A Probabilistic Model of Criticality in a Sequential Public Good Dilemma.

A public good (PG) is a commodity or service made available to all members of a group: its provision depends on the voluntary contribution of its members. Once provided, all members can enjoy the benefits of the PG, regardless of whether they contributed or not; hence, there is a temptation to "free-ride" in the hope that others will contribute. Rapoport (1987) showed that an important factor that affects cooperation (contribution) in a PG dilemma is the extent to which a group member is critical in providing it. Erev and Rapoport (1990) tested a game-theoretic model that yields deterministic predictions about the effects of criticality on cooperation in public good dilemmas. Based on research by Chen, Au, and Komorita (1996), we propose a probabilistic model of criticality. The model is tested and found to fit empirical data. Extensions of the model to situations with uncertain group size or provision point are discussed. Copyright 1998 Academic Press.