Self-organizing collective action: group dynamics by collective reputation

ABSTRACT

This paper analyzes the dynamics of collective action through collective reputation, which indicates the extent to which groups succeed. Many previous works introduced psychological traits such as irrationality and a sense of fairness to explain the diffusion of collective action. However, this paper analyzes the relationship between cooperation and dynamic change in group size using game-theoretic models. The results show the sets of parameters in which positive feedback between cooperation and group size occurs. In these parameter sets, cooperation creates a good collective image (reputation) and encourages outsiders to join the group. In turn, the group expansion gives them incentives to cooperate. Additionally, when this positive feedback functions, punishment is found to be unnecessary for cooperation.

KEYWORDS:

• Dynamics of collective action
• game theory
• group size
• collective reputation

Funding

This work was supported by the Japan Society for the Promotion of Science [Grant-in-Aid for JSPS Fellows (15J11199)]

Notes

¹ Of course, the number of the members exiting the group must be a natural number, but in this paper, it is defined as a real number approximately. This approximation precludes us from predicting the actual dynamics of the group. However, this is not a serious problem in terms of the proof of an equilibrium, because the players calculate the “expected” payoff based on the “expected” number of members, which is not the “actual” number of group members but an “expectation” about the group size.

² Note that in this type of CRE, is defined not as a probability but as a rate for the same reason as in the definition of . Because of this, the change in group size is deterministic (with probability one). Thus, the “expected” number of group members is not an exact expression, because “probability one” is not the probability measure. However, here, we use this expression for future extension to a stochastic model.

³ Note that in this type of CRE, is defined not as a probability but as a rate for the same reason as in the definition of and (see Notes 1 and 2).

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science [Grant-in-Aid for JSPS Fellows (15J11199)]