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Game Theory


TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems Using Game Theory

AI Magazine

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of fare evasion depends on the unpredictability and effectiveness of the patrols. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge.


Predicting Strategic Behavior from Free Text

Journal of Artificial Intelligence Research

The connection between messaging and action is fundamental both to web applications, such as web search and sentiment analysis, and to economics. However, while prominent online applications exploit messaging in natural (human) language in order to predict non-strategic action selection, the economics literature focuses on the connection between structured stylized messaging to strategic decisions in games and multi-agent encounters. This paper aims to connect these two strands of research, which we consider highly timely and important due to the vast online textual communication on the web. Particularly, we introduce the following question: Can free text expressed in natural language serve for the prediction of action selection in an economic context, modeled as a game? In order to initiate the research on this question, we introduce the study of an individual's action prediction in a one-shot game based on free text he/she provides, while being unaware of the game to be played. We approach the problem by attributing commonsensical personality attributes via crowd-sourcing to free texts written by individuals, and employing transductive learning to predict actions taken by these individuals in one-shot games based on these attributes. Our approach allows us to train a single classifier that can make predictions with respect to actions taken in multiple games. In experiments with three well-studied games, our algorithm compares favorably with strong alternative approaches. In ablation analysis, we demonstrate the importance of our modeling choices--the representation of the text with the commonsensical personality attributes and our classifier--to the predictive power of our model.


Optimal No-regret Learning in Repeated First-price Auctions

arXiv.org Machine Learning

We study online learning in repeated first-price auctions with censored feedback, where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid in order to maximize her cumulative payoff. To achieve this goal, the bidder faces a challenging dilemma: if she wins the bid--the only way to achieve positive payoffs--then she is not able to observe the highest bid of the other bidders, which we assume is iid drawn from an unknown distribution. This dilemma, despite being reminiscent of the exploration-exploitation trade-off in contextual bandits, cannot directly be addressed by the existing UCB or Thompson sampling algorithms in that literature, mainly because contrary to the standard bandits setting, when a positive reward is obtained here, nothing about the environment can be learned. In this paper, by exploiting the structural properties of first-price auctions, we develop the first learning algorithm that achieves $O(\sqrt{T}\log^2 T)$ regret bound when the bidder's private values are stochastically generated. We do so by providing an algorithm on a general class of problems, which we call monotone group contextual bandits, where the same regret bound is established under stochastically generated contexts. Further, by a novel lower bound argument, we characterize an $\Omega(T^{2/3})$ lower bound for the case where the contexts are adversarially generated, thus highlighting the impact of the contexts generation mechanism on the fundamental learning limit. Despite this, we further exploit the structure of first-price auctions and develop a learning algorithm that operates sample-efficiently (and computationally efficiently) in the presence of adversarially generated private values. We establish an $O(\sqrt{T}\log^5 T)$ regret bound for this algorithm, hence providing a complete characterization of optimal learning guarantees for this problem.


Predicting Strategic Behavior from Free Text

arXiv.org Artificial Intelligence

The connection between messaging and action is fundamental both to web applications, such as web search and sentiment analysis, and to economics. However, while prominent online applications exploit messaging in natural (human) language in order to predict non-strategic action selection, the economics literature focuses on the connection between structured stylized messaging to strategic decisions in games and multi-agent encounters. This paper aims to connect these two strands of research, which we consider highly timely and important due to the vast online textual communication on the web. Particularly, we introduce the following question: can free text expressed in natural language serve for the prediction of action selection in an economic context, modeled as a game? In order to initiate the research on this question, we introduce the study of an individual's action prediction in a one-shot game based on free text he/she provides, while being unaware of the game to be played. We approach the problem by attributing commonsensical personality attributes via crowd-sourcing to free texts written by individuals, and employing transductive learning to predict actions taken by these individuals in one-shot games based on these attributes. Our approach allows us to train a single classifier that can make predictions with respect to actions taken in multiple games. In experiments with three well-studied games, our algorithm compares favorably with strong alternative approaches. In ablation analysis, we demonstrate the importance of our modeling choices -- the representation of the text with the commonsensical personality attributes and our classifier -- to the predictive power of our model.


No-regret learning dynamics for extensive-form correlated and coarse correlated equilibria

arXiv.org Artificial Intelligence

Recently, there has been growing interest around less-restrictive solution concepts than Nash equilibrium in extensive-form games, with significant effort towards the computation of extensive-form correlated equilibrium (EFCE) and extensive-form coarse correlated equilibrium (EFCCE). In this paper, we show how to leverage the popular counterfactual regret minimization (CFR) paradigm to induce simple no-regret dynamics that converge to the set of EFCEs and EFCCEs in an n-player general-sum extensive-form games. For EFCE, we define a notion of internal regret suitable for extensive-form games and exhibit an efficient no-internal-regret algorithm. These results complement those for normal-form games introduced in the seminal paper by Hart and Mas-Colell. For EFCCE, we show that no modification of CFR is needed, and that in fact the empirical frequency of play generated when all the players use the original CFR algorithm converges to the set of EFCCEs.


Provable Sample Complexity Guarantees for Learning of Continuous-Action Graphical Games with Nonparametric Utilities

arXiv.org Machine Learning

Game theory has been extensively used as a framework to model and study the strategic interactions amongst rational but selfish individual players who are trying to maximize their payoffs. Game theory has been applied in many fields including but not limited to social and political science, economics, communication, system design and computer science. In non-cooperative games each player decides its action based on the actions of others players. These games are characterized by the equilibrium solution concept such as Nash equilibrium (NE) [18] which serves a descriptive role of the stable outcome of the overall behavior of self-interested players (e.g., people, companies, governments, groups or autonomous systems) interacting strategically with each other in distributed settings. Graphical games, introduced within the AI community about two decades ago, graphical games [16], are a representation of multiplayer games which capture and exploit locality or sparsity of direct influences. They are most appropriate for large-scale population games in which the payoffs of each player are determined by the actions of only a small number of other players. Indeed, graphical games played a prominent role in establishing the computational complexity of computing NE in normal-form games as well as in succinctly representable multiplayer games (see, e.g., [5, 6, 7] and the references therein). Graphical games have been studied for both discrete and continuous actions.


6 Python Libraries to Interpret Machine Learning Models and Build Trust - Analytics Vidhya

#artificialintelligence

The'SHapley Additive exPlanations' Python library, better knows as the SHAP library, is one of the most popular libraries for machine learning interpretability. The SHAP library uses Shapley values at its core and is aimed at explaining individual predictions. But wait – what are Shapley values? Simply put, Shapley values are derived from Game Theory, where each feature in our data is a player, and the final reward is the prediction. Depending on the reward, Shapley values tell us how to distribute this reward among the players fairly. We won't cover this technique in detail here, but you can refer to this excellent article explaining how Shapley values work: A Unique Method for Machine Learning Interpretability: Game Theory & Shapley Values! The best part about SHAP is that it offers a special module for tree-based models. Considering how popular tree-based models are in hackathons and in the industry, this module makes fast computations, even considering dependent features.


Microsoft's AI Experiments Are Creating Unbeatable Raid Bosses

#artificialintelligence

Raid bosses are the toughest fights in any massively multiplayer online game, but eventually players always find ways to crack them. Now developers are looking at ways to use cloud computing to give raid bosses a way of fighting back. During one of Microsoft's Game Stack developer livestreams yesterday, software engineer James Trott said that as developers are able to use the resources of the cloud to update and improve their games in real time, the real difficulty will be in not making them too hard. "We worked on a project with Microsoft tech last year for an MMO-like system for bosses that learn player behaviors in raid encounters," Trott said. "As raids go on and people find dominant strategies, the bosses adapt in near real time [and] detect the strategies players are implementing."


Optimising Game Tactics for Football

arXiv.org Artificial Intelligence

In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions and a stochastic game to model the in-match state transitions and decisions. Using this formulation, we propose a method to predict the probability of game outcomes and the payoffs of team actions. Building upon this, we develop algorithms to optimise team formation and in-game tactics with different objectives. Empirical evaluation of our approach on real-world datasets from 760 matches shows that by using optimised tactics from our Bayesian and stochastic games, we can increase a team chances of winning by up to 16.1\% and 3.4\% respectively.


Absolute Shapley Value

arXiv.org Machine Learning

Shapley value is a concept in cooperative game theory for measuring the contribution of each participant, which was named in honor of Lloyd Shapley. Shapley value has been recently applied in data marketplaces for compensation allocation based on their contribution to the models. Shapley value is the only value division scheme used for compensation allocation that meets three desirable criteria: group rationality, fairness, and additivity. In cooperative game theory, the marginal contribution of each contributor to each coalition is a nonnegative value. However, in machine learning model training, the marginal contribution of each contributor (data tuple) to each coalition (a set of data tuples) can be a negative value, i.e., the accuracy of the model trained by a dataset with an additional data tuple can be lower than the accuracy of the model trained by the dataset only. In this paper, we investigate the problem of how to handle the negative marginal contribution when computing Shapley value. We explore three philosophies: 1) taking the original value (Original Shapley Value); 2) taking the larger of the original value and zero (Zero Shapley Value); and 3) taking the absolute value of the original value (Absolute Shapley Value). Experiments on Iris dataset demonstrate that the definition of Absolute Shapley Value significantly outperforms the other two definitions in terms of evaluating data importance (the contribution of each data tuple to the trained model).