Behavioral game theory models serve two purposes: yielding insights into how human decision-making works, and predicting how people would behave in novel strategic settings. A system called GameNet represents the state of the art for predicting human behavior in the setting of unrepeated simultaneous-move games, combining a simple "level-k" model of strategic reasoning with a complex neural network model of non-strategic "level-0" behavior. Although this reliance on well-established ideas from cognitive science ought to make GameNet interpretable, the flexibility of its level-0 model raises the possibility that it is able to emulate strategic reasoning. In this work, we prove that GameNet's level-0 model is indeed too general. We then introduce ElementaryNet, a novel neural network that is provably incapable of expressing strategic behavior. We show that these additional restrictions are empirically harmless, with ElementaryNet and GameNet having statistically indistinguishable performance. We then show how it is possible to derive insights about human behavior by varying ElementaryNet's features and interpreting its parameters, finding evidence of iterative reasoning, learning about the depth of this reasoning process, and showing the value of a rich level-0 specification.

Offline reinforcement learning—learning a policy from a batch of data—is known to be hard for general MDPs. These results motivate the need to look at specific classes of MDPs where offline reinforcement learning might be feasible. In this work, we explore a restricted class of MDPs to obtain guarantees for offline reinforcement learning. The key property, which we call Action Impact Regularity (AIR), is that actions primarily impact a part of the state (an endogenous component) and have limited impact on the remaining part of the state (an exogenous component). AIR is a strong assumption, but it nonetheless holds in a number of real-world domains including financial markets. We discuss algorithms that exploit the AIR property, and provide a theoretical analysis for an algorithm based on Fitted-Q Iteration. Finally, we demonstrate that the algorithm outperforms existing offline reinforcement learning algorithms across different data collection policies in simulated and real world environments where the regularity holds.

Researchers building behavioral models, such as behavioral game theorists, use experimental data to evaluate predictive models of human behavior. However, there is little agreement about which loss function should be used in evaluations, with error rate, negative log-likelihood, cross-entropy, Brier score, and squared L2 error all being common choices. We attempt to offer a principled answer to the question of which loss functions should be used for this task, formalizing axioms that we argue loss functions should satisfy. We construct a family of loss functions, which we dub ``diagonal bounded Bregman divergences'', that satisfy all of these axioms. These rule out many loss functions used in practice, but notably include squared L2 error; we thus recommend its use for evaluating behavioral models.

Software vulnerabilities are ubiquitous and costly. To detect vulnerabilities earlier during development, organizations deploy a set of static analyzers to locate and eventually fix these vulnerabilities before releasing their software. Due to the prohibitive cost of running all available analyzers, organizations must run only a subset of all possible analyzers on their codebases. Choosing this set deterministically leaves recognizable gaps of vulnerability coverage. To overcome these challenges, we present Randomized Best Response (RBR), a method that computes an optimal randomization over size-bounded sets of available static analyzers. RBR models the relationship between malicious users and organizations as a leader-follower Stackelberg security game. Our solution focuses on software vulnerabilities due to their security implications when exploited by malicious users. Using 8 static analyzers for C/C++ and 8 Common Weakness Enumeration (CWE) vulnerability types, we show that RBR outperforms a set of natural baselines by always picking analyzers that achieve a higher benefit to the defender. Through a case study of a large system at Oracle, we show how RBR may be used in a real-world scenario.

Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that the agents the learner will face post-training may have dramatically different behavior than the learner came to expect by interacting with itself. For the special case of two-player constant-sum games, self-play that reaches Nash equilibrium is guaranteed to produce strategies that perform well against any post-training opponent; however, no such guarantee exists for multiplayer games. We show that in games that approximately decompose into a set of two-player constant-sum games (called constant-sum polymatrix games) where global $\epsilon$-Nash equilibria are boundedly far from Nash equilibria in each subgame (called subgame stability), any no-external-regret algorithm that learns by self-play will produce a strategy with bounded vulnerability. For the first time, our results identify a structural property of multiplayer games that enable performance guarantees for the strategies produced by a broad class of self-play algorithms. We demonstrate our findings through experiments on Leduc poker.

Offline reinforcement learning—learning a policy from a batch of data—is known to be hard for general MDPs. These results motivate the need to look at specific classes of MDPs where offline reinforcement learning might be feasible. In this work, we explore a restricted class of MDPs to obtain guarantees for offline reinforcement learning. The key property, which we call Action Impact Regularity (AIR), is that actions primarily impact a part of the state (an endogenous component) and have limited impact on the remaining part of the state (an exogenous component). AIR is a strong assumption, but it nonetheless holds in a number of real-world domains including financial markets. We discuss algorithms that exploit the AIR property, and provide a theoretical analysis for an algorithm based on Fitted-Q Iteration. Finally, we demonstrate that the algorithm outperforms existing offline reinforcement learning algorithms across different data collection policies in simulated and real world environments where the regularity holds.

As increasingly complex software is developed every day, a growing number of companies use static analysis tools to reason about program properties ranging from simple coding style rules to more advanced software bugs, to multi-tier security vulnerabilities. While increasingly complex analyses are created, developer support must also be updated to ensure that the tools are used to their best potential. Past research in the usability of static analysis tools has primarily focused on usability issues encountered by software developers, and the causes of those issues in analysis tools. In this article, we adopt a more user-centered approach, and aim at understanding why software developers use analysis tools, which decisions they make when using those tools, what they look for when making those decisions, and the motivation behind their strategies. This approach allows us to derive new tool requirements that closely support software developers (e.g., systems for recommending warnings to fix that take developer knowledge into account), and also open novel avenues for further static-analysis research such as collaborative user interfaces for analysis warnings.

Driven by recent successes in two-player, zero-sum game solving and playing, artificial intelligence work on games has increasingly focused on algorithms that produce equilibrium-based strategies. However, this approach has been less effective at producing competent players in general-sum games or those with more than two players than in two-player, zero-sum games. An appealing alternative is to consider adaptive algorithms that ensure strong performance in hindsight relative to what could have been achieved with modified behavior. This approach also leads to a game-theoretic analysis, but in the correlated play that arises from joint learning dynamics rather than factored agent behavior at equilibrium. We develop and advocate for this hindsight rationality framing of learning in general sequential decision-making settings. To this end, we re-examine mediated equilibrium and deviation types in extensive-form games, thereby gaining a more complete understanding and resolving past misconceptions. We present a set of examples illustrating the distinct strengths and weaknesses of each type of equilibrium in the literature, and prove that no tractable concept subsumes all others. This line of inquiry culminates in the definition of the deviation and equilibrium classes that correspond to algorithms in the counterfactual regret minimization (CFR) family, relating them to all others in the literature. Examining CFR in greater detail further leads to a new recursive definition of rationality in correlated play that extends sequential rationality in a way that naturally applies to hindsight evaluation.

Hindsight rationality is an approach to playing general-sum games that prescribes no-regret learning dynamics for individual agents with respect to a set of deviations, and further describes jointly rational behavior among multiple agents with mediated equilibria. To develop hindsight rational learning in sequential decision-making settings, we formalize behavioral deviations as a general class of deviations that respect the structure of extensive-form games. Integrating the idea of time selection into counterfactual regret minimization (CFR), we introduce the extensive-form regret minimization (EFR) algorithm that achieves hindsight rationality for any given set of behavioral deviations with computation that scales closely with the complexity of the set. We identify behavioral deviation subsets, the partial sequence deviation types, that subsume previously studied types and lead to efficient EFR instances in games with moderate lengths. In addition, we present a thorough empirical analysis of EFR instantiated with different deviation types in benchmark games, where we find that stronger types typically induce better performance.

Machine learning is often used to aid in human decision-making, sometimes for life-altering decisions like when determining whether or not to grant bail to a defendant or a loan to an applicant. Because of their importance, it is critical to ensure that the processes used to reach these decisions are considered fair. A common approach is to enforce some fairness constraint over the outcomes of a decision maker, but there is no single, generally-accepted definition of fairness. With notable exceptions, most of the literature on algorithmic fairness takes for granted that there will be an inherent trade-off between accuracy and algorithmic fairness. Additionally, most work focuses only on one or two domains, whereas machine learning techniques are used in an increasing number of distinct decision-making contexts with differing pertinent features. In this work, we consider six different decision-making domains: bail, child protective services, hospital resources, insurance rates, loans, and unemployment aid. We focus on the fairness of the process directly, rather than the outcomes. We also take a descriptive approach, using survey data to elicit the factors that lead a decision-making process to be perceived as fair. Specifically, we ask 2157 Amazon Mechanical Turk workers to rate the features used for algorithmic decision-making in one of the six domains as either fair or unfair, as well as to rate how much they agree or disagree with the assignments of eight previously (and one newly) proposed properties to the features. For example, a worker could be asked to rate the feature of "criminal history" as fair or unfair to use in bail decisions, and then rate how much they agree or disagree that "criminal history" is a reliable feature. We show that, in every domain, disagreements in fairness judgements can be largely explained by the assignments of properties (like reliability) to features (like criminal history). We also show that fairness judgements can be well predicted across domains by training the predictor using the property assignments from one domain's data and predicting in another. These findings imply that the properties act as moral determinants for fairness judgements, and that respondents reason similarly about the implications of the properties in all the decision-making domains that we consider. Although our results are mostly consistent across domains, we find some important differences within specific demographic groups in the hospital and insurance domains, indicating that at least some differences in fairness judgements are introduced by demographic differences. However, a single property usually holds the majority of the predictive power. With some exceptions, predictors learning from only the "increases accuracy" property perform better (in all domains) than predictors learning from any combination of the other seven properties, implying that the primary factor affecting respondents' perceptions of the fairness of using a feature for prediction is whether or not a feature increases the accuracy of the decision being made.

In many settings, an effective way of evaluating objects of interest is to collect evaluations from dispersed individuals and to aggregate these evaluations together. Some examples are categorizing online content and evaluating student assignments via peer grading. For this data science problem, one challenge is to motivate participants to conduct such evaluations carefully and to report them honestly, particularly when doing so is costly. Existing approaches, notably peer-prediction mechanisms, can incentivize truth telling in equilibrium. However, they also give rise to equilibria in which agents do not pay the costs required to evaluate accurately, and hence fail to elicit useful information. We show that this problem is unavoidable whenever agents are able to coordinate using low-cost signals about the items being evaluated (e.g., text labels or pictures). We then consider ways of circumventing this problem by comparing agents' reports to ground truth, which is available in practice when there exist trusted evaluators---such as teaching assistants in the peer grading scenario---who can perform a limited number of unbiased (but noisy) evaluations. Of course, when such ground truth is available, a simpler approach is also possible: rewarding each agent based on agreement with ground truth with some probability, and unconditionally rewarding the agent otherwise. Surprisingly, we show that the simpler mechanism achieves stronger incentive guarantees given less access to ground truth than a large set of peer-prediction mechanisms.

It is common in multiagent systems to make a distinction between "strategic" behavior and other forms of intentional but "nonstrategic" behavior: typically, that strategic agents model other agents while nonstrategic agents do not. However, a crisp boundary between these concepts has proven elusive. This problem is pervasive throughout the game theoretic literature on bounded rationality and particularly critical in parts of the behavioral game theory literature that make an explicit distinction between the behavior of "nonstrategic" level-0 agents and "strategic" higher-level agents (e.g., the level-k and cognitive hierarchy models). Overall, work discussing bounded rationality rarely gives clear guidance on how the rationality of nonstrategic agents must be bounded, instead typically just singling out specific decision rules and informally asserting them to be nonstrategic (e.g., truthfully revealing private information; randomizing uniformly). In this work, we propose a new, formal characterization of nonstrategic behavior. Our main contribution is to show that it satisfies two properties: (1) it is general enough to capture all purportedly "nonstrategic" decision rules of which we are aware in the behavioral game theory literature; (2) behavior that obeys our characterization is distinct from strategic behavior in a precise sense.

Behavioral game theory seeks to describe the way actual people (as compared to idealized, "rational" agents) act in strategic situations. Our own recent work has identified iterative models, such as quantal cognitive hierarchy, as the state of the art for predicting human play in unrepeated, simultaneous-move games. Iterative models predict that agents reason iteratively about their opponents, building up from a specification of nonstrategic behavior called level-0. A modeler is in principle free to choose any description of level-0 behavior that makes sense for a given setting. However, in practice almost all existing work specifies this behavior as a uniform distribution over actions. In most games it is not plausible that even nonstrategic agents would choose an action uniformly at random, nor that other agents would expect them to do so. A more accurate model for level-0 behavior has the potential to dramatically improve predictions of human behavior, since a substantial fraction of agents may play level-0 strategies directly, and furthermore since iterative models ground all higher-level strategies in responses to the level-0 strategy. Our work considers models of the way in which level-0 agents construct a probability distribution over actions, given an arbitrary game. We considered a large space of alternatives and, in the end, recommend a model that achieved excellent performance across the board: a linear weighting of four binary features, each of which is general in the sense that it can be computed from any normal form game. Adding real-valued variants of the same four features yielded further improvements in performance, albeit with a corresponding increase in the number of parameters needing to be estimated. We evaluated the effects of combining these new level-0 models with several iterative models and observed large improvements in predictive accuracy.

In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experience. To investigate learning in such a repeated secretary problem we conduct a large-scale behavioral experiment in which people search repeatedly from fixed distributions. In contrast to prior investigations that find no evidence for learning in the classical scenario, in the repeated setting we observe substantial learning resulting in near-optimal stopping behavior. We conduct a Bayesian comparison of multiple behavioral models which shows that participants' behavior is best described by a class of threshold-based models that contains the theoretically optimal strategy. In fact, fitting such a threshold-based model to data reveals players' estimated thresholds to be surprisingly close to the optimal thresholds after only a small number of games.

Predicting the behavior of human participants in strategic settings is an important problem in many domains. Most existing work either assumes that participants are perfectly rational, or attempts to directly model each participant's cognitive processes based on insights from cognitive psychology and experimental economics. In this work, we present an alternative, a deep learning approach that automatically performs cognitive modeling without relying on such expert knowledge. We introduce a novel architecture that allows a single network to generalize across different input and output dimensions by using matrix units rather than scalar units, and show that its performance significantly outperforms that of the previous state of the art, which relies on expert-constructed features.

We describe Mechanical TA, an automated peer review system, and report on our experience using it over three years. Mechanical TA differs from many other peer review systems by involving human teaching assistants (TAs) as a way to assure review quality. Human TAs both evaluate the peer reviews of students who have not yet demonstrated reviewing proficiency and spot check the reviews of students who have. Mechanical TA also features "calibration" reviews, allowing students to quickly gain experience with the peer-review process. We used Mechanical TA for weekly essay assignments in a class of about 70 students, a course design that would have been impossible if every assignment had had to be graded by a TA. We show evidence that it helped to support student learning, leading us to believe that the system may also be useful to others.

Behavioral game theory seeks to describe the way actual people (as compared to idealized, ``rational'' agents) act in strategic situations. Our own recent work has identified iterative models (such as quantal cognitive hierarchy) as the state of the art for predicting human play in unrepeated, simultaneous-move games [Wright and Leyton-Brown 2012]. Iterative models predict that agents reason iteratively about their opponents, building up from a specification of nonstrategic behavior called level-0. The modeler is in principle free to choose any description of level-0 behavior that makes sense for the given setting; however, in practice almost all existing work specifies this behavior as a uniform distribution over actions. In most games it is not plausible that even nonstrategic agents would choose an action uniformly at random, nor that other agents would expect them to do so. A more accurate model for level-0 behavior has the potential to dramatically improve predictions of human behavior, since a substantial fraction of agents may play level-0 strategies directly, and furthermore since iterative models ground all higher-level strategies in responses to the level-0 strategy. Our work considers ``meta-models'' of level-0 behavior: models of the way in which level-0 agents construct a probability distribution over actions, given an arbitrary game. We evaluated many such meta-models, each of which makes its prediction based only on general features that can be computed from any normal form game. We evaluated the effects of combining each new level-0 meta-model with various iterative models, and in many cases observed large improvements in the models' predictive accuracies. In the end, we recommend a meta-model that achieved excellent performance across the board: a linear weighting of features that requires the estimation of five weights.

It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies. However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players' initial behavior in normal-form games. In this paper, we consider a wide range of widely-studied models from behavioral game theory. For what we believe is the first time, we evaluate each of these models in a meta-analysis, taking as our data set large-scale and publicly-available experimental data from the literature. We then propose modifications to the best-performing model that we believe make it more suitable for practical prediction of initial play by humans in normal-form games.