Behavioural Isomorphism, Cognitive Economy and Recursive Thought in Non-Transitive Game Strategy
Round 1
Reviewer 1 Report
My understanding is that this paper attempts to make two points:
1. Many of the different strategies of interest in analyzing the play of rock paper scissors are behaviorally isomorphic.
2. This isomorphism can be used to study the attribution, agency and acquisition of players’ strategies.
I think that most people who study play in RPS have a general sense of the first point, however the taxonomy the authors lay out and the mapping of the isomorphism is more thorough than I have seen elsewhere.
Unfortunately, I do not understand the second point. Discussion of important questions related to attribution and agency do not seem connected to the behaviorally isomorphic strategies. The authors say:
1. “However, the empirical use of differentially described but behaviourally isomorphic RPS strategy help to resolve this issue.”
2. “The manipulation of 306 perceived opponent agency against a backdrop of behavioural isomorphism then becomes a 307 robust paradigm within which these questions can be addressed.”
But they do not explain how, or their explanation of how is unclear. Do the behaviorally isomorphic strategies have different predictions for the response to perceived agency? Or is the idea that players can change the complexity of their strategy without changing the strategy? But how would the experimenter know?
Author Response
I thank the reviewer for pointing out the lack of clarity regarding how behavioural isomorphism might help to promote the study of attribution, agency and acquisition. This section has now been extended with specific examples regarding how such empirical studies might play out.
For example, with respect to opponent attribution, I discuss the implications of a manipulation where “identical opponent behaviour could be described to the participant in two different ways across separate blocks: “the computer’s strategy will be based on your previous selection” vs. “the computer’s strategy will be based on its last selection and outcome” (Dyson, Sundvall, Forder & Douglas, 2018, p. 1484).” As noted in the original and current version of the manuscript “the other-upgrade strategy is outwardly and somewhat aggressively framed in terms of its exclusive focus on the opponent, while the self-outcome strategy is inwardly framed in terms of its more complex focus on the interaction between the previous item played by the organism and previous trial outcome.” Therefore, this is one way in which the impact of perceived high (other-upgrade) or low (self-outcome) competitive threat on behaviour could be operationalized without recourse to actual behavioural change between the opponents. Hopefully this starts to highlight the potential utility of identifying the behavioural isomorphism between certain RPS strategies.
With respect to strategy acquisition and individuals with Autistic Spectrum Disorder (ASD), I now make the concrete prediction that “if the same behaviour can be described in both a social (other-) and non-social (self-) way, then individual with ASD might show faster and more reliable acquisition of learning when the description of their opponent’s actions is more consistently framed within their own cognitive style (i.e., non-social or self-focused).”
Reviewer 2 Report
This review focus on decision-making process in repeated Rock-Paper-Scissors (RPS) game. The authors provide a taxonomy of RPS strategies. Frequency-based, cycle-based and outcome-based strategies are considered. The overview of their investigation in wide fields is given. It is shown that there is a behavioral isomorphism between self-outcome and other-cycle strategies, but they differ in the information set required for making a decision (cognitive economy). It is proposed to invoke recursive thought to RPS strategies, but it fails to distinguish between lower- and higher-order cognition. The clear and simple examples are given. The main idea is that the behavioral isomorphism can be applied for investigating attribution, agency and acquisition of the strategies in RPS and other games.
The review is interesting, meets the scope of the Journal and gives the trend of future research.
The only correction to be made: line 247 should be “(n)=W” instead of “S(n)=W”
Author Response
I thank the reviewer for their comments and have now corrected the error in line 247
Round 2
Reviewer 1 Report
The authors addressed my main concern about the clarity of the argument to the paper. A few minor corrections/comments
in the second sentence of the abstract the word "predictable" is confusing. Does The author mean that players tend to follow a deterministic strategy? Or that strategies are unpredictable?
In the fourth sentence, the "a)" should be before the first "whether"
at the end of the cycle-based strategy section, the author references "self-outcome strategies", which have not yet been defined. The sentence could be moved to the subsequent section or amended to make it clear that it is referencing the subsequent section
the sentence "data should as these could help to reveal…" Should read "data such as these could help to reveal"
on the next page it should say "additionally, identifying those individuals for whom" instead of "for who"
the last paragraph of the paper is a page and 1/2 long. It should be two or three paragraphs
Author Response
The authors addressed my main concern about the clarity of the argument to the paper. A few minor corrections/comments
I thank the reviewer for taking the time to review the manuscript again and identify a number of points, which have now been corrected below
in the second sentence of the abstract the word "predictable" is confusing. Does The author mean that players tend to follow a deterministic strategy? Or that strategies are unpredictable?
That section of the abstract has now been re-written in the hope of improving clarity: “In the non-transitive game Rock, Paper, Scissors (RPS), the only technique that guarantees the lack of exploitation is to perform randomly in accordance with mixed-strategy. However, such behaviour is thought to be outside bounded rationality and so decision-making can become deterministic, predictable and ultimately exploitable.”
In the fourth sentence, the "a)" should be before the first "whether"
Changed to “RPS strategies are discussed in terms of a) whether the relevant computations”
at the end of the cycle-based strategy section, the author references "self-outcome strategies", which have not yet been defined. The sentence could be moved to the subsequent section or amended to make it clear that it is referencing the subsequent section
This sentence has now been moved to the section on ‘outcome-based strategy’: “What is critical to the current review is other-cycle strategies (see above) are behaviourally equivalent to the implementation of self-outcome strategies.”
the sentence "data should as these could help to reveal…" Should read "data such as these could help to reveal"
Changed to “Data such as these could help to reveal”
on the next page it should say "additionally, identifying those individuals for whom" instead of "for who"
Changed to “identifying those individuals for whom automated”
the last paragraph of the paper is a page and 1/2 long. It should be two or three paragraphs
The final paragraph has now been broken up into two, more manageable sections.
