Continuous and Step-level Pay-off Functions in Public Good Games: A Conceptual Analysis

Conflicts between individuals’ and collective interests are ubiquitous in social life. Numerous experimental studies have investigated the resolution of such conflicts using public good games with either continuous or step-level payoff functions. A conceptual analysis using both classic game theory and social exchange theory shows that these two types of games are fundamentally different. A continuous function game is a social dilemma in that it contains a conflict between individual and collective interests whereas a step-level game is primarily a social coordination game. Thus, we conclude that one can not safely generalize results from step-level to continuous form games. Additionally, our analysis shows that the distinction between continuous and single-step games can be blurred by segmenting a continuous function into steps or adding steps to a single-step game. We identify characteristics of the payoff function that conceptually mark the transition from a dilemma to a coordination problem.