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: We provide a theory of strategic interactions in static games in the presence of ignorance, i.e., when players cannot produce beliefs as probability measures (or similia) concerning the uncertain elements present in the interaction they are involved in. Assuming only players' ordinal preferences as transparent, we investigate players that are either optimistic or pessimistic, that we deem tropical players. To explicitly formalize these attitudes, we employ tools from interactive epistemology, by defining the corresponding epistemic events in epistemic possibility structures, which are the counterpart of epistemic type structures suited for our analysis in the presence of ignorance, We show that the behavioral implications related to common belief in these events have algorithmic counterparts in terms of iterative deletion procedures. While optimism is related to Point Rationalizability, to capture pessimism we introduce a new algorithm, deemed Wald Rationalizability. We show that the algorithmic procedure capturing optimism selects a subset of the strategies selected by the algorithmic procedure capturing pessimism. Additionally, we compare both algorithmic procedures to an analogous algorithm based on Börgers dominance, deemed Börgers Rationalizability, and we show that in generic static games both Point Rationalizability and Wald Rationalizability select a subset of the actions selected by Börgers Rationalizability. More generally, while we prove that dropping the genericity assumption does not change the relation between Point Rationalizability and Börgers Rationalizability, we show that Wald and Börgers Rationalizability are not comparable in their behavioral implications, and we shed light on why this difference emerges. Finally, we explore connections to strategic wishful thinking.
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.