Yoshida Wako, Dolan Ray J, Friston Karl J
The Wellcome Trust Centre for Neuroimaging, University College London, UK.
PLoS Comput Biol. 2008 Dec;4(12):e1000254. doi: 10.1371/journal.pcbi.1000254. Epub 2008 Dec 26.
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.
本文介绍了一种“心理理论”模型，即我们如何表征他人的意图和目标，以优化我们之间的互动。我们借鉴最优控制和博弈论的观点，提出一种“心理博弈论”。首先，我们从由效用或奖励规定的价值函数角度来考虑目标表征。关键在于，在我表征你的价值函数、你表征我的价值函数、你表征我对你的价值函数的表征等等无限循环的假设下，联合价值函数和随之产生的行为会被递归地优化。然而，如果我们假设递归程度是有界的，那么参与者需要估计对手的递归程度（即复杂程度）以做出最优反应。这就引出了一个根据行为交互推断对手复杂程度的问题。我们表明，根据序贯博弈中的选择，可以推断参与者是否相互进行推断并量化他们的复杂程度。这基于比较有推断和无推断情况下的选择生成模型。通过“猎鹿博弈”的模拟数据和真实数据展示了模型比较。最后，我们指出，通过优化效用函数本身（通过亲社会效用）可以实现完全相同的复杂行为，从而产生看似无私但并不复杂的参与者。这在层级博弈论和协同进化的生态学层面可能具有相关性。
