Subgame-Perfect Equilibria in Stochastic Timing Games

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies -- in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.Comment: 27 pages, 1 figur

Stuttgart – a Livable City: The global Agenda 2030 at a local level Baseline study depicting the Sustainable Development Goals (SDGs)

The United Nations adopted the Agenda 2030 in 2015. This was a basis for the transition to a world in which economic efficiency, ecological compatibility and social justice can be in accord with one another. The Agenda 2030 addresses all states (“every country is a developing country”) at an international, national and, just as much, at a regional and local level. An essential component of Agenda 2030 are the 17 goals for a sustainable development (Sustainable Development Goals, SDGs). To achieve the goals of Agenda 2030 the focus is on partnerships between various actors from administration, politics, business and civil society. In the further development of the Sustainable Development Strategy for Germany in 2017 the Federal Government oriented itself systematically towards the Agenda 2030 with the 17 SDGs. Many other German states also developed strategies geared towards the SDGs. In Baden-Württemberg the Advisory Council of the State Government prepared a proposal as to how the SDGs could be integrated into the state-specific guidelines for sustainable development. The municipalities, having a close relationship with the residents, play a particular role when it comes to implementing Agenda 2030. To map out the status of sustainable development on a quantitative basis of SDGs and at a local level, seven organisations started a nationwide project in 2017 “SDG indicators for municipalities” – proposals for SDGs at a local level: Association of German Cities, German County Association, German Association of Towns and Municipalities, German Institute for Urban Studies (Difu), Federal Institute for Building, Urban Affairs and Spatial Research, Service Agency Communities in One World of Engagement Global and the Bertelsmann Foundation. As one of the first municipalities in Germany the State Capital Stuttgart took on the challenging task of pilot-testing the “SDG indicators for municipalities” from June to October 2018. A second phase between July and September 2019 saw the update of the data. The baseline study was carried out in cooperation with the Bertelsmann Foundation and Difu. The SDG baseline study for the State Capital Stuttgart has two main objectives: first, to analyse the current status of the city on the basis of data in place as regards social, ecological and economic sustainability and to improve the possibilities of a target-oriented, strategic development of the city’s measures; second, with this SDG baseline study to make a methodological contribution to a target-oriented strategic, further development of SDG indicators for an appropriate and effective design for the SDG baseline-studies in municipalities. The different starting conditions make a comparison of cities neither possible nor envisaged – however, the municipalities will receive a toolbox so they can gauge their own development. A qualitative depiction of selected programmes and measures of the State Capital Stuttgart complements the quantitative baseline study. These descriptions give an impression of the spectrum of the measures which can be taken with a view to sustainability. This should also address the issue in other cities and communities. Stuttgart sees itself here as an impulse-giver, but also as a learner, in a national and international network of local actors. The SDGs offer a comprehensive target system for sustainability and, at the same time, they point out possible conflicts of interests. The implementation of strategic objectives requires continuous monitoring. The participative, cross-divisional process of the baseline study shows that the tried and tested SDG indicators for municipalities are a suitable instrument to be quantitatively supportive in realising the existing objectives and approaches of the State Capital Stuttgart for social, ecological and economic sustainability. It was constructive to discuss the SDG indicators methodologically on a cross-sectoral basis, and to select and expand on issues to do justice to the distinctiveness of a municipality. This way, the cross-divisional knowledge management and the understanding of the correlations between the individual sustainability measures could be strengthened. All divisions and departments of the City of Stuttgart worked with enormous commitment on this report. Based on SDG indicators, this baseline study has for the first time developed a cross-sectoral instrument for a regular, all-embracing monitoring of correlations of social, economic and ecological sustainability. This forms an important basis for future recommendations and an effective action on the part of politics, administration and urban society which will help to serve the further development of municipal objectives and measures of implementing the SDGs in the State Capital Stuttgart. The present executive summary provides an overview of the methodological approach, a compilation of the selected indicators as well as the main results with regards to the process and further development of SDG- indicators

Subgame-perfect equilibria in stochastic timing games

Abstract: We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps

Developing Successful Sustainability Strategies: Strategies for a Sustainable Future in Germany, Europe and Worldwide

In Germany, strategies for a sustainable future were initially and primarily developed at the municipal level in the form of local agenda processes. In addition, in 2002, the federal government decided on a “National Sustainability Strategy,” which was subsequently continuously updated. Sustainability strategies were also adopted in various federal states and at least partially further developed. The challenges of political sustainability strategies at the level of the states comprise mainly two areas

Subgame-Perfect Equilibria in Stochastic Timing Games

Riedel F, Steg J-H. Subgame-Perfect Equilibria in Stochastic Timing Games. Center for Mathematical Economics Working Papers. Vol 524. Bielefeld: Center for Mathematical Economics; 2014.We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies – in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications

Realism and Experiments: Investigating Virtual Reality Experiments

Experimental research is a fundamental component of scientific inquiry, but the realism of experimental settings may be limited due to a trade-off between internal and external validity. Virtual Reality technology offers a potential solution to this problem by creating highly controlled, yet realistic experimental settings. In this study, we investigate the potential of VR to increase perceived realism in experimental research by identifying and examining the effects of VR experiments on participants\u27 perceived realism. In our experiment, we compare the level of perceived realism between artificial scenarios presented as text vignettes and in VR. Our findings indicate that VR experiments elicite a significantly higher level of perceived realism compared to text-based experiments. Additionally, we use partial least squares structural equation modeling to investigate the identified concepts. We recommend that researchers consider using VR technology to enhance the realism of experimental settings and improve the validity of their findings

Continuous-Time Public Good Contribution under Uncertainty

Ferrari G, Riedel F, Steg J-H. Continuous-Time Public Good Contribution under Uncertainty. Center for Mathematical Economics Working Papers. Vol 485 Version February 2015. Bielefeld: Center for Mathematical Economics; 2015.We study a continuous-time problem of public good contribution under uncertainty for an economy with a finite number of agents. Each agent aims to maximize his expected utility allocating his initial wealth over a given time period between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study the corresponding social planner problem and the case of strategic interaction between the agents. These problems are set up as stochastic control problems with both monotone and classical controls representing the cumulative contribution into the public good and the consumption of the private good, respectively. We characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions, which in turn allow to identify a universal signal process that triggers the public good investments. Further we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions need not affect the degree of free-riding

Continuous-Time Public Good Contribution under Uncertainty

Ferrari G, Riedel F, Steg J-H. Continuous-Time Public Good Contribution under Uncertainty. Center for Mathematical Economics Working Papers. Vol 485. Bielefeld: Center for Mathematical Economics; 2013.We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with an finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study the corresponding social planner problem and the case of strategic interaction between the agents and we characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions. Suitably combining arguments from Duality Theory and the General Theory of Stochastic Processes, we prove an abstract existence result for a Nash equilibrium of our public good contribution game. Also, we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions do not affect free-riding