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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.
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.
This paper explores entrepreneurs’ initially intended exit strategies and compares them to their final exit paths using an inductive approach that builds on the grounded theory methodology. Our data shows that initially intended and final exit strategies differ among entrepreneurs. Two groups of entrepreneurs emerged from our data. The first group comprises entrepreneurs who financed their firms through equity investors. The second group is made up of entrepreneurs who financed their businesses solely with their own equities. Our data shows that the first group originally intended a financial harvest exit strategy and settled with this harvest exit strategy. The second group initially intended a stewardship exit strategy but did not succeed. We used the theory of planned behavior and the behavioral agency model to analyze our data. By examining our results from these two theoretical perspectives, our study explains how entrepreneurs’ exit intentions lead to their actual exit strategies.
This research examines the impact of online display advertising and paid search advertising relative to offline advertising on firm performance and firm value. Using proprietary data on annualized advertising expenditures for 1651 firms spanning seven years, we document that both display advertising and paid search advertising exhibit positive effects on firm performance (measured by sales) and firm value (measured by Tobin's q). Paid search advertising has a more positive effect on sales than offline advertising, consistent with paid search being closest to the actual purchase decision and having enhanced targeting abilities. Display advertising exhibits a relatively more positive effect on Tobin's q than offline advertising, consistent with its long-term effects. The findings suggest heterogeneous economic benefits across different types of advertising, with direct implications for managers in analyzing advertising effectiveness and external stakeholders in assessing firm performance.
Most event studies rely on cumulative abnormal returns, measured as percentage changes in stock prices, as their dependent variable. Stock price reflects the value of the operating business plus non-operating assets minus debt. Yet, many events, in particular in marketing, only influence the value of the operating business, but not non-operating assets and debt. For these cases, the authors argue that the cumulative abnormal return on the operating business, defined as the ratio between the cumulative abnormal return on stock price and the firm-specific leverage effect, is a more appropriate dependent variable. Ignoring the differences in firm-specific leverage effects inflates the impact of observations pertaining to firms with large debt and deflates those pertaining to firms with large non-operating assets. Observations of firms with high debt receive several times the weight attributed to firms with low debt. A simulation study and the reanalysis of three previously published marketing event studies shows that ignoring the firm-specific leverage effects influences an event study's results in unpredictable ways.
Knowledge of consumers' willingness to pay (WTP) is a prerequisite to profitable price-setting. To gauge consumers' WTP, practitioners often rely on a direct single question approach in which consumers are asked to explicitly state their WTP for a product. Despite its popularity among practitioners, this approach has been found to suffer from hypothetical bias. In this paper, we propose a rigorous method that improves the accuracy of the direct single question approach. Specifically, we systematically assess the hypothetical biases associated with the direct single question approach and explore ways to de-bias it. Our results show that by using the de-biasing procedures we propose, we can generate a de-biased direct single question approach that is accurate enough to be useful for managerial decision-making. We validate this approach with two studies in this paper.
In recent years, European regulators have debated restricting the time an online tracker can track a user to protect consumer privacy better. Despite the significance of these debates, there has been a noticeable absence of any comprehensive cost-benefit analysis. This article fills this gap on the cost side by suggesting an approach to estimate the economic consequences of lifetime restrictions on cookies for publishers. The empirical study on cookies of 54,127 users who received ∼128 million ad impressions over ∼2.5 years yields an average cookie lifetime of 279 days, with an average value of €2.52 per cookie. Only ∼13 % of all cookies increase their daily value over time, but their average value is about four times larger than the average value of all cookies. Restricting cookies’ lifetime to one year (two years) could potentially decrease their lifetime value by ∼25 % (∼19 %), which represents a potential decrease in the value of all cookies of ∼9 % (∼5%). Most cookies, however, would not be affected by lifetime restrictions of 12 or 24 months as 72 % (85 %) of the users delete their cookies within 12 (24) months. In light of the €10.60 billion cookie-based display ad revenue in Europe, such restrictions would endanger €904 million (€576 million) annually, equivalent to €2.08 (€1.33) per EU internet user. The article discusses these results' marketing strategy challenges and opportunities for advertisers and publishers.
Even as online advertising continues to grow, a central question remains: Who to target? Yet, advertisers know little about how to select from the hundreds of audience segments for targeting (and combinations thereof) for a profitable online advertising campaign. Utilizing insights from a field experiment on Facebook (Study 1), we develop a model that helps advertisers solve the cold-start problem of selecting audience segments for targeting. Our model enables advertisers to calculate the break-even performance of an audience segment to make a targeted ad campaign at least as profitable as an untargeted one. Advertisers can use this novel model to decide whether to test specific audience segments in their campaigns (e.g., in randomized controlled trials). We apply our model to data from the Spotify ad platform to study the profitability of different audience segments (Study 2). Approximately half of those audience segments require the click-through rate to double compared to an untargeted campaign, which is unrealistically high for most ad campaigns. Our model also shows that narrow segments require a lift that is likely not attainable, specifically when the data quality of these segments is poor. We confirm this theoretical finding in an empirical study (Study 3): A decrease in data quality due to Apple’s introduction of the App Tracking Transparency (ATT) framework more negatively affects the click-through rate of narrow (versus broad) audience segments.
Small businesses face major challenges to becoming more innovative. These challenges are particularly prevalent in emerging economies where high uncertainties are a barrier to innovation. We know from previous studies that linkages to universities, on the one hand, and public procurement, on the other, support large and innovative firms in their efforts to become more innovative. However, we do not know whether these positive effects also hold true for small businesses. In this paper, we focus on how policy strategies reducing information, market and financial uncertainties shape small businesses’ innovation in China. Based on a sample of 926 small businesses derived from the World Bank Enterprises Survey in China (2012), we find that university-industry linkages enhance innovation, though only when it comes to minor forms of innovation. In line with the resource-based view of the firm, this effect is stronger for small businesses with higher capabilities. Moreover, we show that bidding for or delivering contracts to public sector clients has a positive effect on innovation, and in particular of major forms of innovation. In the bidding selection process, private firms and firms with higher capabilities are selected. Our findings show that both policy strategies have enhanced innovation, though with different effects on the degree of novelty. We attribute this finding to the different degrees of uncertainties they address.