von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc

Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending publication.) Last conference version: submitted March 30, 2012 to UAI 2012. First conference version: entitled, Learning Influence Games, initially submitted on June 1, 2010 to NIPS 201

Common Knowledge, Communication, and Public Reason

In this Article I explain why game theory has been so unsuccessful in accounting for the role of language in social interaction. I begin by exploring some of its most basic difficulties in this respect, in games of pure coordination, and trace these difficulties back to the most fundamental organizing concepts in the theory of games, namely, Nash equilibrium and common knowledge of rationality. Nash thinkers and Nash actors, I argue, are doomed to have very impoverished conversations as Nash talkers. The sorts of conversations they will have will leave them paralyzed in games of pure coordination and largely uncooperative in games where their interactions are at least partially characterized by conflicts of interest. These conversations are impoverished because they attempt to forge only a causal connection across the verbal exchanges between rational actors, not a conceptual one. What is needed is the richer sort of conversation that is idealized by law, that is, one where there is an interpenetration of concepts and commitments in the use of language between rational actors, the sort of thing we see under a truly shared or public reason. Law\u27s reasonable thinkers, I argue, are more capable of coordinating, and law\u27s reasonable talkers more capable of cooperating, than their Nash counterparts because, under objective reasonableness, they are committed to a more public conception of their conduct shaping what they do together

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when the empirical distribution on action profiles generated by every behavior strategy in one can also be generated by an appropriately chosen behavior strategy in the other. This paper provides a characterization of empirical equivalence. The central idea is to relate a game's information structure to the conditional independencies in the empirical distributions it generates. We present a new analytical device, the influence opportunity diagram of a game, describe how such a diagram is constructed for a given extensive-form game, and demonstrate that it provides a complete summary of the information needed to test empirical equivalence between two games.Causality, structural uncertainty, extensive form games