Equilibrium in a civilized jungle

The jungle model with an equal number of agents and objects is enriched by adding a language, which is a set of orderings over the set of agents. An assignment of an agent to an object is justified within a group of agents if there is an ordering according to which that agent is the best suited in the group. A civilized equilibrium is an assignment such that every agent is the strongest in the group of agents consisting of himself and those who wish to be assigned to the object and can be justified within this group. We present (i) conditions under which the equilibrium in a civilized jungle is identical to the jungle equilibrium, (ii) a connection between the power relation and the language that is essentially necessary and sufficient for the existence of a Pareto efficient civilized equilibrium, and (iii) an analogue to the second welfare theorem.