Binary choice models with aversion to inequality. Individual interactions vs. mean-field interaction

For several decades the problem of common goods has been intensively discussed and studied not only by economists, but also by politicians. One particular field of study concerns the problem of social choices realized by collective decisions, or rather individual decisions within some social collective (group). Several analytical models of using common-pool resources are proposed. Most approaches adopted within welfare economics are restricted to the maxim of this part of economics, i.e. to the maximization of the utility function. It was however discovered a long time ago that social interactions may play a significant role. In particular, aversion to inequality can be taken into account as the quantitative manifestation of the human sense of justice. Based on a simple binary choice model it is shown in this paper that by including social interactions into the decisional system of using a common-good resource, it is possible to reveal many stationary states (system multistability). Some of these stationary states may be more, and some others less beneficial from the global point of view. In this paper we investigate the eventual differences introduced by different forms of interactions between individuals. The status of the so-called mean-field approach is also examined.