Mutualisms: cooperation between species: Difference between revisions
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In the simplest and most intuitive instance of the prisoner's dilemma, the donation game, two players meet and decide whether to cooperate and provide a benefit \(b\) to their interaction partner at a cost \(c\) (\(b>c>0\)) or to defect, which entails no costs and provides no benefits. If both cooperate each gets \(b-c\) but if one defects then the defector gets \(b\) and shirks the costs of cooperation, while the cooperator is stuck with the costs \(-c\). Finally if both defect, no one gets anything. The interaction is conveniently summarized in a payoff matrix (for the row player): | In the simplest and most intuitive instance of the prisoner's dilemma, the donation game, two players meet and decide whether to cooperate and provide a benefit \(b\) to their interaction partner at a cost \(c\) (\(b>c>0\)) or to defect, which entails no costs and provides no benefits. If both cooperate each gets \(b-c\) but if one defects then the defector gets \(b\) and shirks the costs of cooperation, while the cooperator is stuck with the costs \(-c\). Finally if both defect, no one gets anything. The interaction is conveniently summarized in a payoff matrix (for the row player): | ||
\begin{ | \begin{array}{cc} | ||
& C\qquad D\\ | |||
\begin{matrix} | |||
\label{eq:pd} | \label{eq:pd} | ||
C\\D | |||
\end{matrix} | \end{matrix} | ||
\end{ | & \begin{pmatrix} | ||
b-c & -c\\ | |||
b & 0 | |||
\end{pmatrix} | |||
\end{array} | |||
Thus, both players prefer mutual cooperation over mutual defection, yet defection yields the higher payoff regardless of what the partner does and hence the conflict of interest arises. | Thus, both players prefer mutual cooperation over mutual defection, yet defection yields the higher payoff regardless of what the partner does and hence the conflict of interest arises. | ||