Political Violence and Evolutionary Game Theory: A Methodological Introduction

Political Violence and Evolutionary Game Theory:  A Methodological Introduction
Author: Wajzer, Mateusz
Almanac: History & Mathematics:Investigating Past and Future

Classical game theory is one of the basic methods of scientific analysis of political phenomena. The models developed on this basis are used in the studies of electoral and legislative behaviour, in the analysis of processes of forming political coalitions, and in the analysis of issues related to democratization, national security and armed conflicts. Evolutionary game theory has developed from classical game theory. This theory is referred to in this article, which presents selected possibilities of using single-population evolutionary models in studies of political violence transmission. On the basis of the analysis of two population variants, the article describes the changes in the prevalence of selected behavioural traits and answers the questions regarding the asymptotic states of evolutionary processes and their stability. The study uses Hawk-Dove and Hawk-Dove-Retaliator type games. The calculations were carried out using the R program.

Keywords: political violence, evolutionary game theory, mathematical models, Hawk-Dove game, Hawk-Dove-Retaliator game.

Where there is conflict over values, access to resources or power, violent behaviour usually occurs. For this reason, violence and politics must be seen as inextricably connected social phenomena. The main objective of political violence is to influence the political process. This goal is achieved through actions that can cause physical and/or mental harm to political opponents. Such activities include insulting, intimidating, blackmailing, blocking communication routes, occupying government buildings, kidnapping, physical assault, political murder, terrorism, and in extreme cases also participation in a coup d'état, revolution or civil war (Mider 2013: 706–707; 2017: 43–44).

Political violence is of interest to the representatives of multiple scientific disciplines, such as political science (Kalyvas 2006; Tausch 2007; Hatemi and McDermott 2012; McDermott et al. 2013), sociology (Malešević 2010; Vertigans 2011), psychology (Ofreneo and de Vela 2006; Michaels 2017), law (Schabas 2000; Walker 2011) or history (Bercé 1987; Raaflaub 2007). Research is conducted within the framework of theoretical and methodological orientations, which are often extremely different. Some researchers limit their analysis to the cultural paradigm only, trying to find the determinants of political violence among the values and norms adopted in a given society (e.g., Ofreneo and de Vela 2006), while others recognize the relevance of extra-cultural factors, for example neurobiological or genetic ones (see e.g., Hatemi and McDermott 2012; McDermott et al. 2013). This article focuses not on the causes of political violence or its possible consequences, but on the process of spreading violent behaviour in human populations. It shows how evolutionary game theory models may be used in the studies of the transmission of political violence.[1]

The article consists of three parts. The first part provides a concise introduction to evolutionary game theory. It describes such notions as the Nash equilibrium, evolutionarily stable strategies and replicator dynamics. In the second part, selected models are analyzed. The starting point for the analyses was the Hawk-Dove interaction scheme (the game is also known as Chicken). The article is concluded with a summary.

A Crash Course in Evolutionary Game Theory

A research in classical game theory involves interactive situations, i.e. situations involving two or more individuals. Depending on the research objectives and adopted assumptions, they can be people, companies, political parties, states, etc. These individuals are called players, and the situation they find themselves in – a game. Classical game theory assumes the rationality of the players, which means that they should choose strategies that produce the best possible results while being aware that their opponents are doing exactly the same. Conversely, according to its original purpose, evolutionary game theory allows for modelling interactions between genetically determined organisms within specific biological populations. Individuals from the same population usually participate in a game where the same resources are at stake. Two adult males may compete for a female, herd domination or fertile territories with abundant resources. The aim of the fight is, therefore, to take control of the resources, which significantly increase the ability to survive and to pass on one's genes to the next generations. The result of such a game is determined by the strategies (genetically determined behavioural traits) applied by individual players. As a result, the strategies with higher average payoffs (fitness) gain an advantage in subsequent generations due to the increased reproduction rate of the players using these strategies (Maynard Smith and Price 1973: 15; Vincent and Brown 2005: 72–75).

Summary and Discussion

The article presents selected possibilities of using single-population evolutionary models in studies of political violence. The analyses began with the basic Hawk-Dove model, assuming that the costs of conflict were higher than the expected profit (b < c). In this configuration, an evolutionarily stable state was established, which was a stable proportion of Hawks and Doves in the population. If we were to assume, however, that the expected profit from victory outweighed the losses from defeat (b > c), the Hawk strategy would eliminate the Dove strategy from the population entirely. In other words, the Hawk strategy would be an evolutionarily stable strategy. In the next step, the basic model was made more specific, taking into account the strategy of Retaliators. As a result, the population evolved either to a homogeneous state – 100 % Retaliators – or to a state in which 60 % of the population were Hawks and 40 % – Doves. The trajectory of population evolution was determined by the initial prevalence of each individual strategy.

The replicator equation was applied in the study. It was assumed, however, that the evolutionary process does not occur through the extinction of carriers of inferior genes but through the imitation of behaviours of higher utility. Therefore, it was assumed that replicator dynamics is the basic variant of imitation dynamics. Of course, it is possible to use other selection dynamics, whose essence is imitation. The examples include Maynard Smith's replicator dynamics (1982) and imitative logit (or i-logit) dynamics (Weibull 1997). The same applies to the time over which the changes in the population occur. The replicator equation assumes that it is continuous time. An alternative will be to use a discrete-time version of the replicator dynamics (Thomas 1986).

Finally, there arises a question of fundamental importance. How accurately do the evolutionary game theory models describe processes taking place in complex social networks? First of all, it should be remembered that any models are simplified representations of the studied phenomena. This means that the features considered by the researchers as insignificant are omitted at the initial stages of the research. Although models may become more concrete in time, they will always constitute reduced iterations of reality. Secondly, in social sciences (with the possible exception of economics), there is usually not enough data to build models that can claim to provide approximations with the precision expected from the natural sciences. Therefore, when examining specific historical processes, such as the process of radicalization of political attitudes that precedes revolutions and wars, religious and ethnic antagonisms, or the spread of destructive social norms, it must be taken into account that the models of evolutionary game theory will not show how these processes take place in actuality, but only how they would take place under certain arbitrary assumptions. Finally, evolutionary game theory models have considerable heuristic value, which can help identify further research directions.


The author is grateful to Dr K. Argasinski for helpful comments and suggestions.


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[1] Evolutionary game theory is used to investigate a wide range of social and political phenomena that are based on the use of violence. Let us just mention fundamentalism (Arce and Sandler 2003), religious and ethnic conflicts (Qin et al. 2014; Luo, Chakraborty, and Sycara 2011) or civil violence (Goh et al. 2006; Quek, Tan, and Abbass 2009).

[2] Replicators are relatively durable, self-replicating structures that determine strategic behaviours in a game. In biological games, genetic replicators are subject to selection and mutation, while in non-biological games this applies to social or cultural replicators.

[3] One of the direct consequences of the differences in the course of the evolutionary process is the need for a different interpretation of payoffs. In biological games, they are considered in terms of fitness, i.e. the number of offspring inheriting the strategy of their parents. Conversely, in social games, we do not talk about fitness, but about utility, which is related to the choice of a given strategy.

[4] It should be remembered that they are far-reaching simplifications. Therefore, they do not show how the phenomenon under investigation actually takes place nor do they explain why it does; they only show how it could occur under certain arbitrary assumptions.

[5] Interaction schemes used in the article are taken from The Logic of Animal Conflict (Maynard Smith and Price 1973) and Evolution and the Theory of Games (Maynard Smith 1982). The simulations were carried out using the Evolutionary Games library (Gebele and Staudacher 2017) available within the R program (R Core Team 2017).

[6] If we assume that country X has democratic rules for the election of its political representatives, the benefits and costs can be directly reduced to the level of public support measured in percentage points.