Endogenous thresholds and assurance networks in collective action

This article treats a multi-player Stag Hunt where each player may have a different threshold (the number of other players that need to act along with the player for benefits of collective action to arise). Players are modeled as solving the strategic-uncertainty problem of whether or not to act, by assuring each other of their willingness to act. We show that in equilibrium there may, but need not, be homophily (players with the same thresholds seek assurance from each other) or a threshold-based social hierarchy (players with high thresholds, or “conservatives,” seek assurance from players with low thresholds, or “radicals,” but not vice versa). Put otherwise, a new strategic-uncertainty problem arises, namely, the problem of who should seek assurance from whom. We propose that players solve this problem by forming core-periphery assurance networks, with a number of players equal to the largest threshold in the core, and the remaining players in the periphery.