Game theory of mind

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

Price distortions and public information: theory, experiments and simulations

This paper studies the effects on the asset price of the introduction of a public signal in the presence of asymmetric private information in a decentralized market. We introduce an artificial market model populated by boundedly rational agents with heterogeneous levels of reasoning: sophisticated and naive traders. The model captures the main impacts of public information analyzed in the laboratory experiments reported by Ruiz-Buforn et al. (2019). Public information, when correct, coordinates market activity, improving price convergence to the fundamentals. By contrast, unwarranted public information pushes prices away from fundamentals. This strong influence of public information on prices is primarily driven by its common knowledge property

Cyclic game dynamics driven by iterated reasoning

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning--what you think I think you think--will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a "hopping" behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.Comment: 8 pages, 4 figures, and supplementary informatio

An Experiment on Prediction Markets in Science

Prediction markets are powerful forecasting tools. They have the potential to aggregate private information, to generate and disseminate a consensus among the market participants, and to provide incentives for information acquisition. These market functionalities can be very valuable for scientific research. Here, we report an experiment that examines the compatibility of prediction markets with the current practice of scientific publication. We investigated three settings. In the first setting, different pieces of information were disclosed to the public during the experiment. In the second setting, participants received private information. In the third setting, each piece of information was private at first, but was subsequently disclosed to the public. An automated, subsidizing market maker provided additional incentives for trading and mitigated liquidity problems. We find that the third setting combines the advantages of the first and second settings. Market performance was as good as in the setting with public information, and better than in the setting with private information. In contrast to the first setting, participants could benefit from information advantages. Thus the publication of information does not detract from the functionality of prediction markets. We conclude that for integrating prediction markets into the practice of scientific research it is of advantage to use subsidizing market makers, and to keep markets aligned with current publication practice

On the origin of utility, weighting, and discounting functions: How they get their shapes and how to change their shapes

We present a theoretical account of the origin of the shapes of utility, probability weighting, and temporal discounting functions. In an experimental test of the theory, we systematically change the shape of revealed utility, weighting, and discounting functions by manipulating the distribution of monies, probabilities, and delays in the choices used to elicit them. The data demonstrate that there is no stable mapping between attribute values and their subjective equivalents. Expected and discounted utility theories, and also their descendants such as prospect theory and hyperbolic discounting theory, simply assert stable mappings to describe choice data and offer no account of the instability we find. We explain where the shape of the mapping comes from and, in describing the mechanism by which people choose, explain why the shape depends on the distribution of gains, losses, risks, and delays in the environment

Occasional errors can benefit coordination

The chances solving a problem that involves coordination between people are increased by introducing robotic players that sometimes make mistakes. This finding has implications for real-world coordination problems

Are groups more rational than individuals? A review of interactive decision making in groups

Many decisions are interactive; the outcome of one party depends not only on its decisions or on acts of nature but also on the decisions of others. In the present article, we review the literature on decision making made by groups of the past 25 years. Researchers have compared the strategic behavior of groups and individuals in many games: prisoner's dilemma, dictator, ultimatum, trust, centipede and principal-agent games, among others. Our review suggests that results are quite consistent in revealing that groups behave closer to the game-theoretical assumption of rationality and selfishness than individuals. We conclude by discussing future research avenues in this area

Time preferences and risk aversion: tests on domain differences

The design and evaluation of environmental policy requires the incorporation of time and risk elements as many environmental outcomes extend over long time periods and involve a large degree of uncertainty. Understanding how individuals discount and evaluate risks with respect to environmental outcomes is a prime component in designing effective environmental policy to address issues of environmental sustainability, such as climate change. Our objective in this study is to investigate whether subjects' time preferences and risk aversion across the monetary domain and the environmental domain differ. Crucially, our experimental design is incentivized: in the monetary domain, time preferences and risk aversion are elicited with real monetary payoffs, whereas in the environmental domain, we elicit time preferences and risk aversion using real (bee-friendly) plants. We find that subjects' time preferences are not significantly different across the monetary and environmental domains. In contrast, subjects' risk aversion is significantly different across the two domains. More specifically, subjects (men and women) exhibit a higher degree of risk aversion in the environmental domain relative to the monetary domain. Finally, we corroborate earlier results, which document that women are more risk averse than men in the monetary domain. We show this finding to, also, hold in the environmental domain