The endogenous formation of leadership in collective actions using the modified timing decisions algorithm

The paper explores endogenous formation of leadership within a collective which aggregate income dependents on effort invested by each member. The timing decisions mechanism is modified into a multi-step game. At each step formation of leadership occurs across agents who invest no effort up to that point. Each agent chooses between active and waiting strategy. By choosing the active strategy, agents put in their effort considering the effort by agents at earlier steps. By choosing the waiting strategy, agents abstain from effort at the current step. In a final step all agents who had chosen the waiting strategy invest their effort. We assume that agents will choose the active strategy in pursuance of maximum guaranteed gain. A case is examined where an agent choosing a strategy has no information on the actions of agents who are yet to invest their effort. We show that the optimum value of the leader's effort per the maximin criterion equals the amount of effort which the agent would invest as a Stackelberg leader relative to all other agents who have not invested efforts at earlier steps. We prove that for every outcome of the two-period timing decisions game, a Pareto-dominant outcome exists within a multi-step game.