Periodic Reporting for period 3 - SUExp (Strategic Uncertainty: An Experimental Investigation)
Reporting period: 2021-11-01 to 2023-04-30
Understanding how individuals or groups interact is at the core of virtually every economic and social problem. A central difficulty in studying such interactions is the fact that in practice, players face strategic uncertainty. This uncertainty – uncertainty about how others play the game – is important for determining one’s own behaviour. While there is a strong theoretical tradition geared towards the investigation of strategic uncertainty (Epistemic Game Theory), there have been few attempts to empirically investigate the role of strategic uncertainty on behaviour. This project delivers a comprehensive empirical study of strategic uncertainty.
The main goal of the project is to empirically investigate strategic uncertainty and incorporate these insights into game theoretic models. It focuses on three aspects:
(1) Sources of strategic uncertainty: where does strategic uncertainty come from and how can it be modelled?
(2) Decision making under strategic uncertainty: how do subjects behave when faced with strategic uncertainty?
(3) Behavioural models: how best to incorporate strategic uncertainty into game theoretic models?
Building on theoretical insights from game theory, epistemic game theory, and decision theory and using the methodological tools of experimental economics, this project aims to improve our understanding of how strategic uncertainty impacts behaviour and works towards incorporating these insights into game theoretic models.
The main goal of the project is to empirically investigate strategic uncertainty and incorporate these insights into game theoretic models. It focuses on three aspects:
(1) Sources of strategic uncertainty: where does strategic uncertainty come from and how can it be modelled?
(2) Decision making under strategic uncertainty: how do subjects behave when faced with strategic uncertainty?
(3) Behavioural models: how best to incorporate strategic uncertainty into game theoretic models?
Building on theoretical insights from game theory, epistemic game theory, and decision theory and using the methodological tools of experimental economics, this project aims to improve our understanding of how strategic uncertainty impacts behaviour and works towards incorporating these insights into game theoretic models.
This section reviews the specific projects that I have been running as of June 2021. I classify these projects according to the aspects (1) - (3) described above and list them in order below. This numbering will also be used to refer to particular projects in the later sections of the report.
(1) Sources of strategic uncertainty: where does strategic uncertainty come from and how can it be modelled?
(a) Reasoning about rationality versus reasoning about strategic behaviour (with Amanda Friedenberg and Willemien Kets)
(b) The persistence of reasoning models (with Amanda Friedenberg)
(c) Strategic ability and beliefs (with Amanda Friedenberg)
(d) Testing epistemic conditions in the lab.
Project (a) demonstrates the importance of separating a player’s strategic ability (ability to perform iterative reasoning) from their beliefs about others rationality (which guides beliefs about actions of others) and develops a methodology to separately identify these two. Doing so allows us to investigate whether uncertainty about rationality is a source of strategic uncertainty. We find that uncertainty about rationality is a main determinant of behaviour and that the residual component (what people believe if they do not believe rationality) is payoff dependent and cannot be captured by existing models. The data collection for this project is complete as of March 2021 and we are working on completing a draft of the paper. This project has been presented at various invited workshops and seminars.
Project (b) expands on project (a) to investigate the stability of these reasoning models at the individual level. For example, if a subject makes choices as if she believes rationality with probability p, will she behave consistently with that assumption in another setting? We plan to collect the data for this project in Fall 2021/Spring 2022.
Project (c) investigates ‘good’ measures of strategic reasoning. In project (a) we developed methodological tools to separately identify strategic ability from beliefs. In this project we correlate these measures with other existing measures of strategic ability and behaviour in games. Are measures that explicitly account for strategic uncertainty more predictive of behaviour in games? Does our measure of strategic ability correlate better with other cognitive characteristics? We plan to collect the data for this project in Fall 2021/Spring 2022.
Project (d) revisits testing epistemic conditions in the laboratory. A previous paper of mine (Econometrica 2015) developed a methodology for identifying reasoning about rationality in the lab. However, this methodological approach was based explicitly on the assumption of no strategic uncertainty. This project develops a new methodology for identifying minimum rationality bounds under the presence of strategic uncertainty. The data for this project should be collected by Spring 2022.
(2) Decision making under strategic uncertainty: how do subjects behave when faced with strategic uncertainty?
(a) Analogy based expectations in games (with Philippe Jehiel)
(b) Deliberate stochastic choice (with Evan Calford and Yoram Halevy)
(c) Sophistication (with Yoram Halevy and Johannes Hoelzemann)
(d) Comparing behavioural and epistemic models of iterative reasoning (with Adam Brandenburger and Amanda Friedenberg)
Project (a) explores behaviour under strategic uncertainty by exploring the interaction of strategic and fundamental uncertainty in incomplete information games. We explore an explanation of behaviour based on analogy-based expectations in which players deal with strategic uncertainty by aggregating information in a boundedly rational way. The data for this project will be collected in Summer/Fall 2021.
Project (b) explores behaviour under strategic uncertainty by investigating the interaction of strategic uncertainty and non-expected utility preferences. We aim to investigate whether strategic uncertainty leads to deliberate mixing. The data for this project will be collected Fall 2021/Spring 2022.
Project (c) investigates whether beliefs about opponent’s ability matters. Specifically, whether believing others are more sophisticated than you leads to greater strategic uncertainty and whether this uncertainty is ambiguous. The data for this project will likely be collected Fall 2022.
Project (d) explores the relationship between behavioural models of iterative reasoning (specifically, the level-k model) and epistemic game theory notions of iterative reasoning. This project is theoretical in nature and arose out of the need to better understand the two disparate methodologies of behavioural and epistemic game theory. A draft is complete and has been presented at invited seminars (VSET, Caltech).
(3) Behavioural models: how best to incorporate strategic uncertainty into game theoretic models?
(a) Heterogeneity in games (with David Freeman)
Project (a) explores whether strategic uncertainty is a source of heterogeneity in games. If beliefs about others are not consistent with what others are actually doing (as is the typical game theoretic assumption), this opens the door for heterogenous beliefs. To what extent do heterogenous beliefs explain behaviour and how best can this heterogeneity be incorporated into game theoretic models? This project is still in the planning stages.
(1) Sources of strategic uncertainty: where does strategic uncertainty come from and how can it be modelled?
(a) Reasoning about rationality versus reasoning about strategic behaviour (with Amanda Friedenberg and Willemien Kets)
(b) The persistence of reasoning models (with Amanda Friedenberg)
(c) Strategic ability and beliefs (with Amanda Friedenberg)
(d) Testing epistemic conditions in the lab.
Project (a) demonstrates the importance of separating a player’s strategic ability (ability to perform iterative reasoning) from their beliefs about others rationality (which guides beliefs about actions of others) and develops a methodology to separately identify these two. Doing so allows us to investigate whether uncertainty about rationality is a source of strategic uncertainty. We find that uncertainty about rationality is a main determinant of behaviour and that the residual component (what people believe if they do not believe rationality) is payoff dependent and cannot be captured by existing models. The data collection for this project is complete as of March 2021 and we are working on completing a draft of the paper. This project has been presented at various invited workshops and seminars.
Project (b) expands on project (a) to investigate the stability of these reasoning models at the individual level. For example, if a subject makes choices as if she believes rationality with probability p, will she behave consistently with that assumption in another setting? We plan to collect the data for this project in Fall 2021/Spring 2022.
Project (c) investigates ‘good’ measures of strategic reasoning. In project (a) we developed methodological tools to separately identify strategic ability from beliefs. In this project we correlate these measures with other existing measures of strategic ability and behaviour in games. Are measures that explicitly account for strategic uncertainty more predictive of behaviour in games? Does our measure of strategic ability correlate better with other cognitive characteristics? We plan to collect the data for this project in Fall 2021/Spring 2022.
Project (d) revisits testing epistemic conditions in the laboratory. A previous paper of mine (Econometrica 2015) developed a methodology for identifying reasoning about rationality in the lab. However, this methodological approach was based explicitly on the assumption of no strategic uncertainty. This project develops a new methodology for identifying minimum rationality bounds under the presence of strategic uncertainty. The data for this project should be collected by Spring 2022.
(2) Decision making under strategic uncertainty: how do subjects behave when faced with strategic uncertainty?
(a) Analogy based expectations in games (with Philippe Jehiel)
(b) Deliberate stochastic choice (with Evan Calford and Yoram Halevy)
(c) Sophistication (with Yoram Halevy and Johannes Hoelzemann)
(d) Comparing behavioural and epistemic models of iterative reasoning (with Adam Brandenburger and Amanda Friedenberg)
Project (a) explores behaviour under strategic uncertainty by exploring the interaction of strategic and fundamental uncertainty in incomplete information games. We explore an explanation of behaviour based on analogy-based expectations in which players deal with strategic uncertainty by aggregating information in a boundedly rational way. The data for this project will be collected in Summer/Fall 2021.
Project (b) explores behaviour under strategic uncertainty by investigating the interaction of strategic uncertainty and non-expected utility preferences. We aim to investigate whether strategic uncertainty leads to deliberate mixing. The data for this project will be collected Fall 2021/Spring 2022.
Project (c) investigates whether beliefs about opponent’s ability matters. Specifically, whether believing others are more sophisticated than you leads to greater strategic uncertainty and whether this uncertainty is ambiguous. The data for this project will likely be collected Fall 2022.
Project (d) explores the relationship between behavioural models of iterative reasoning (specifically, the level-k model) and epistemic game theory notions of iterative reasoning. This project is theoretical in nature and arose out of the need to better understand the two disparate methodologies of behavioural and epistemic game theory. A draft is complete and has been presented at invited seminars (VSET, Caltech).
(3) Behavioural models: how best to incorporate strategic uncertainty into game theoretic models?
(a) Heterogeneity in games (with David Freeman)
Project (a) explores whether strategic uncertainty is a source of heterogeneity in games. If beliefs about others are not consistent with what others are actually doing (as is the typical game theoretic assumption), this opens the door for heterogenous beliefs. To what extent do heterogenous beliefs explain behaviour and how best can this heterogeneity be incorporated into game theoretic models? This project is still in the planning stages.
By the end of the final period of this project, I aim to complete the ongoing projects listed above. I plan to have projects (1a-d) and (2a-d) published or submitted and to at least have the draft papers for projects in (3) ready for submission to academic journals. All these projects aim to provide novel perspectives and important contributions to the literature. I expect that the majority of them will be published in either a top general journal in economics or a top field journal in game theory or experimental economics.