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This cumulative dissertation contains four self-contained chapters on stochastic games and learning in intertemporal choice.
Chapter 1 presents an experiment on value learning in a setting where actions have both immediate and delayed consequences. Subjects make a series of choices between abstract options, with values that have to be learned by sampling. Each option is associated with two payoff components: One is revealed immediately after the choice, the other with one round delay. Objectively, both payoff components are equally important, but most subjects systematically underreact to the delayed consequences. The resulting behavior appears impatient or myopic. However, there is no inherent reason to discount: All rewards are paid simultaneously, after the experiment. Elicited beliefs on the value of options are in accordance with choice behavior. These results demonstrate that revealed impatience may arise from frictions in learning, and that discounting does not necessarily reflect deep time preferences. In a treatment variation, subjects first learn passively from the evidence generated by others, before then making a series of own choices. Here, the underweighting of delayed consequences is attenuated, in particular for the earliest own decisions. Active decision making thus seems to play an important role in the emergence of the observed bias.
Chapter 2 introduces and proves existence of Markov quantal response equilibrium (QRE), an application of QRE to finite discounted stochastic games. We then study a specific case, logit Markov QRE, which arises when players react to total discounted payoffs using the logit choice rule with precision parameter λ. We show that the set of logit Markov QRE always contains a smooth path that leads from the unique QRE at λ = 0 to a stationary equilibrium of the game as λ goes to infinity. Following this path allows to solve arbitrary finite discounted stochastic games numerically; an implementation of this algorithm is publicly available as part of the package sgamesolver. We further show that all logit Markov QRE are ε-equilibria, with a bound for ε that is independent of the payoff function of the game and decreases hyperbolically in λ. Finally, we establish a link to reinforcement learning, by characterizing logit Markov QRE as the stationary points of a game dynamic that arises when all players follow the well-established reinforcement learning algorithm expected SARSA.
Chapter 3 introduces the logarithmic stochastic tracing procedure, a homotopy method to compute stationary equilibria for finite and discounted stochastic games. We build on the linear stochastic tracing procedure (Herings and Peeters 2004), but introduce logarithmic penalty terms as a regularization device, which brings two major improvements. First, the scope of the method is extended: it now has a convergence guarantee for all games of this class, rather than just generic ones. Second, by ensuring a smooth and interior solution path, computational performance is increased significantly. A ready-to-use implementation is publicly available. As demonstrated here, its speed compares quite favorable to other available algorithms, and it allows to solve games of considerable size in reasonable times. Because the method involves the gradual transformation of a prior into equilibrium strategies, it is possible to search the prior space and uncover potentially multiple equilibria and their respective basins of attraction. This also connects the method to established theory of equilibrium selection.
Chapter 4 introduces sgamesolver, a python package that uses the homotopy method to compute stationary equilibria of finite discounted stochastic games. A short user guide is complemented with discussion of the homotopy method, the two implemented homotopy functions logit Markov QRE and logarithmic tracing, and the predictor-corrector procedure and its implementation in sgamesolver. Basic and advanced use cases are demonstrated using several example games. Finally, we discuss the topic of symmetries in stochastic games.
Central banks sowing the seeds for a green financial sector? NGFS membership and market reactions
(2024)
In December 2017, during the One Planet Summit in Paris, a group of eight central banks and supervisory authorities launched the “Network for Greening the Financial Sector” (NGFS) to address challenges and risks posed by climate change to the global financial system. Until 06/2023 an additional 69 central banks from all around the world have joined the network. We find that the propensity to join the network can be described as a function in the country’s economic development (e.g., GDP per capita), national institutions (e.g., central bank independence), and performance of the central bank on its mandates (e.g., price stability and output gap). Using an event study design to examine consequences of network expansions in capital markets, we document that a difference portfolio that is long in clean energy stocks and short in fossil fuel stocks benefits from an enlargement of the NGFS. Overall, our results suggest that an increasing number of central banks and supervisory authorities are concerned about climate change and willing to go beyond their traditional objectives, and that the capital market believes they will do so.
The transition to a future electricity system based primarily on wind and solar PV is examined for all regions in the contiguous US. We present optimized pathways for the build-up of wind and solar power for least backup energy needs as well as for least cost obtained with a simplified, lightweight model based on long-term high resolution weather-determined generation data. In the absence of storage, the pathway which achieves the best match of generation and load, thus resulting in the least backup energy requirements, generally favors a combination of both technologies, with a wind/solar PV (photovoltaics) energy mix of about 80/20 in a fully renewable scenario. The least cost development is seen to start with 100% of the technology with the lowest average generation costs first, but with increasing renewable installations, economically unfavorable excess generation pushes it toward the minimal backup pathway. Surplus generation and the entailed costs can be reduced significantly by combining wind and solar power, and/or absorbing excess generation, for example with storage or transmission, or by coupling the electricity system to other energy sectors.
By computing a volatility index (CVX) from cryptocurrency option prices, we analyze this market’s expectation of future volatility. Our method addresses the challenging liquidity environment of this young asset class and allows us to extract stable market implied volatilities. Two alternative methods are considered to compute volatilities from granular intra-day cryptocurrency options data, which spans over the COVID-19 pandemic period. CVX data therefore capture ‘normal’ market dynamics as well as distress and recovery periods. The methods yield two cointegrated index series, where the corresponding error correction model can be used as an indicator for market implied tail-risk. Comparing our CVX to existing volatility benchmarks for traditional asset classes, such as VIX (equity) or GVX (gold), confirms that cryptocurrency volatility dynamics are often disconnected from traditional markets, yet, share common shocks.
Do leaders who build a sense of shared social identity in their teams thereby protect them from the adverse effects of workplace stress? This is a question that the present paper explores by testing the hypothesis that identity leadership contributes to stronger team identification among employees and, through this, is associated with reduced burnout. We tested this model with unique datasets from the Global Identity Leadership Development (GILD) project with participants from all inhabited continents. We compared two datasets from 2016/2017 (n = 5290; 20 countries) and 2020/2021 (n = 7294; 28 countries) and found very similar levels of identity leadership, team identification and burnout across the five years. An inspection of the 2020/2021 data at the onset of and later in the COVID-19 pandemic showed stable identity leadership levels and slightly higher levels of both burnout and team identification. Supporting our hypotheses, we found almost identical indirect effects (2016/2017, b = −0.132; 2020/2021, b = −0.133) across the five-year span in both datasets. Using a subset of n = 111 German participants surveyed over two waves, we found the indirect effect confirmed over time with identity leadership (at T1) predicting team identification and, in turn, burnout, three months later. Finally, we explored whether there could be a “too-much-of-a-good-thing” effect for identity leadership. Speaking against this, we found a u-shaped quadratic effect whereby ratings of identity leadership at the upper end of the distribution were related to even stronger team identification and a stronger indirect effect on reduced burnout.
The pricing of digital art
(2023)
The intersection of recent advancements in generative artificial intelligence and blockchain technology has propelled digital art into the spotlight. Digital art pricing recognizes that owners derive utility beyond the artwork’s inherent value. We incorporate the consumption utility associated with digital art and model the stochastic discount factor and risk premiums. Furthermore, we conduct a calibration analysis to analyze the effects of shifts in the real and digital economy. Higher returns are required in a digital market upswing due to increased exposure to systematic risk and digital art prices are especially responsive to fluctuations in business cycles within digital markets.
Using a field study at a German brokerage, we investigate advised individual investors’ behavior and outcomes after self-selecting into a flat-fee scheme (percentage of portfolio value) for mutual funds. In a difference-in-differences setting, we compare 699 switchers to propensity-score-matched advisory clients who remained in the commission-based scheme. Switchers increase their portfolio values, improve portfolio diversification, and increase their portfolio performance. They also demand more financial advice and follow more advisor recommendations. We argue that switchers attribute a higher quality to the unchanged advisory services.
We study the role mutual funds play in the recovery from fast intraday crashes based on data from the National Stock Exchange of India for a single large stock. During normal times, trading activity and liquidity provision by mutual funds is negligible compared to other traders at around 4% of overall activity. Nevertheless, for the two intraday market-wide crashes in our sample, price recovery took place only after mutual funds moved in. Market stability may require the presence of well-capitalized standby liquidity providers for recovery from fast crashes.
The recent COVID-19 pandemic represents an unprecedented worldwide event to study the influence of related news on the financial markets, especially during the early stage of the pandemic when information on the new threat came rapidly and was complex for investors to process. In this paper, we investigate whether the flow of news on COVID-19 had an impact on forming market expectations. We analyze 203,886 online articles dealing with COVID-19 and published on three news platforms (MarketWatch.com, NYTimes.com, and Reuters.com) in the period from January to June 2020. Using machine learning techniques, we extract the news sentiment through a financial market-adapted BERT model that enables recognizing the context of each word in a given item. Our results show that there is a statistically significant and positive relationship between sentiment scores and S&P 500 market. Furthermore, we provide evidence that sentiment components and news categories on NYTimes.com were differently related to market returns.