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How robust is the welfare state when facing open borders? An evolutionary game-theoretic model

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Abstract

How robust is the welfare state when confronting open borders? To answer that question, we develop an evolutionary game-theoretic model combined with an ingroup–outgroup model. The simulations reveal that welfare states in general will transform into low-welfare societies unless the societies in time generate a sufficiently large amount of social recognition of the reciprocators in such a crisis. The recognition implies that the “always cooperators” in favour of supportive policies towards free riders need to step down and hand over privileges to those willing to reciprocate, namely the “willing punishers”. The open-border society is modelled by letting a small amount of random types enter the society each year. Interestingly, it is not the defectors who compromise high-welfare societies. Instead, it is the excessive presence of cooperators who crowd out the reciprocators, thus making society increasingly vulnerable to free riding. This accentuates the need for timely recognition and actions against the risk of moving towards a low-welfare society.

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Notes

  1. We use the two-person prisoner’s dilemma game (Table 1) as a reference for how individuals interact. Although highly stylized, the game has been applied widely in modelling actual human interactions.

  2. The experiment of Quervain et al. (2004) report a positive correlation between activity in certain parts of the brain and the willingness to incur costs to punish. The fact that people differ in those brain activities may explain why only a fraction of subjects are willing to punish in experiments.

  3. Let \(\pi^{i} \left( {i,j} \right)\) be payoff of type \(i\) from meeting type \(j\), while let \(\pi^{j} \left( {i,j} \right)\) be type \(j\)’s payoff from meeting type \(i\). The direct payoffs are \(\pi^{WP} \left( {WP,AD} \right) = a\) and \(\pi^{AD} \left( {WP,AD} \right) = d\). Punishment costs for the Willing Punisher type are \(p^{WP} > 0\) and the effects of punishment costs on Always Defectors are \(p^{AD} > p^{WP}\). For simplicity, we assume that \(a - p^{AD} = d - p^{WP} = p\).

  4. Definition of an evolutionary stable strategy. The two strategies \(i,j\), can be depicted as follows. Assume that strategy \(j\) has a very low frequency when it begins attempting to invade the population. Furthermore, assume that strategy \(i\) is stable if \(E\left( {i,i} \right) > E\left( {j,i} \right)\) or \(E\left( {i,i} \right) = E\left( {j,i} \right)\; and\; E\left( {i,j} \right) > \left( {j,j} \right)\).

  5. Proof that a proportion of Willing Punishers exist in society, denoted by \(\bar{X}^{WP}\), below which \(X_{t}^{AD} \to 1\). Let \(X_{t}^{AD}\) be small, denoted by \(\varepsilon_{t}\). We have that \(\Pi _{t}^{AC} -\Pi _{t}^{WP} = \varepsilon_{t} \left( {d - p} \right) > 0.\) Therefore, over time, \(\frac{{X_{t}^{AC} }}{{X_{t}^{WP} }}\) increases. If we assume that \(\varepsilon_{t}\) is extremely small such that the average payoff in society is approximately c, then we have that \(\Pi _{t}^{AD} = dX_{t}^{AC} + pX_{t}^{WP}\), while \(\Pi _{t}^{A} = c\). \(\Pi _{t}^{AD} =\Pi _{t}^{A}\) if \(d(1 - X_{t}^{WP} ) + pX_{t}^{WP} = c = > c = > \bar{X}_{t}^{WP} = \frac{c - d}{p - d}\). If \(= 4,\, d = 6,\, p = - 1 = > \bar{X}^{WP} \cong 0.28\).

  6. For more on governance narratives, see, e.g., Bevir and Rhodes (2010) and Hajer and Wagenaar (2003).

  7. Facchini (2016) describes a feedback model wherein an individual believes that action A will result in outcome B. However, if information invalidates that belief, a state of cognitive dissonance occurs, which will open a ‘window’ of opportunity for reform. Denial or withholding of information can postpone that opportunity. If, over time, mounting evidence contradicts the initial belief, the justification cost increases. Again, according to Facchini (2016), individuals are inclined to change their ideologies when justification costs become excessively high. Such costs will rise if a growing number of individuals oppose the initial beliefs, if scientific authorities condemn those beliefs or simply when the cost of withholding evidence is excessively high. In our setting, changing ideology simply means supporting another narrative. See also Kaplan et al. (2016) for a neurological explanation of such political confirmation bias.

  8. See Brandt (2014) for an explanation and consequences of such a policy process.

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Acknowledgements

An earlier version of this paper was presented at the European Public Choice Meeting in Budapest, April 2017, and we deeply thank the other participants. Furthermore, a special note of thanks goes to three anonymous reviewers and the editor for helpful comments.

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  1. Department of Sociology, Environmental and Business Economics, University of Southern Denmark, Niels Bohrs Vej 9, 6700, Esbjerg, Denmark

    Urs Steiner Brandt

  2. Department of Political Science, Aarhus University, Bartholins Allé 7, 8000, Aarhus C, Denmark

    Gert Tinggaard Svendsen

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Correspondence to Gert Tinggaard Svendsen.

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Brandt, U.S., Svendsen, G.T. How robust is the welfare state when facing open borders? An evolutionary game-theoretic model. Public Choice 178, 179–195 (2019). https://doi.org/10.1007/s11127-018-0622-5

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