Strategic Cautiousness as an Expression of Robustness to Ambiguity (with Peio Zuazo-Garin)
Games and Economic Behavior 119 (2020), 197—215
Abstract: Economic predictions often hinge on two intuitive premises: agents rule out the possibility of others choosing unreasonable strategies ('strategic reasoning'), and prefer strategies that hedge against unexpected behavior ('cautiousness'). These two premises conflict and this undermines the compatibility of usual economic predictions with reasoning-based foundations. This paper proposes a new take on this classical tension by interpreting cautiousness as robustness to ambiguity. We formalize this via a model of incomplete preferences, where (i) each player's strategic uncertainty is represented by a possibly non-singleton set of beliefs and (ii) a rational player chooses a strategy that is a best-reply to every belief in this set. We show that the interplay between these two features precludes the conflict between strategic reasoning and cautiousness and therefore solves the inclusion-exclusion problem raised by Samuelson (1992). Notably, our approach provides a simple foundation for the iterated elimination of weakly dominated strategies.
Abstract: Assuming only ordinal preferences as transparent, we study players interacting under the veil of ignorance, that cannot produce beliefs as probability measures but rather have coarse beliefs represented as subsets of opponents' actions. These players follow either maxmax or maxmin decision criteria. The criteria can be identified as optimistic and pessimistic attitudes, respectively, which we refer to as "tropical". Explicitly formalizing these attitudes and how players reason under ignorance, we characterize the behavioral implications related to common belief in these events: while optimism is related to Point Rationalizability, a new algorithm -- Wald Rationalizability -- captures pessimism. Our characterizations allow us to uncover novel connections and results: (i) regarding optimism, we prove that dropping the (implicit) assumption that whatever a player believes is also true allows to capture wishful thinking à la Yildiz (2007), thus reversing an existence failure described therein; (ii) by studying how pessimism and optimism relate to Börgers dominance, we shed light on the appropriate notion of rationality in ordinal games; (iii) finally, with respect to pessimism, our analysis identifies Wald Rationalizability as the limit point of players becoming infinitely risk averse, hence, clarifying the conceptual underpinnings behind a discontinuity in the analysis of Rationalizability in presence of varying risk attitudes hinted in Weinstein (2016).
Working Paper: arXiv
Informational Robustness of Common Belief in Rationality
Abstract: In this note, I explore the implications of informational robustness under the assumption of common belief in rationality. That is, predictions for incomplete-information games which are valid across all possible information structures. First, I address this question from a global perspective and then generalize the analysis to allow for localized informational robustness.
Working Paper: arXiv
Binary Classification Tests, Imperfect Standards, and Ambiguous Information
Abstract: New binary classification tests are often evaluated relative to another established test. For example, rapid Antigen test for the detection of SARS-CoV-2 are assessed relative to more established PCR tests. In this paper, I argue that the new test (i.e. the Antigen test) describes ambiguous information and therefore allows for a phenomenon called dilation -- an extreme form of non-informativeness. As an example, I present hypothetical test data satisfying the WHO's minimum quality requirement for rapid Antigen tests which leads to dilation. The ambiguity in the information arises from a missing data problem due to imperfection of the established test: the joint distribution of true infection and test results is not observed. Using results from Copula theory, I construct the (usually non-singleton) set of all these possible joint distributions, which allows me to address the new test's informativeness. This analysis leads to a simple sufficient conditions to make sure that a new test is not a dilation. Finally, I illustrate my approach with applications to actual test data. Rapid Antigen tests satisfy my sufficient condition easily and are therefore informative. A bit more problematic might be other approaches like chest CT scans.
How many people are infected? A case study on SARS-CoV-2 prevalence in Austria
Abstract: Using recent data from voluntary mass testing, I provide credible bounds on prevalence of SARS-CoV-2 for Austrian counties in early December 2020. When estimating prevalence, a natural missing data problem arises: no test results are generated for non-tested people. In addition, tests are not perfectly predictive for the underlying infection. This is particularly relevant for mass SARS-CoV-2 testing as these are conducted with rapid Antigen tests, which are known to be somewhat imprecise. Using insights from the literature on partial identification, I propose a framework addressing both issues at once. I use the framework to study differing selection assumptions for the Austrian data. Whereas weak monotone selection assumptions provide limited identification power, reasonably stronger assumptions reduce the uncertainty on prevalence significantly.
Working Paper: arXiv
Adversarial Bilateral Information Design
Abstract: Information provision is a significant component of business-to-business interaction. Furthermore, the provision of information is often conducted bilaterally. This precludes the possibility of commitment to a grand information structure if there are multiple receivers. Consequently, in a strategic situation, each receiver needs to reason about what information other receivers get. Since the information provider does not know this reasoning process, a motivation for a robustness requirement arises: the provider seeks an information structure that performs well no matter how the receivers actually reason. In this paper, I provide a general method to study how to optimally provide information under these constraints. The main result is a representation theorem, which makes the problem tractable by reformulating it as a linear program in belief space. Furthermore, I provide novel bounds on the dependence among receivers’ beliefs, which provide even more tractability in some special cases.