Fixed typos in paper.md

Author: JDatPNW

paper/paper.md

@@ -52,15 +52,15 @@ This paper aims to explain the functionality and the structure of the framework,
 ## Introduction / Literature Review
 Public Good Games illustrate the tragedy of the commons, see [@hardin1968tragedy] for the standard reference which is both widely cited and still controversially discussed [@mildenberger2019tragedy]. These games have been intensively studied before, with an increasing interest in the asymmetric variant of the game [@mcginty2013public; @hintze2020inclusive]. Typically, game theoretical problems are solved using rigourous mathematical analysis, but that approach reaches its limits when it comes to the stochastic and random behavior of the evolutionary process [@adami2016evolutionary]. Consequently, computational models, such as this one, are used.
 
-One problem of using computational models in research, is their oftentimes limited expandability. APGG remedies this problem by providing a modular framework, that is designed to be easily extended in a vein similar to [@bohm2017mabe; @richter2019evo].
+One problem of using computational models in research, is their oftentimes limited expandability. APGG remedies this problem by providing a modular framework that is designed to be easily extended in a vein similar to [@bohm2017mabe; @richter2019evo].
 
 ## What is a Public Goods Game
 The tragedy of the commons describes an important social and economical phenomenon which pitches self interest against the interests of a group. Players in a Public Goods Game (PGG) can either contribute to a common pool (cooperate) or withhold their contribution (defect). The money collected in the pool is increased by a multiplicative synergy factor, and then equally distributed amongst the players. It becomes immediately clear that the defecting players will always receive the same as the cooperators, but end up having more money than the cooperators due to the amount they withheld before. The tragedy specifically describes the dilemma, that if all players would cooperate the total amount received by everyone would be higher, but the greed (or self interest) of the defectors prevents that favourable outcome.
 
 The question is how to overcome the tragedy of the commons. In social societies, often institutions, regulations, and incentives are used [@fehr2002altruistic; @hintze2020inclusive]. In the theoretical context, all of this becomes abstracted as costly punishment [@hardin1968tragedy]. This costly punishment has been shown to affect human behavior [@fehr2002altruistic] and can indeed lead to the evolution of cooperation [@hintze2015punishment]. Another option that alters the outcome towards cooperation could be asymmetric distribution of resources, as it can be found in many animal hierarchies. Hyenas for example have a steep despotic index [@smith2007rank] while also cooperating with each other, supporting the idea of asymmetric payoffs potentially leading to cooperation.
 
 ## Statement of Need
-Studying evolution in a biological systems is cumbersome, to say the least [@lenski2017experimental]. Consequently, using computational models becomes a viable alternative. However, for new experiments to build on previous results, the modeling software needs to be extendable. This leads to a challenging problem. Future users will independently modify the software to suit their own needs, with no regard for other users. This could create an ever growing tree of alternative versions, that might not be compatible with each other. Here, a modular design (see \autoref{fig:Classes}) approach is used, such that possible future users can define custom modules. However, those modules will remain interoperable, because interfaces are well defined.
+Studying evolution in biological systems is cumbersome, to say the least [@lenski2017experimental]. Consequently, using computational models becomes a viable alternative. However, for new experiments to build on previous results, the modeling software needs to be extendable. This leads to a challenging problem. Future users will independently modify the software to suit their own needs, with no regard for other users. This could create an ever growing tree of alternative versions, that might not be compatible with each other. Here, a modular design (see \autoref{fig:Classes}) approach is used, such that possible future users can define custom modules. However, those modules will remain interoperable, because interfaces are well defined.
 
 ## Code Overview
 
@@ -111,7 +111,7 @@ To illustrate that the software is capable of reproducing scientific results, we
 In that experiment the synergy factor in the public goods game was varied and the outcome of evolution, given that factor, determined.
 When the synergy factor is low, we expect defectors to win, while cooperators should thrive when synergy is high.
 However, in this variant of the game, agents can also punish, and punishment can modulate the response of agents to the synergy factor.
-The expectation was, that punishment should allow agents to cooperate at lower synergy factors, and one should observe punishment to increase around this critical point.
+The expectation was that punishment should allow agents to cooperate at lower synergy factors, and one should observe punishment to increase around this critical point.
 Interestingly, agents' probabilities to cooperate and to punish evolved as expected, and punishment lowered the critical point, but the chance to punish went from 0.0 to 0.5 (drifting).
 \autoref{fig:Figure6} confirms both the phenomenon of drifting as well as the fact that at a synergy level of around 4.0 there are hardly any defectors left. 
 
@@ -149,6 +149,6 @@ After the initial development of the APGG software different groups of students
 Since APGG is written in a modular fashion, adding to and expanding on the existing code base should be easy to do, and therefore our tool allows anyone who wants to conduct experiments to write their specific use cases into APGG. Creating these extentions has already been tested [@hintze2020inclusive], and shown to work easily. Further additions can also be contributed to the github repository via pull requests. APGG will remain under further development for future experiments by Jochen Staudacher (Kempten University, Germany) and Arend Hintze (Dalarna University, Sweden).
 
 ## Acknowledgements
-The authors would like to thank Marcel Stimberg and Yanjie Zhou for their careful reviews which helped improved both our software and paper as well as Antonello Lobianco for some helpful comments and suggestions. We are indebted to Nikoleta Glynatsi for editing our paper and for always being there for our procedural questions. Jochen Staudacher thanks the funding of the Bavarian State Ministry of Science and Arts.
+The authors would like to thank Marcel Stimberg and Yanjie Zhou for their careful reviews which helped improve both our software and paper as well as Antonello Lobianco for some helpful comments and suggestions. We are indebted to Nikoleta Glynatsi for editing our paper and for always being there for our procedural questions. Jochen Staudacher thanks the funding of the Bavarian State Ministry of Science and Arts.
 
 ## References