Review Reports - High Cost of Survival Promotes the Evolution of Cooperation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, the authors explore the impact of survival costs on the evolution of cooperation. They adopt the iterated prisoner's dilemma model with two strategies, ALLC and ALLD. Their theoretical analysis shows that a relatively high survival cost promotes the evolution of cooperative behavior. Although the idea is interesting, the current version of the paper is not suitable for publication in Games due to the following concerns:

1. The authors use one paragraph to explain how their model differs from previous studies about “No-Play option”. However, I find their statement not very convincing. In my opinion, their current model is similar to the following model with “No-Play option”: i) the maximum number of rounds are set to t; ii) individuals in the game are allowed to cancel the interaction with their opponents early based on their game payoffs; iii) the probabilities to continue the next interaction are denoted as q_X (X belongs to {T, R, P, S}) and all individuals share the same q_X; iv) if one individual choose to cancel the interaction, the other individual also ceases to play. The authors may consider to revise their model for novelty.

2. Even if we adopt the current descriptions of the model, i.e., individuals with low stage payoffs will not survive, the model has flaws. For instance, if q_S=0 and q_R=1, a group of (ALLC, ALLC) will survive for t rounds. On the other hand, a group of (ALLD, ALLC) will play just one round of the game since ALLC dies after the first round. However, the current model does not tell what ALLD obtains for the rest t-1 rounds. If ALLD receive zero payoff for the second round, ALLD may also die. In this case, the payoff of ALLD vs ALLC is zero, not T. Unless the authors assume that the time needed for one round of play under (ALLC, ALLC) and (ALLD, ALLC) differs. The authors need to carefully consider the payoff outcomes of their models.

3. The model here in some sense represents the relationship between host and virus. The virus may reduce its immediate gains and keep its host alive in order to reproduce. However, the current investigations only consider extreme strategies such as ALLD, which seeks only for immediate gains. There may be some interesting interactions between host and virus if the authors could consider more strategies.

4. The references are old (most of them are published before 2012, just one in 2021), which does not cover the latest findings. It would be better if the authors could link their work to the recent progress of the field.

5. I will not cover other issues like incorrect notations and typos here. I recommend the authors to conduct a thorough review.

Overall, I encourage the authors to address my concerns above. The paper in its current form, in my opinion, is not suitable for publication.

Comments on the Quality of English Language

None.

Author Response

Thank you for your useful comments and suggestions, which help us improve the quality of our work. Please, see the revised version of the paper with changes highlighted.

The authors use one paragraph to explain how their model differs from previous studies about “No-Play option”. However, I find their statement not very convincing. In my opinion, their current model is similar to the following model with “No-Play option”: i) the maximum number of rounds are set to t; ii) individuals in the game are allowed to cancel the interaction with their opponents early based on their game payoffs; iii) the probabilities to continue the next interaction are denoted as q_X (X belongs to {T, R, P, S}) and all individuals share the same q_X; iv) if one individual choose to cancel the interaction, the other individual also ceases to play. The authors may consider to revise their model for novelty.

We appreciate Reviewer 1’s comments about the model’s connection to the “No-Play” option. While we briefly addressed the issue in the original version, the discussion could be substantially improved. In the revision, we clarify how our model is qualitatively different from models employing the “No-Play” option.

In prior “No-Play” models, a player chooses to withdraw from further interaction to avoid being exploited and thus preserve a higher payoff (or utility). With the No-Play option, the player leaves the game voluntarily to protect their remaining resources or avoid future losses. In our model, the exit is forced by survival failure, not by choice. An exploited cooperator in our framework does not decide to end the interaction. Rather, if their payoff falls below the metabolic cost M, they are forcibly removed from the game. There is no payoff-preserving mechanism in that exit. The exploited cooperator receives the lowest payoff S, and if S < M, is effectively forced out without saving anything. This is drastically different from strategic exit, where the agent deliberately locks in some positive payoff instead of remaining in a losing interaction.

Importantly, in a typical No-Play model, an individual’s “exit” payoff is often larger than what they would get if they stayed and ended up with mutual defection. In our model, the forced exit leads to the lowest possible payoff. It is the worst possible outcome. This distinction alone makes our model distinct from a No-Play model. The key novelty is that survival is an endogenous result of game payoffs crossing a threshold M, and not a player’s choice.

In the revised version of the paper, we elaborate on these points for the readers.

Even if we adopt the current descriptions of the model, i.e., individuals with low stage payoffs will not survive, the model has flaws. For instance, if q_S=0 and q_R=1, a group of (ALLC, ALLC) will survive for t rounds. On the other hand, a group of (ALLD, ALLC) will play just one round of the game since ALLC dies after the first round. However, the current model does not tell what ALLD obtains for the rest t-1 rounds. If ALLD receive zero payoff for the second round, ALLD may also die. In this case, the payoff of ALLD vs ALLC is zero, not T. Unless the authors assume that the time needed for one round of play under (ALLC, ALLC) and (ALLD, ALLC) differs. The authors need to carefully consider the payoff outcomes of their models.

We appreciate the opportunity to clarify how our survival and payoff accounting works.

Technically, whether the defector playing against a cooperator (ALLD playing ALLC) obtains a payoff T or zero does not matter for the substantive results of the model: either way, we observe the evolution of cooperation due to relatively high metabolic cost. With that said, it is necessary to clarify the payoff structure in our evolutionary model.

The payoff T that a defector receives does “count” in that round and can confer real evolutionary advantages—even if that defector (or their partner) ultimately dies in a subsequent round. In an evolutionary game-theoretic sense, receiving T means that in that round, the defector’s fitness or payoff increases by T. That is not retroactively wiped out if the game ends later. In an evolutionary setting, per-round payoffs translate into reproductive success over time. The fact that subsequent rounds do not occur (due to partner death) does not negate the payoff T already earned.

The crucial difference is that (ALLC, ALLC) can accumulate multiple rounds of payoff R (and hence survive longer), whereas (ALLD, ALLC) typically obtains a one-shot T and then loses future rounds once the cooperator is gone.

The model here in some sense represents the relationship between host and virus. The virus may reduce its immediate gains and keep its host alive in order to reproduce. However, the current investigations only consider extreme strategies such as ALLD, which seeks only for immediate gains. There may be some interesting interactions between host and virus if the authors could consider more strategies.

Thank you for these interesting observations. We now include them in our Discussion at the end of the paper. Specifically, we discuss more nuanced strategies beyond purely cooperative (ALLC) and purely exploitative (ALLD) ones. Indeed, viruses often exhibit “tempered” exploitation (e.g., lower virulence) to avoid killing the host prematurely, thereby prolonging the opportunity to reproduce. This behavior in evolutionary game terms can be seen as an intermediate strategy between unconditional cooperation and maximal defection. As Reviewer 3 notices as well, this is potentially one condition in which the model may fail to produce the evolution of cooperation.

The references are old (most of them are published before 2012, just one in 2021), which does not cover the latest findings. It would be better if the authors could link their work to the recent progress of the field.

Other reviewers raise similar concerns and suggest a number of recent relevant papers. The literature context has been updated with more recent publications.

I will not cover other issues like incorrect notations and typos here. I recommend the authors to conduct a thorough review.

We have conducted a thorough review of spelling, grammar, and notations.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the authors extend the PD framework by introducing metabolic costs of survival in an iterated PD game (IPD), where players engage in repeated interactions over multiple rounds. They assume that survival depends on the payoffs players receive in each round. If a participant's payoff falls below the survival threshold, the participant will exit the game. Through theoretical analysis, they have demonstrated that the system remains evolutionarily stable when the cost of survival is sufficiently high, meaning that exploited cooperators have a low probability of survival. They derived a rule for the evolutionary stability of cooperation. This paper provides a novel perspective to explain how cooperation becomes evolutionarily stable under resource scarcity. The topic of this paper is worth investigation. The results presented are new and meaningful as far as I am concerned. Here I have a few comments for the authors to improve their paper. My detailed comments are as follows.

1. Given that the research results are presented in the form of theoretical analysis, would it be possible for the author to provide numerical simulation results to further substantiate the conclusions?

2. The references are insufficiently recent.

3. The manuscript would benefit from polishing the English style and grammar.

Author Response

Thank you for your support and suggestions. Please, see the revised version of the paper with changes highlighted.

Given that the research results are presented in the form of theoretical analysis, would it be possible for the author to provide numerical simulation results to further substantiate the conclusions?

We appreciate the suggestion to provide a numerical simulation of the theoretical model. The simulation supports our substantive conclusion that a higher metabolic cost promotes the evolution of cooperation. The resulting visualization should help readers with an intuitive understanding of the results and the evolutionary dynamics. The simulation figure comparing low and high costs of survival is now included in the main text. We are also adding a Python replication of the model, which can be easily run by readers.

The references are insufficiently recent.

We revised the literature context with more recent references.

The manuscript would benefit from polishing the English style and grammar.

We have conducted a thorough review of spelling and grammar.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript explores the evolution of cooperation in Iterated Prisoner’s Dilemma (IPD), by incorporating survival dynamics and metabolic costs as central mechanisms. It argues that high survival costs can promote cooperative behaviors by disproportionately reducing the survival of exploited cooperators, leading to enhanced social welfare. The study proposes novel theoretical insights and a mathematical model to support its claims.

While providing interesting insights and being based on a relatively novel, understudied, and promising observation, there are some points that I believe should be addressed before final publication.

The integration of metabolic survival costs into the classical IPD framework is an innovative approach. However, there are previous related work, such as Salahshour, M., 2023. Evolution as a result of resource flow in ecosystems: Ecological dynamics can drive evolution. Plos one, 18(10), p.e0286922., which should be discussed. Also, the citation is brief and misses much of the recent development and relevant work. For instance, on survival cost, Zhang, X. and Lu, S., 2024. The effect of survival pressure-based defector reward behavior on cooperation in spatial prisoner’s dilemma games. PloS one, 19(11), p.e0311612., on participation cost, Salahshour, M., 2021. Evolution of cooperation in costly institutions exhibits Red Queen and Black Queen dynamics in heterogeneous public goods. Communications biology, 4(1), p.1340., on cost of cooperation, Smaldino, P.E., Schank, J.C. and McElreath, R., 2013. Increased costs of cooperation help cooperators in the long run. The American Naturalist, 181(4), pp.451-463., and more recent work on IPD.
Also, the mechanisms has similarities with known mechanisms, including those mentioned above. This point should be clarified.

2. 2. The study lacks empirical data or simulations to validate the proposed model. Incorporating these, for instance, an agent-based simulation would strengthen its claims.

Fixed strategies (ALLC and ALLD) may oversimplify real-world interactions, which often involve mixed or conditional strategies. It would be good if the authors address how the results change upon introducing conditional strategies.

While the implications of high survival costs for cooperative dynamics are discussed, the broader ecological and sociopolitical consequences warrant deeper exploration. The authors should improve the discussion of the implecations of their work, such as in real world scenarios.

The manuscript asserts broad applicability but does not sufficiently explore boundary conditions where the model may fail. This overgeneraliazation should be addressed.

Author Response

Thank you for your support and specific suggestions, especially with respect to the literature review and specific references. Please, see the revised version of the paper with changes highlighted.

While providing interesting insights and being based on a relatively novel, understudied, and promising observation, there are some points that I believe should be addressed before final publication.

The integration of metabolic survival costs into the classical IPD framework is an innovative approach. However, there are previous related work, such as Salahshour, M., 2023. Evolution as a result of resource flow in ecosystems: Ecological dynamics can drive evolution. Plos one, 18(10), p.e0286922., which should be discussed. Also, the citation is brief and misses much of the recent development and relevant work. For instance, on survival cost, Zhang, X. and Lu, S., 2024. The effect of survival pressure-based defector reward behavior on cooperation in spatial prisoner’s dilemma games. PloS one, 19(11), p.e0311612., on participation cost, Salahshour, M., 2021. Evolution of cooperation in costly institutions exhibits Red Queen and Black Queen dynamics in heterogeneous public goods. Communications biology, 4(1), p.1340., on cost of cooperation, Smaldino, P.E., Schank, J.C. and McElreath, R., 2013. Increased costs of cooperation help cooperators in the long run. The American Naturalist, 181(4), pp.451-463., and more recent work on IPD.

Also, the mechanisms has similarities with known mechanisms, including those mentioned above. This point should be clarified.

We revised the literature context with more recent references, including the ones that you mentioned. Please, see the revised manuscript with changes highlighted. All references mentioned in the comment have been added to the main text.

The study lacks empirical data or simulations to validate the proposed model. Incorporating these, for instance, an agent-based simulation would strengthen its claims.

This is similar to the suggestions made by Reviewer 2. We now include an agent-based model simulating the theoretical results and providing visualizations of evolutionary dynamics. Indeed, such a computational model not only provides additional support for the theoretical model but also helps with an intuitive understanding of the results and dynamics for the readers.

Fixed strategies (ALLC and ALLD) may oversimplify real-world interactions, which often involve mixed or conditional strategies. It would be good if the authors address how the results change upon introducing conditional strategies.

We now mention more complicated strategies such as “moderate” defection (defectors who may be able to partially exploit cooperators in the context of continuous payoffs, for instance).

While the implications of high survival costs for cooperative dynamics are discussed, the broader ecological and sociopolitical consequences warrant deeper exploration. The authors should improve the discussion of the implications of their work, such as in real world scenarios.

The manuscript asserts broad applicability but does not sufficiently explore boundary conditions where the model may fail. This overgeneralization should be addressed.

These points are now discussed in the conclusion. Please see the revised version with changes highlighted. We also discuss model’s limiting assumptions.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I thank the authors for addressing all my previous comments. The quality of the revised manuscript has improved a lot. I have no further comments.

Reviewer 3 Report

Comments and Suggestions for Authors

The revised manuscript is much improved and I am happy to recommend its publication.