The influence of the agents’ personal qualities on the exogenous formation of Stackelberg leadership in a collective action model

Abstract

Within a mathematical modelling framework, we analyse conditions that prevent a self-governed collective from breaking out of an inefficient Nash equilibrium and attaining Pareto-preferable outcomes. It is assumed that by each member’s individual efforts aggregate income is created being equally distributed among members of a collective. Effort invested by each agent is complementary, i.e. increased effort by any individual agent increases marginal income produced by any other agent. Each agent’s goal is to maximize their own individual gain. We propose a model built for the collective income function with constant income elasticity per each agent’s effort that abides to the condition of decreasing returns. All members of the collective wield identical influence on the size of the income. Within a timingdecisions mechanism, each member of the collective faces the dilemma: whether to deploy an active strategy i.e., put in their effort during the first time period, or opt for a follower’s strategic timing and invest their effort during the second time period. The follower’s strategy yields greater gains, but only when some other agents choose the active strategy. In the event that not a single active agent appears, the entire collective falls into the trap of inefficient Nash equilibrium. We show that as the number of active agents grows, cumulate gains increase for all members of the collective. Maximum gains obtainable by a follower exceed the highest gain of an active agent, and are received only if the follower is the last agent remaining. It follows, therefore, that this maximum winner must be a risk-taking, egotistic optimist.