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We study the problem of modeling a population of agents pursuing unknown goals subject to unknown computational constraints. In standard models of bounded rationality, sub-optimal decision-making is simulated by adding homoscedastic noise to optimal decisions rather than actually simulating constrained inference. In this work, we introduce a latent inference budget model (L-IBM) that models these constraints explicitly, via a latent variable (inferred jointly with a model of agents’ goals) that controls the runtime of an iterative inference algorithm. L-IBMs make it possible to learn agent models using data from diverse populations of suboptimal actors. In three modeling tasks—inferring navigation goals from routes, inferring communicative intents from human utterances, and predicting next moves in human chess games—we show that L-IBMs match or outperforms Boltzmann models of decision-making under uncertainty. Moreover, the inferred inference budgets are themselves meaningful, efficient to compute, and correlated with measures of player skill, partner skill and task difficulty. 

When applied to question answering and other text generation tasks, language models (LMs) may be queried generatively (by sampling answers from their output distribution) or discriminatively (by using them to score or rank a set of candidate outputs). These procedures sometimes yield very different predictions. How do we reconcile mutually incompatible scoring procedures to obtain coherent LM predictions? We introduce a new training-free, game-theoretic procedure for language model decoding. Our approach casts language model decoding as a regularized imperfect-information sequential signaling game—which we term the CONSENSUS GAME—in which a GENERATOR seeks to communicate an abstract correctness parameter using natural language sentences to a DISCRIMINATOR. We develop computational procedures for finding approximate equilibria of this game, resulting in a decoding algorithm we call EQUILIBRIUM-RANKING. Applied to a large number of tasks (including reading comprehension, commonsense reasoning, mathematical problem-solving, and dialog), EQUILIBRIUM-RANKING consistently, and sometimes substantially, improves performance over existing LM decoding procedures—on multiple benchmarks, we observe that applying EQUILIBRIUM- RANKING to LLaMA-7B outperforms the much larger LLaMA-65B and PaLM- 540B models. These results highlight the promise of game-theoretic tools for addressing fundamental challenges of truthfulness and consistency in LMs. 

We present a game-theoretic model of pragmatics that we call ReCo (for Regularized Conventions). This model formulates pragmatic communication as a game in which players are rewarded for communicating successfully and penalized for deviating from a shared, “default” semantics. As a result, players assign utterances context-dependent meanings that jointly optimize communicative success and naturalness with respect to speakers’ and listeners’ background knowledge of language. By using established game-theoretic tools to compute equilibrium strategies for this game, we obtain principled pragmatic language generation procedures with formal guarantees of communicative success. Across several datasets capturing real and idealized human judgments about pragmatic implicature, ReCo matches, or slightly improves upon, predictions made by Iterated Best Response and Rational Speech Acts models of language understanding.