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We experimentally study intention-based social influence in standard and modified Ultimatum and Impunity games. Standard games with bi-dimensional strategy vectors let individuals decide independently in the role of proposer and responder and allow fairness intentions to be role dependent. Uni-dimensional strategy vectors in modified games constrain individuals to consistent offers and acceptance thresholds. To induce social influence, we randomly match participants in groups of four, which are minimally identified by colors. Social influence is assessed by how one reacts to information about median group intention(s). The 
factorial experimental design varies the order of the two game types and the strategy vector dimensionality. Social influence, depending on the game type and strategy dimensionality, significantly impacts participants’ behavior compared to their own intention. At the aggregate level, however, these differences cancel each other out. As there are more constraints on the action space, uni-dimensionality increases strategic concerns.
