Project Alexandria

2.3d Collective Action Failures

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Collective Action Failure

A collective action failure occurs when a collective action game’s Nash equilibrium is not Pareto efficient. Collective action failures are corrected by a persuasive authority which removes the inconsistency.

Examples

Prisoner's Dilemma

Consider a classic game of the Prisoner’s Dilemma, where each prisoner can either cooperate or defect. Their payoffs represent the amount of utility they get from their sentencing, such that the smaller the sentence, the happier the prisoner:

\begin{document}
 
\begin{tikzpicture}
   % Draw the vertical lines
   \draw (0, 0) -- (0, -3);
   \draw (1.5, 0) -- (1.5, -3);
   \draw (3, 0) -- (3, -3);
 
   % Draw the horizontal lines
   \draw (0, 0) -- (3, 0);
   \draw (0, -1.5) -- (3, -1.5);
   \draw (0, -3) -- (3, -3);
 
   % Add labels for players
   \node at (1.5, 1) {Prisoner 2};
   \node[rotate=90] at (-1, -1.5) {Prisoner 1};
 
   % Add labels for Player 2's choices
   \node at (0.75, 0.25) {C};
   \node at (2.25, 0.25) {D};
 
   % Add labels for Player 1's choices
   \node at (-0.25, -0.75) {C};
   \node at (-0.25, -2.25) {D};
 
   % Add payoffs for each cell
   \node at (0.75, -0.75) {(2, 2)};
   \node at (2.25, -0.75) {(0, 3)};
 
   \node at (0.75, -2.25) {(3, 0)};
   \node at (2.25, -2.25) {(1, 1)};
\end{tikzpicture}
 
\end{document}

Through a best response analysis, we see that the Nash equilibrium is at . However, this is inconsistent with the collective good of the prisoners. As such, coercive authority is granted to a state actor, forcing the prisoners to act in a Pareto efficient manner and choosing . This is known as the liberal justification for a coercive state, where people freely enact an authority to guarantee that they behave in a certain way.

Graph View