Does playing strategic games improve your performance on other tasks in which you
have to reason about someone else’s beliefs and intentions, as in for example a
falsebelief task? Both tasks require theory of mind—the ability to reason about someone’s
desires, beliefs, and intentions. In reasoning about others’ minds, we can distinguish
different orders of reasoning. When we reason about the reality (e.g., this abstract),
we talk about zeroth-order theory of mind. First-order theory of mind is when we
reason about someone’s mental states (e.g., I think you find this abstract interesting to
read). Second-order is reasoning about someone who reasons about someone’s mental
states (e.g., I think that you think that I find this abstract interesting to read) and so
forth. Several training studies have shown transfer between first-order theory of mind
tasks [
The first task is a turn-based strategy-game called marble drop designed by
Meijering et al. [
The second task is a false-belief task. In a false-belief task, a story is told while corresponding pictures are presented to the participant. In the story, an item is moved from one location to the other. This movement is not observed by all characters in the story. Thus, one or more characters have false beliefs about the location of the item. After the presentation of the story, participants are asked to reason about the beliefs of one of the characters in the story. In the story modeled in this study, a mother gives a piece of chocolate to her son Murat. Her daughter Ayla, who witnesses the gift, gets angry because she does not get one. Now, Murat puts the chocolate into the drawer and leaves the scene. Ayla then takes the chocolate out of the drawer and hides it in the toy box—however, Murat is secretly looking through the window and sees Ayla hiding the chocolate, without Ayla noticing him. Now, Ayla also leaves the scene and the mother enters. At the end of the story, the mother finds the chocolate in the toy box and then puts it near the TV. Participants are then asked where Ayla thinks that Murat is going to look for the chocolate. To answer this question, second-order theory of mind is required because the participant has to reason about Ayla’s belief about Murat’s belief. In this case, Murat thinks that the chocolate is in the toy box, because he did not see the mother move the chocolate. Ayla however, unaware of the fact that Murat observed her, thinks that Murat will look in the drawer—the location where he originally put it. The zeroth-order question in this story is “Where is the chocolate?” The correct answer to this question is the TV—the location where the mother last put the chocolate.
In 1901, Woodsworth and Thorndike [
In this study, an extension of the cognitive architecture ACT-R [
The model of the marble drop game is based on a forward-reasoning plus
backtracking algorithm [
The model for the false belief task is inspired on the model of Arslan, Taatgen, and Verbrugge [10]. Whereas their model has all the story facts in its declarative memory, the current model builds an internal representation as the story is presented. At the end of the story, it tries to backtrack the actions and observations of each of the characters. First, the model will come up with a zeroth-order answer, the current location of the chocolate. Next, the model backtracks the movements of the chocolate and checks who performed or observed these actions. The model then infers the beliefs of the characters and answers the question.
In total, the model was run 20 times in four conditions that each had three blocks of 40 trials. The first two control conditions consisted of three blocks of the marble drop game (md-md-md) and three blocks of the false belief task (fb-fb-fb). The last two transfer conditions consisted of two blocks of the marble game with one block of the marble drop game in between and vice versa (fb-md-fb and md-fb-md, respectively). To examine transfer, only log-transformed reaction times of correct trials are considered. If the difference of the experimental block 2 and control block 3 is divided by the difference of the control bock 2 and control block 3, the transfer between the two tasks can be calculated. The transfer for the false-belief task on the marble drop game is 11.14%. The transfer for the marble drop game on the false-belief task is 44.2%. As can be seen in Fig. 1, the last block of the fb-md-fb condition (green line) lies between the second and third block of the fb-fb-fb condition (red line). A t-test shows that the reaction times indeed differ for the second control block and the second experimental block (t = -3.67, p > 0.002). In contrast, the error bars of last block in the md-fb-md condition (blue line) do overlap with the error bars of the second block of the control condition md-md-md (purple line). Also, a t-test does not reveal any significant differences (t = -0.59, p = 0.563). 4
Transfer is found for the marble-drop task onto the false-belief task, but not the other way around. This finding could be explained by the complexity of both tasks. The marble drop task is a more complex task and requires more use of the workingmemory than the false-belief task—thus the model gets more training in specific working-memory strategies when doing marble drop. For developmental studies, the difference in complexity might mask transfer-effects. A recent study showed indeed that there is no transfer from the false-belief task onto the marble-drop game [11]. Whether there is transfer the other way around still remains an open question.
Further eye-tracking studies could help validate or invalidate proposed models. Furthermore, learning effects that occur in the last block could potentially inflate the amount of transfer found. Modelling a non-related task of the similar complexity that also demand inhibition and recursion could control these issues. 5 of the 12th International Conference on Cognitive Modeling, pp. 1426-1431. Carleton University, Ottawa (2013) 10. Arslan, B., Taatgen, N.A., Verbrugge, R.: Modeling Developmental Transitions in Reasoning about False Beliefs of Others. In R. West & Stewart (Eds.), Proceedings of the 12th International Conference on Cognitive Modeling, pp. 77-82. Carleton University, Ottawa (2013) 11. Arslan, B., Verbrugge, R., Taatgen, N.A., Hollebrandse, B.: Teaching Children to Attribute Second-order False Belief: A Training Study. In J. Szymanik & R Verbrugge (Eds.), Proceedings Second Workshop ‘Reasoning about Other Minds: Logical and Cognitive Perspectives’: CEUR proceedings. (forthcoming)