real Options Theory In “Dynamic Stability of Cooperative Investment under Uncertainty,” Ketelaars, Borm, and Kort study an investment project involving multiple stakeholders. The research was prompted by the fact that many infrastructure projects, such as Feyenoord City in Rotterdam, Netherlands, and the new Berlin airport, failed or were significantly delayed. Recognizing that the various stakeholders have outside options, the authors combine concepts from cooperative game theory and real options to analyze a coalitional and dynamic stability concept. They characterize the proportional investment scheme as the scheme that maximizes total project value and results in the earliest investment timing. They show that dynamic stability can be present when the market is stable and when the market is growing and volatile. However, the proportional investment scheme is more sensitive to dynamic instability in a market with high profit growth and low profit uncertainty, or vice versa.

This paper considers a firm’s investment decision determining the timing and capacity level in a dynamic setting with demand uncertainty. Its investment is financed by borrowing from a lender that has market power, generating a capital market inefficiency. We show that the firm’s investment is subject to double marginalization in the sense that the need for external financing results in a considerably smaller investment and thus, a reduction in welfare. In addition, we find that the presence of the bankruptcy option mitigates the double-marginalization effect unless the bankruptcy cost is small. The firm’s investment size is increasing in bankruptcy costs, albeit at the expense of an investment delay. Based on this, an increase of bankruptcy costs raises social welfare. This paper was accepted by Tomasz Piskorski, finance. Funding: X. Wen and H. Dawid gratefully acknowledge support from the Deutsche Forschungsgemeinschaft [Grant SFB 1283/2 2021–317210226]. The authors acknowledge financial support from the Center of Interdisciplinary Research at Bielefeld University [Research Group “Economic and Legal Challenges in the Advent of Smart Products”]. K. J. M. Huisman is appointed to a special chair at Tilburg University that is funded by ASML. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.01152 .

We examine the optimal behavior of carbon-emitting companies operating under the European Union Emission Trading System (EU ETS), under which firms are obliged to purchase emission permits on the secondary market if their emissions exceed their allowance. Specifically, we consider the scenario where firms are endowed with the (real) option to undertake a “green” investment to cut their emissions and, thus, permit expenditures. The central challenge is the determination of the optimal time for investment within a stochastic framework characterized by uncertainty in EU ETS permit prices. We address the problem for a heterogeneous group of companies with diverse technological capabilities across industrial sectors. Furthermore, we incorporate a price floor for permit prices to mirror policy efforts aimed at promoting green transition by elevating emission costs. We solve this problem analytically and through numerical simulations calibrated to real market data. In addition to offering insights into individual firm behavior, our findings can support regulators in refining environmental policies, particularly regarding the role of permits price floor and its potential to expedite the green transition.

The objective of this paper is to analyze an incumbent–entrant model under uncertainty. The entrant observes the realization of the random variable(s) prior to making decisions regarding market entry and capacity selection, leaving the uncertainty entirely on the incumbent’s side. The sources of this uncertainty pertain to the characteristics of the entrant’s product and the entry costs the entrant must incur before becoming operational. The key findings indicate that uncertainty generally enhances entry, and, apart from blockaded entry, entry deterrence and accommodated entry, the incumbent can pursue entry deterrence with a certain probability.