Periodic Reporting for period 4 - LTCSEI (Learning through Categories in Social and Economic Interactions)
Reporting period: 2022-07-01 to 2023-06-30
Summary of the context and overall objectives of the project
Economic theory and game theory are often criticized on the ground that the models used to make policy recommendations rely on excessive and unrealistic assumptions about the understanding of economic agents. Recent crisis episodes such as the 2008 subprime crisis which were not well anticipated by economists have magnified the feeling that something should be done to improve the plausibility of economic models. While this is a daunting task for the economics profession, the project “Learning Through Categories in Social and Economic Interactions” develops methodological steps with this objective in mind. The general premise of the project is that in complex environments, agents form their views of the world based only on coarse statistics that describe incompletely or coarsely how the economy behaves as a function of the fundamentals. A notion of equilibrium referred to as the analogy-based expectation equilibrium is considered for that kind of environments that parallels the familiar notions of equilibrium such as the Walrasian or Nash equilibrium used in the standard rationality case. The purpose of the ERC project is to explore the economic consequences of such an alternative approach while making further progress on the choice of aggregate statistics to be considered by economic agents. Insights from game theory as well as statistics, machine learning, and psychology are combined to make the approach more practical.
Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far
The project “Learning Through Categories in Social and Economic Interactions” had several objectives. I review here how the work performed during the period covered by the report fits into the various objectives.
1) Develop applications of the analogy-based expectation equilibrium based on natural assumptions about what is accessible in the datasets from previous interactions. 1
1.1) A first illustration is an investment decision problem in which investors only observe the profitability of those projects that were previously adopted but not those projects that were declined. This has led to my first significant publication related to the ERC "Investment strategy and selection bias: An equilibrium perspective on overoptimism”. In the model developed there, an individual investor receives a noisy signal about the prospect of her project, where the signal can be thought of as the initial impression the project makes on her. Importantly, the investor does not a priori know how the signal she receives is statistically related to the profitability of the project. To inform her decision whether or not to implement the project, she looks around at previously implemented projects that look similar to her project (in the sense of generating the same initial impression on her), and she considers the observed average returns of such projects as a proxy for the expected return she can expect if she implements the project. This procedure creates a bias because the investor does not see all projects but only those that were implemented. Interestingly, the selection bias is shaped by the investment decisions of others which were made similarly, thereby leading to an equilibrium formulation of the problem which can be cast in the framework of the analogy-based expectation equilibrium. An output of this research is that as long as different investors do not generate impressions in exactly the same way (maybe because different investors do not attach the same weight to all characteristics of projects), the procedure leads to biases in equilibrium. Moreover, under natural assumptions, one obtains that investors are overoptimistic about the prospect of their projects, thereby leading to excessive investments as compared to the first-best. Another research output concerns the effect of having some share of investors who would make their investment decisions optimally (maybe because such investors are more experienced). The main finding there is that such experienced investors make the bias of other less experienced investors worse, thereby suggesting a negative externality that experienced investors can exert on selection neglect investors.
That entrepreneurs tend to be overoptimistic about their own projects has been documented in a number of surveys. The above publication suggests a mechanism through which this may occur, which is unrelated to an intrinsic characteristic of the entrepreneurs but may arise due to naïve extrapolations from selected samples. This constitutes a significant advance as it suggests a novel perspective on an old established observation about entrepreneurs’ overconfidence.
1.2) Another illustration is an ongoing project with Konrad Mierendorff in the context of auctions in which it is assumed that bidders never get to observe the beliefs of previous bidders, but only their bids and the ex post values of goods. More precisely, in this project, we consider an auction environment in which to form their beliefs about the link of other bids to the fundamentals of the economy (how they value the good for sale), some bidders only have access from past interactions to bids and ex post values but not to the beliefs held by the bidders at the time the bids were submitted. Specifically, we consider a simple setting in which at the time of the auction, bidders only observe a noisy signal about their future ex post values. While the ex post values as well as the bids are made publicly available to new bidders, the signals are not. We use the ex post payoff relevant analogy partition to represent the beliefs of such bidders. The main research question concerns whether in the presence of both such bidders and more experienced (rational) bidders, some auction formats can lead to good efficiency properties in the sense of allocating goods to those who value them most based on the information available at the time of the auction. We show that even though the underlying setting is one of private values, bidders reasoning in this way may end up submitting suboptimal bids when the signals are correlated across bidders, even in the English auction. After illustrating that inefficiencies may then arise in first-price or second-price auctions when there is a mix of rational and less sophisticated bidders, we establish that in rich enough statistical environments, no auction format allows to obtain a fully efficient allocation. This project can be viewed as part of broader theme in which I explore the implications of analogy partitions that do not depend on the beliefs of agents. In this application, it is shown that such a way of reasoning may lead to substantial inefficiencies even in cases in which one would normally think the second-price auction has good efficiency properties.
1.3) A third illustration concerns the study of strategic communication with forgetful liars, which has led to an article to be published in Theoretical Economics. The premise of this study is that it seems plausible that when one tells the truth it is easy to remember it but when one lies, it is somehow harder to remember the details of the lie. Assuming liars after a lie only have access to the aggregate distribution of lies from past interactions and not how the lie depends on the state of the economy leads to an analogy-based expectation equilibrium formulation of the problem. Novel insights are then obtained, as for example it shows an interest in asking related/similar questions several times in an attempt to better discipline the informed party into lying less. Developing elaborations of the basic approach, it also illustrates that more complex communication protocols in which questions are not always asked in the same format may have a better disciplining device than more straightforward communication protocols in which questions are always asked in the same manner. Such insights which are in agreement with experimental works developed by psychologists are in line with what common sense suggests about the functioning of criminal investigations. They can also be used in the future research to think of how to alleviate further the incentive constraints arising in a variety of economic applications.
2) Use inputs from statistics and machine learning to structure the choice of analogy partitions (the original formulation in the ERC proposal was probably a bit less precise than this, but developments during the review period have led to this refined formulation)
I am currently developing a a joint project with Giacomo Weber, a student starting a PhD with the ERC funding that combines the ideas of K-Means clustering with the analogy-based expectation equilibrium, proposing a notion of stable analogy-based expectation equilibrium. It notes that in some cases, the use of distributions of analogy partitions is required to guarantee the existence of such stable analogy-based expectation equilibrium. Finally, an application to games with strategies complements suggests that in this case no mixing is required, but mixing appears as necessary in games with strategic substitutes.
3) Develop experimental designs in relation to the analogy-based expectation equilibrium.
3.1) A first project related to this is an experimental study of deception developed with David Ettinger. David Ettinger and I have designed an experiment with an Expert/Agent relationship consisting of several rounds with one round being more important than the others. Intuitively, the Expert could use a deceptive tactic consisting of being truthful until the key period and then lying at the key period. In the rational case, this would not be effective because the agent should be aware that such a tactic can be used and optimally adjust his behavior accordingly. When agents reason coarsely by considering the aggregate behaviors across all time periods of the various types of experts (whether honest – these are implemented through machines always telling the truth in the lab or humans -these are subjects in the lab and with objectives opposite to those of the agent), one can show that such a deceptive tactic can work in the sense of delivering higher expected payoff than other strategies. In the experiment, we indeed observe that such a tactic pays off compared to the other employed strategies, and we suggest that the collected experimental data can be well organized by assuming that three quarters of subjects reason coarsely.
3.2) As a follow-up of the publication on investment described above, in an ongoing experimental work with Kai Barron and Steffen Huck, I am currently testing a simplified version of the proposed mechanism in the lab and the obtained results replicate qualitatively the theoretical insights obtained in the theory paper.
3.3) A third project in relation to this is an experiment with Juni Singh, a PhD student of mine who has just completed her PhD, on the Valuation equilibrium, which is the reinforcement learning counterpart of the analogy-based expectation equilibrium as defined in Jehiel and Samet (2007). The results found in an urn choice experiment suggests that in the face of unfamiliar urns with similar attributes (color in the experiment), subjects behave in line with the Valuation equilibrium, seeking to attach an aggregate value to urns as a function of their color rather than learning the values of the urns separately.
4) Develop a systematic exploration of the various models of bounded rationality (initially planned as a book project)
Responding to an invitation at the World Congress of the Econometric Society, I have developed a chapter to be published in the Econometric Society monograph series that is focused on the analogy-based expectation equilibrium but which also discusses at length other approaches to bounded rationality in particular in how they differ from and relate to the analogy-based expectation equilibrium. This chapter will be longer than usual and it can be viewed as fulfilling the objective of relating my approach to other approaches of bounded rationality, which I initially had planned to address through the writing of a book.
5) Miscellaneus
As is often the case, when thinking of projects, one gets ideas that were not initially anticipated and that fit broadly but imperfectly with the initial objectives. These include the following projects that have a bounded rationality component but are not directly connected to the core theme of analogy-based expectation equilibrium. First, the work on bundler’s dilemma with Milo Bianchi in which we explore possible reasons for the flurry of junk securities in the pre-2008 financial crisis. Second, the experimental work with Marco Angrisani, Antonio Guarino and Toru Kitagawa in which we explore whether observed behaviour in a social learning experiment can better be explained with models of overconfidence or models with other forms of bounded rationality including the analogy-based expectation equilibrium. Third, the theoretical work with Jakub Steiner in which we explore how storage constraints can make selective memory desirable from an evolutionary perspective.
1) Develop applications of the analogy-based expectation equilibrium based on natural assumptions about what is accessible in the datasets from previous interactions. 1
1.1) A first illustration is an investment decision problem in which investors only observe the profitability of those projects that were previously adopted but not those projects that were declined. This has led to my first significant publication related to the ERC "Investment strategy and selection bias: An equilibrium perspective on overoptimism”. In the model developed there, an individual investor receives a noisy signal about the prospect of her project, where the signal can be thought of as the initial impression the project makes on her. Importantly, the investor does not a priori know how the signal she receives is statistically related to the profitability of the project. To inform her decision whether or not to implement the project, she looks around at previously implemented projects that look similar to her project (in the sense of generating the same initial impression on her), and she considers the observed average returns of such projects as a proxy for the expected return she can expect if she implements the project. This procedure creates a bias because the investor does not see all projects but only those that were implemented. Interestingly, the selection bias is shaped by the investment decisions of others which were made similarly, thereby leading to an equilibrium formulation of the problem which can be cast in the framework of the analogy-based expectation equilibrium. An output of this research is that as long as different investors do not generate impressions in exactly the same way (maybe because different investors do not attach the same weight to all characteristics of projects), the procedure leads to biases in equilibrium. Moreover, under natural assumptions, one obtains that investors are overoptimistic about the prospect of their projects, thereby leading to excessive investments as compared to the first-best. Another research output concerns the effect of having some share of investors who would make their investment decisions optimally (maybe because such investors are more experienced). The main finding there is that such experienced investors make the bias of other less experienced investors worse, thereby suggesting a negative externality that experienced investors can exert on selection neglect investors.
That entrepreneurs tend to be overoptimistic about their own projects has been documented in a number of surveys. The above publication suggests a mechanism through which this may occur, which is unrelated to an intrinsic characteristic of the entrepreneurs but may arise due to naïve extrapolations from selected samples. This constitutes a significant advance as it suggests a novel perspective on an old established observation about entrepreneurs’ overconfidence.
1.2) Another illustration is an ongoing project with Konrad Mierendorff in the context of auctions in which it is assumed that bidders never get to observe the beliefs of previous bidders, but only their bids and the ex post values of goods. More precisely, in this project, we consider an auction environment in which to form their beliefs about the link of other bids to the fundamentals of the economy (how they value the good for sale), some bidders only have access from past interactions to bids and ex post values but not to the beliefs held by the bidders at the time the bids were submitted. Specifically, we consider a simple setting in which at the time of the auction, bidders only observe a noisy signal about their future ex post values. While the ex post values as well as the bids are made publicly available to new bidders, the signals are not. We use the ex post payoff relevant analogy partition to represent the beliefs of such bidders. The main research question concerns whether in the presence of both such bidders and more experienced (rational) bidders, some auction formats can lead to good efficiency properties in the sense of allocating goods to those who value them most based on the information available at the time of the auction. We show that even though the underlying setting is one of private values, bidders reasoning in this way may end up submitting suboptimal bids when the signals are correlated across bidders, even in the English auction. After illustrating that inefficiencies may then arise in first-price or second-price auctions when there is a mix of rational and less sophisticated bidders, we establish that in rich enough statistical environments, no auction format allows to obtain a fully efficient allocation. This project can be viewed as part of broader theme in which I explore the implications of analogy partitions that do not depend on the beliefs of agents. In this application, it is shown that such a way of reasoning may lead to substantial inefficiencies even in cases in which one would normally think the second-price auction has good efficiency properties.
1.3) A third illustration concerns the study of strategic communication with forgetful liars, which has led to an article to be published in Theoretical Economics. The premise of this study is that it seems plausible that when one tells the truth it is easy to remember it but when one lies, it is somehow harder to remember the details of the lie. Assuming liars after a lie only have access to the aggregate distribution of lies from past interactions and not how the lie depends on the state of the economy leads to an analogy-based expectation equilibrium formulation of the problem. Novel insights are then obtained, as for example it shows an interest in asking related/similar questions several times in an attempt to better discipline the informed party into lying less. Developing elaborations of the basic approach, it also illustrates that more complex communication protocols in which questions are not always asked in the same format may have a better disciplining device than more straightforward communication protocols in which questions are always asked in the same manner. Such insights which are in agreement with experimental works developed by psychologists are in line with what common sense suggests about the functioning of criminal investigations. They can also be used in the future research to think of how to alleviate further the incentive constraints arising in a variety of economic applications.
2) Use inputs from statistics and machine learning to structure the choice of analogy partitions (the original formulation in the ERC proposal was probably a bit less precise than this, but developments during the review period have led to this refined formulation)
I am currently developing a a joint project with Giacomo Weber, a student starting a PhD with the ERC funding that combines the ideas of K-Means clustering with the analogy-based expectation equilibrium, proposing a notion of stable analogy-based expectation equilibrium. It notes that in some cases, the use of distributions of analogy partitions is required to guarantee the existence of such stable analogy-based expectation equilibrium. Finally, an application to games with strategies complements suggests that in this case no mixing is required, but mixing appears as necessary in games with strategic substitutes.
3) Develop experimental designs in relation to the analogy-based expectation equilibrium.
3.1) A first project related to this is an experimental study of deception developed with David Ettinger. David Ettinger and I have designed an experiment with an Expert/Agent relationship consisting of several rounds with one round being more important than the others. Intuitively, the Expert could use a deceptive tactic consisting of being truthful until the key period and then lying at the key period. In the rational case, this would not be effective because the agent should be aware that such a tactic can be used and optimally adjust his behavior accordingly. When agents reason coarsely by considering the aggregate behaviors across all time periods of the various types of experts (whether honest – these are implemented through machines always telling the truth in the lab or humans -these are subjects in the lab and with objectives opposite to those of the agent), one can show that such a deceptive tactic can work in the sense of delivering higher expected payoff than other strategies. In the experiment, we indeed observe that such a tactic pays off compared to the other employed strategies, and we suggest that the collected experimental data can be well organized by assuming that three quarters of subjects reason coarsely.
3.2) As a follow-up of the publication on investment described above, in an ongoing experimental work with Kai Barron and Steffen Huck, I am currently testing a simplified version of the proposed mechanism in the lab and the obtained results replicate qualitatively the theoretical insights obtained in the theory paper.
3.3) A third project in relation to this is an experiment with Juni Singh, a PhD student of mine who has just completed her PhD, on the Valuation equilibrium, which is the reinforcement learning counterpart of the analogy-based expectation equilibrium as defined in Jehiel and Samet (2007). The results found in an urn choice experiment suggests that in the face of unfamiliar urns with similar attributes (color in the experiment), subjects behave in line with the Valuation equilibrium, seeking to attach an aggregate value to urns as a function of their color rather than learning the values of the urns separately.
4) Develop a systematic exploration of the various models of bounded rationality (initially planned as a book project)
Responding to an invitation at the World Congress of the Econometric Society, I have developed a chapter to be published in the Econometric Society monograph series that is focused on the analogy-based expectation equilibrium but which also discusses at length other approaches to bounded rationality in particular in how they differ from and relate to the analogy-based expectation equilibrium. This chapter will be longer than usual and it can be viewed as fulfilling the objective of relating my approach to other approaches of bounded rationality, which I initially had planned to address through the writing of a book.
5) Miscellaneus
As is often the case, when thinking of projects, one gets ideas that were not initially anticipated and that fit broadly but imperfectly with the initial objectives. These include the following projects that have a bounded rationality component but are not directly connected to the core theme of analogy-based expectation equilibrium. First, the work on bundler’s dilemma with Milo Bianchi in which we explore possible reasons for the flurry of junk securities in the pre-2008 financial crisis. Second, the experimental work with Marco Angrisani, Antonio Guarino and Toru Kitagawa in which we explore whether observed behaviour in a social learning experiment can better be explained with models of overconfidence or models with other forms of bounded rationality including the analogy-based expectation equilibrium. Third, the theoretical work with Jakub Steiner in which we explore how storage constraints can make selective memory desirable from an evolutionary perspective.
Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)
I see three achievements that are either complete or in progress going beyond the state of the art. These include the work on overoptimism and selection neglect in investment decision problems (theory published, experiment in progress) to the extent that it sheds new light on the observed overconfidence of entrepreneurs that could possibly be explained as resulting from an imperfect access to datasets; the work on auction design with the payoff relevant analogy partition (joint with Konrad Mierendorff) to the extent that it alters the conclusion that familiar auctions formats such as the Vickrey auction should necessarily be efficient in private value settings; and the work (joint with Giacomo Weber) using techniques from machine learning to endogenize the analogy partitions (in progress) to the extent that it combines in a completely new way insights from remote literatures.