Organizational change: From community to firm

Abstract

In the framework of mathematical modelling, we examine a self-governed collective whose members create aggregate income through individual effort, which income is then distributed between members per pre-negotiated relative shares. Each agent’s seeking maximum individual gain leads the collective into a non-efficient Nash equilibrium. To achieve equilibrium in a Pareto-preferable outcome, coordination of efforts is required. In our article, certain members of the collective united by a coalition based on mutual trust coordinate their efforts. We show that under a coalitional strategy aimed at maximizing coalitional gain, individual gains are increased across the collective. However, for each non-cooperated agent the set share in the income still acts as a limiting factor in their choice of invested effort. To increase its efforts further, the coalition offers each noncooperated agent a contract whereby the agent foregoes their share in the income for the benefit of the coalition, in exchange for a reward per their invested effort. As the contract takes effect, the organization undergoes fundamental change consisting in the transformation of a collective of individuals with equal rights into a hierarchical economic organization. We offer a set of models describing such organizational change at the stage of forming the contract and at the subsequent stage of implementation. For the contract formation stage, we identify the conditions under which each agent gains more by entering into the contract than by rejecting it. At the contract implementation stage, we identify the conditions wherein equilibrium values of each agent’s efforts assume their communally-optimal value.

Keywords:

collective action, Nash equilibrium, Pareto-improvement, stimulus contract, coalition