Corruption and paradoxes in alliances

In order to study corruption when a person can adjudicate over property rights, we extend the Tullock contest model by letting identical workers and a non-productive enforcer, who is more effective at fighting, contest over a resource. Property rights for output are well defined, but it is not so for the resource. If the enforcer assigns the resource in the way he was mandated, then the grand coalition forms with no corruption. There is corruption if he colludes with a subset of the workers and gets a transfer; this coalition then fights over the resource against other groups of workers. For general cost effort functions, if the enforcer is effective enough and marginal productivity of labor is adequately low, addition of the enforcer to a coalition increases the sum of payoffs of its members and generates negative externalities on other coalitions; that is, to divide and rule becomes an attractive prospect. This matches the empirical association between corruption and labor productivity or income inequality.