Escaping the tragedy of the commons through targeted punishment - PubMed (original) (raw)

. 2015 Aug 26;2(8):150223.

doi: 10.1098/rsos.150223. eCollection 2015 Aug.

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Escaping the tragedy of the commons through targeted punishment

Samuel Johnson. R Soc Open Sci. 2015.

Abstract

Failures of cooperation cause many of society's gravest problems. It is well known that cooperation among many players faced with a social dilemma can be maintained thanks to the possibility of punishment, but achieving the initial state of widespread cooperation is often much more difficult. We show here that there exist strategies of 'targeted punishment' whereby a small number of punishers can shift a population of defectors into a state of global cooperation. We conclude by outlining how the international community could use a strategy of this kind to combat climate change.

Keywords: climate change; cooperation; social dilemma.

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Figures

Figure 1.

Figure 1.

(a) Stationary proportion of cooperators, ρ, for a range of rationality, β, and punishment, π, from Monte Carlo simulations of the model when all cooperators punish all defectors, and initially all _N_=200 players cooperate. (Results are the averages over 100 realizations.) (b) As before, but now all players initially defect. (c) Fixed points of the dynamics against β, when _π_=0.4; stable fixed points are depicted in red, unstable ones in blue. (d) As in (c), but with _π_=0.6. (e) Fixed points of the dynamics against π, when _β_=2.5. (The fixed-point analysis is described in Methods.)

Figure 2.

Figure 2.

Diagrams illustrating the two strategies of targeted punishment described in the main text: (a) the ‘single file strategy’ and (b) the ‘groups strategy’ with groups of size _ν_=3 and a threshold _θ_=2/3. Players are arranged from most to least inherently cooperative; those currently cooperating are shown in red and those defecting in blue. A black arrow indicates a defector who is considered at fault (and therefore liable to be punished) according to the strategy, while a grey arrow signals a cooperator who would be at fault if she were defecting.

Figure 3.

Figure 3.

(a) As figure 1_b_ (all players initially defect), but now the ‘single file strategy’ is applied. (b) As in figure 1_b_, but under the ‘groups strategy’ with ν_=10 and θ_=80%. (See the main text and figure 2 for descriptions of these strategies.) (c) Difference between figure 1_a (all players initially cooperate) and figure 3_a. (d) Difference between figures 1_a_ and 3_b_. (e) Speed v_=N/τ, where τ is the number of time steps required to achieve global cooperation, for the situation in figure 3_a. (f) Speed v for the case of figure 3_b_.

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