Peer review of: Evolving cooperation in multichannel games (2020)

Reviewers' Comments: 
 
Reviewer #1: 
Remarks to the Author: 
This paper studies the evolution of cooperation in multichannel games. The authors introduce a 
general framework of multichannel games, where two or more individuals interact with each other 
simultaneously over different channels, and each channel is a repeated game. In such multichannel 
games, a choice of strategies in one channel can affect strategic decisions in another. The authors 
show through analytical calculations and evolutionary simulations that this strategic linking enhances 
cooperative behavior in a variety of social dilemmas, including the donation game. The approach 
introduced in this paper is a natural generalization of previous approaches to studying the evolution of 
cooperation in repeated games and it represents a type of situation that can be expected to occur 
frequently in the real world. The paper is well-written and will be of interest to a wide range of 
researchers working on game theory and the evolution of cooperation. In addition, the Supplementary 
Information is comprehensive and informative. 
 
I have only a few minor comments that may help to improve the paper. 
 
1. Since many of the simulations are for large ensembles it would be interesting to have some sense 
of the statistical distribution of the results. Therefore, it would probably be better to replace the bar 
graphs in figures 2, 4 and S9 with box-and-whisker plots. 
 
2. The authors have considered in addition to the donation game also the snowdrift game and the 
volunteer’s dilemma, however, it might also be interesting to consider the stag hunt game. While the 
stag hunt game is something of a Cinderella in game theory, it might nevertheless be very interesting 
to study this game in the context of multichannel games. It would be natural to consider both 
scenarios in which players engage in two stag hunt games and in a stag hunt game combined with a 
donation game. The sculling game introduced in (Iyer, S. and Killingback, T., 2016, Evolution of 
cooperation in social dilemmas on complex networks. PLoS Computational Biology 12 (2), e1004779) 
represents a version of the stag hunt game that is analogous to the donation game and snowdrift 
game, and so may be well suited to such a study. 
 
3. On a technical point, the authors calculate the payoffs in the infinitely iterated games from the 
stationary distribution of a Markov chain - do they have a formula for the payoffs that is analogous to 
the Press-Dyson determinant formula? 
 
 
 
Reviewer #2: 
Remarks to the Author: 
In this well-written paper the authors have extended the evolutionary games by allowing the players 
to use different (including correlated) reactive strategies in games played simultaneously. This feature 
eliminates the similarity to spin systems in physical models. Using numerical simulations they consider 
multi-agent models where the pair interactions are restricted to a set of repeated donation games. It 
is found that if the agents can link their their concurrently ongoing interactions then they learn to 
coordinate their behavior that will be beneficial for them. These processes are discussed for several 
important cases. I think that the present models include relevant novelties that are present in real 
systems and this idea will initiate a large scale of further activities. Thus I recommend the publication 
of this interesting and important manuscript after some minor corrections detailed below: 
 
In the present analyses the pair interactions are limited to donation games that do not include 

coordination (or anti-coordination) type interactions which can introduce additional Nash equilibria and 
modify the evolutionary process. I suggest specifying clearly the interactions by substituting "donation 
game" for "game" in the Abstract, Introduction, and Discussion.