which subjects appropriate more than in the *SNE*. If all players in a group are inequity averse and given the parameters of the Ostrom et al. experiment, the range of possible Nash equilibria is where is *always* an equilibrium independent of α_{i} and β_{i} .^{7}

So far we have concentrated on symmetric equilibria. However, there are also asymmetric equilibria. The following proposition provides the details.^{8}

*(i) If there are at least k players with* *then there is an equilibrium with less appropriation than in the SNE. In this equilibrium at least k players choose the same appropriation* the other players j choose higher appropriation levels. (ii) If there is no k such that there are at least k players with *then there is no equilibrium with less appropriation than in the SNE.*

*Corollary 1: If there are* *or more selfish players, then there is no equilibrium with less appropriation than in the SNE.*

The intuition of Proposition 3 is straightforward. To get more efficient equilibria than the *SNE* requires that a relatively large fraction of subjects have rather high combinations. Notice that because 0 < β_{i} < 1 and α_{i} > β_{i} , the expression is between zero and one. This means that for the only equilibrium is the *SNE*. Only if *k* is higher than *n*/2 there are combinations to ensure a more efficient equilibrium. For example, if the group size is 8, it takes at least 5 nonegoistic players to reach such an equilibrium. In this case the combinations of these 5 subjects must be at least The more people who are nonselfish, the weaker is the requirement for Thus, to reach a more efficient outcome, it takes either many subjects with moderate combinations or it takes fewer subjects (but still more than *n*/2) with very high combinations. Notice that the expression rises in β_{i} and decreases in α_{i}. It is therefore more likely to reach more efficient outcomes if subjects have a rather large utility loss from advantageous inequality, and a rather small utility loss from disadvantageous inequality.