Summary

In this paper, the author stressed a very important water issue. The private systems and wells contamination issued by septic systems, and this might cause many types of social dilemmas. The author. Has developed a water game theory for private water systems starting with 2 and then with N-players applied then a symmetric as well as an asymmetric game with more uncertainty related mainly with the groundwater flow direction and the different possibility of contamination. All this has been applied to learn more about the interlinkages between the choice of the septic system upgrading, wells contamination, and social dilemmas. To do so, the author applied a groundwater model. To have more clearance about. The different probabilities are related to the uncertainty around the groundwater flow direction and the possibility of contamination (self-contamination and cross-contamination) by the septic systems.

At the end of the game (study), we expect to have a straightforward decision (policy solutions) that can help in solving this social dilemma with less cost.

General comments: 

1) Title: reflect very well the main question of the paper

2) Introduction: well, framed, and organized, but the author needs to check for more recent references.

3) Two household contamination games: this part is very well described. 

• However, there is a need to clarify if the game is cooperative or not cooperative before heading to the Nash equilibrium (non-cooperative). 
• The author needs to explain why he has chosen to go with the non-cooperative choice, even if it was very clear that the author wanted to stress out the social dilemma cause. But it would be great to clarify the rationality behind the choice.
• Why the author did not consider all the parts of the game: elements of action (finite or infinite), information set (complete information or incomplete information game), numbers of the same play in a game (one-shot game and repeated game).

4) Symmetric two-player games: from lines 113 to 121: the paragraph is a bit complicated, there is clear contradiction and redundancy in explaining the upgrading and non-upgrading choice.

5) Groundwater model: the author mentioned that the modeling part could be determined by any groundwater model, but he did not explain the rationale behind selecting /using the MODFLOW model.

6) Case study: 

• The existing groundwater data are mainly based on assumptions, does the author performed any data collection or had access to any national database?
• It is important to have the year of any collected data
• Does wells capture radius (rs) is sufficient to calibrate a groundwater model? In my knowledge in the case of groundwater flow modeling we need more than the Rs parameter, we need for example the recharge and hydraulic conductivity supported by field data.
• The model validation is absent, does the author validate the model data?
• The author took too much space to explain the game (almost 10 pages), however, he didn’t well calibrate and validate his groundwater model and he didn’t clearly explain and apply the game for the case study.

7) Discussion: the discussion is good, but it is too general and does not directly reflect the results from the selected case study. The author here only explained more about the different types of social dilemmas.

8) Conclusion: we expected after applying the game to a case study to have some applicable policy recommendations/solutions, but the author didn’t provide any straightforward solutions.

Specific comments:

1) Symmetric two-player games: from the line 113 to 121: the paragraph is a bit complicated, there is clear contradiction and redundancy in explaining the upgrading and non-upgrading choice

2) Line 337: The other player will reciprocate if she (he) has sufficient assurance of the other player’s buy-in.

3) I think that the references listed below worth to be sited in this publication: 

• Raquel S, Ferenc S, Emery C Jr, Abraham R. Application of game theory for a groundwater conflict in Mexico. J Environ Manage. 2007 Sep;84(4):560-71. DOI: 10.1016/j.jenvman.2006.07.011. Epub 2006 Sep 22. PMID: 16996197.
• Ariel Dinar and Margaret Hogarth (2015), "Game Theory and Water Resources: Critical Review of its Contributions, Progress and Remaining Challenges", Foundations and Trends® in Microeconomics: Vol. 11: No. 1–2, pp 1-139. http://dx.doi.org/10.1561/0700000066

General comments:

The article combines game theory with groundwater modelling to analyse social dilemmas and potential policy solutions related with groundwater contamination. This is a timely contribution given that groundwater contamination remains a widespread challenge. The authors' detailed description of the  the game theoretical model and the groundwater modelling is informative and helpful - especially for readers not familiar with the framework proposed. I also find the application of the framework to a real-world scenario interesting. I believe further work on the case study and the discussion section would contribute to strengthen the paper. To this end, I provide some suggestions below.

The authors show the relevance of the methodology presented by applying it to the case of St. Joseph County. I would suggest the authors to further contextualize the case study. For instance, it would be of interest to include more data about the socio-economic status of residents of the two sites considered (Centre Township and Granger CDP) and housing density as well as some more information about environmental policies in place to tackle groundwater use/contamination. This would be helpful to assess the potential of the framework to understand real-world cases. Recent work on water security in the context of the US has highlighted significant inequalities that I believe it is worth discussing either in the presentation of the case study or in the discussion session, see for instance:

• Meehan, K., Jurjevich, J.R., Chun, N.M. and Sherrill, J., 2020. Geographies of insecure water access and the housing–water nexus in US cities. Proceedings of the National Academy of Sciences, 117(46), pp.28700-28707.
• Meehan, K., Jepson, W., Harris, L.M., Wutich, A., Beresford, M., Fencl, A., London, J., Pierce, G., Radonic, L., Wells, C. and Wilson, N.J., 2020. Exposing the myths of household water insecurity in the global north: A critical review. Wiley Interdisciplinary Reviews: Water, 7(6), p.e1486.

The discussion is limited to describe different social dilemmas and propose (rather vague) policy solutions. The author could work to further develop the discussion section with specific reference to the case study. For instance, I am missing a clear statement indicating to which extend the framework proposed is helpful to i) describe real-world social dilemma, ii) identify (applicable) policy solutions.

I would also suggest to further reflect on the limitations of the proposed framework especially in relation to policy solutions in a real-world scenario and to the uncertainties in the modelling. For instance, the authors assume the players are homogeneously located, do not have perfect information and they face similar costs and emit comparable pollution (l.356). How does such assumptions influence the results, especially in terms of identifying policy solutions? Loss in home value is considered as an estimate for the cost of contamination, while in the conclusion the authors suggest that more data are needed, they could also explain how does this assumption influence the findings. Moreover, I was wondering if and how the choice to focus on a case study located in the US (and not for instance a case in the Global South where groundwater contamination is also a pressing challenge) would influence the author’s assessment of the potential of the framework to understand social dilemmas and advice policy making.

Minor comments:

Title: the authors might want to consider to specify that the study focuses on a case study located in the US.

l.9 – Repetition of ‘three’

l.25 – Here and in other sections the authors refer to “private water systems”. Perhaps the term household water systems or domestic water systems would be more appropriate in order to distinguish the water systems considered in the paper and avoid confusion with i.e. a privatized pipe-born networked systems.

l. 320-321 – It is unclear to what the letters B and E refer to.