Who Matters in Coordination Problems?

We consider a common investment project that is vulnerable to a self-fulfilling coordination failure and hence is strategically risky. Based on their private information, agents - who have heterogeneous investment incentives - form expectations or "sentiments" about the project's outcome. We find that the sum of these sentiments is constant across different strategy profiles and it is independent of the distribution of incentives. As a result, we can think of sentiment as a scarce resource divided up among the different payoff types. Applying this finding, we show that agents who benefit little from the project's success have a large impact on the coordination process. The agents with small benefits invest only if their sentiment towards the project is large per unit investment cost. As the average sentiment is constant, a subsidy decreasing the investment costs of these agents will "free up" a large amount of sentiment, provoking a large impact on the whole economy. Intuitively, these agents, insensitive to the project's outcome and hence to the actions of others, are influential because they modify their equilibrium behavior only if the others change theirs substantially.