Existence and verification of Nash equilibria in non-cooperative contribution games with resource contention

In resource contribution games, a class of non-cooperative games, the players want to obtain a bundle of resources and are endowed with bags of bundles of resources that they can make available into a common for all to enjoy. Available resources can then be used towards their private goals. A player is potentially satisfied with a profile of contributed resources when his bundle could be extracted from the contributed resources. Resource contention occurs when the players who are potentially satisfied, cannot actually all obtain their bundle. The player's preferences are always single-minded (they consider a profile good or they do not) and parsimonious (between two profiles that are equally good, they prefer the profile where they contribute less). What makes a profile of contributed resources good for a player depends on their attitude towards resource contention. We study the problem of deciding whether an outcome is a pure Nash equilibrium for three kinds of players' attitudes towards resource contention: public contention-aversity, private contention-aversity, and contention-tolerance. In particular, we demonstrate that in the general case when the players are contention-averse, then the problem is harder than when they are contention-tolerant. We then identify a natural class of games where, in presence of contention-averse preferences, it becomes tractable, and where there is always a Nash equilibrium.