Game Theory of Mind

By Wako Yoshida, R. J. Dolan, Karl J. Friston. 2008

305 citations recorded by the source corpus.

This paper introduces a model of ‘theory of mind’, namely, how we represent the intentions and goals of others to optimise our mutual interactions. We draw on ideas from optimum control and game theory to provide a ‘game theory of mind’. First, we consider the representations of goals in terms of value functions that are prescribed by utility or rewards. Critically, the joint value functions and ensuing behaviour are optimised recursively, under the assumption that I represent your value function, your representation of mine, your representation of my representation of yours, and so on ad infinitum. However, if we assume that the degree of recursion is bounded, then players need to estimate the opponent's degree of recursion (i.e., sophistication) to respond optimally. This induces a problem of inferring the opponent's sophistication, given behavioural exchanges. We show it is possible to deduce whether players make inferences about each other and quantify their sophistication on the basis of choices in sequential games. This rests on comparing generative models of choices with, and without, inference. Model comparison is demonstrated using simulated and real data from a ‘stag-hunt’. Finally, we note that exactly the same sophisticated behaviour can be achieved by optimising the utility function itself (through prosocial utility), producing unsophisticated but apparently altruistic agents. This may be relevant ethologically in hierarchal game theory and coevolution.

Subfields: Management Science and Operations Research, Safety Research, Sociology and Political Science

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Citations in the corpus

The Hanabi Challenge: A New Frontier for AI Research (2019, background): “signiﬁcant ﬁnancial support for this work that could have inﬂuenced its outcome.”
Machine Theory of Mind (2018, background): “…RL (Ng et al., 2000; Abbeel & Ng, 2004), Bayesian inference (Lucas et al., 2014; Evans et al., 2016), Bayesian Theory of Mind (Baker et al., 2011; Jara-Ettinger et al., 2016; Baker et al., 2017) or game theory (Camerer et al., 2004; Yoshida et al., 2008; Camerer, 2010; Lanctot et al., 2017).”
Optimal control as a graphical model inference problem (2009, neutral): “The type of approximate inference method that should be used depends very much on the details of the control problems.”
A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning (2017, methodology): “We would also like to investigate fast online adaptation [1, 21] and the relationship to computational Theory of Mind [107, 4], as well as generalized (transferable) oracles over similar opponent policies using successor features [6].”
Emergent Communication through Negotiation (2018, methodology): “This is consistent with experiments using models based on Theory of Mind: boundedly rational agents can collectively beneﬁt by making inferences about the sophistication levels and beliefs of their opponents, and there is evidence that this occurs in human behavior (Yoshida et al., 2008).”
Coordinate to cooperate or compete: Abstract goals and joint intentions in social interaction (2016, background): “In this work we focus speciﬁcally on the high-level goals of cooperation and competition but other high-level goals such as teaching, punishing or communication are also relevant in these games and will be investigated in future work.”
Theory of Mind and Preference Learning at the Interface of Cognitive Science, Neuroscience, and AI: A Review (2022, methodology): “We cover these concepts to varying degrees in this review, but detailed reviews for each are provided in the following papers (Game ToM in Yoshida et al., 2008; Observational Reinforcement Learning in Albrecht and Stone, 2018; Inverse Reinforcement Learning in Arora and Doshi, 2021 and Bayesian ToM…”
Rational quantitative attribution of beliefs, desires and percepts in human mentalizing (2017, methodology): “Generative models of multiple agents’ interactive behaviour can be expressed as Markov games 48 , and simpler game-theoretical models have already been useful in modelling other theory of mind tasks 49 .”
Help or Hinder: Bayesian Models of Social Goal Inference (2009, unknown): “Complex agents We assume that the social agent j uses its model of other agents’ planning process to compute P (Ai|S, Gi), for i 6= j, allowing for accurate prediction of other agents’ actions.”
The Minds of Many: Opponent Modeling in a Stochastic Game (2017, background): “Other approaches [Yoshida et al., 2008; Pereira et al., 2011] keep a model to learn beliefs about opponents’ actions and a separate model to infer the complexity of opponent strategies, whereas De Weerd et al. [2013b] integrate beliefs about opponent behaviour with inference about the…”
Computational psychiatry (2011, background): “[79] used the human player’s observed behavior to estimate the sophistication level (depth of recursion) of their inference about the computer agent’s beliefs (theory of mind).”
Algorithms for the Greater Good! On Mental Modeling and Acceptable Symbiosis in Human-AI Collaboration (2018, methodology): “The problem is made harder since such models often involve second order mental models (Allan 2013; Yoshida, Dolan, and Friston 2008).”
Backplay: "Man muss immer umkehren" (2018, unknown): “…that standard independent multi-agent learning does not produce agents that are able to cooperate in social dilemmas (Leibo et al., 2017; Lerer & Peysakhovich, 2017; Peysakhovich & Lerer, 2017; Foerster et al., 2017) or risky coordination games (Yoshida et al., 2008; Peysakhovich & Lerer, 2018).”
Exploring the Nature of 'Trader Intuition' (2010, background): “In the context of strategic games, recent studies successfully identify patterns in the moves of one's opponent on which ToM builds (Hampton et al. (2008), Yoshida, Dolan, and Friston (2008)).”
Insights from the application of computational neuroimaging to social neuroscience. (2013, methodology): “To investigate the computations underlying the tracking of an opponents sophistication, Yoshida et al. [37,38 (cid:2)(cid:2) ] employed Bayesian inference over predictive models of strategic behavior, incorporating the increasing cognitive effort required by increasing strategic sophistication.”