 The above representations of the tragedy of the commons make the simplifying assumptions that the costs and benefits of cooperation are the same for each player, that the cost of cooperation is independent of the number of players who cooperate, and that the size of the benefit (\(0\) or \(B)\)) depends only on whether the number of cooperators exceeds the threshold. A somewhat more general account would replace \(C\) and \(B\) by functions \(C(i,j)\) and \(B(i,j)\), representing the cost of cooperation to player \(i\) when he is one of exactly \(j\) players who cooperate and the benefit to player \(i\) when exactly \(j\) players cooperate. We suppose that there is some threshold \(t\) for minimally effective cooperation so that \(B(i,j)\) is not defined unless \(j \gt t\). We may also assume additional cooperation never reduces the benefit \(i\) gets from effective cooperation, i.e., \(B(i,j+1) \ge B(i,j)\) when \(j \gt t\) and that additional defection never reduces the cost \(i\) bears in cooperating, i.e., \(C(i,j+1) \ge C(i,j)\). Now suppose, in addition, that, once the threshold of effective cooperation has been exceeded, any benefit one gets from from the presence of an additional cooperator is exceeded by one's cost of cooperation and that the costs of ineffective cooperation are genuine, i.e., for all players \(i\), \(B(i,j) \gt ( B(i,j+1)+C(i,j+1) )\) when \(j\) is greater than \(t\) and \(0 \gt C(i,j)\) when \(j\) is less than or equal to \(t\). Finally, suppose that the benefits to each player \(i\), of effective cooperation exceed the costs, i.e., for \(j \gt t\), \(B(i,j)+C(i,j) \gt 0\). We then have a tragedy of the commons game, which presents a familiar dilemma: defection benefits an individual in every circumstance (except the one where exactly \(t\) others cooperate) but everybody is better off in any state of effective cooperation than in any state without it. This account could be easily be modified to allow threshold of minimally effective cooperation to differ from one individual to another (\(i\)'s clean water requirements might be more stringent than \(j\)'s for example) or to allow \(B\) to be defined everywhere (thus eliminating the threshold, so that we always benefit from another's cooperation). The resulting game would still have its PD flavor.