We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find a stark contrast between how groups and individuals play, with payoffs playing a primary role in equilibrium selection when individuals play, but the structure of the voting rule playing the primary role when groups play. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments.

We explore play between groups where one member of each 2-person group dictates the play of that group and is therefore responsible for the payoff of the other group member. We compare this to play when the game is the same, but each person is playing only for herself. Consistent with the principle of responsibility-alleviation described in Charness (2000), we find that a sense of responsibility for the welfare of others has an effect. While the issue of responsibility does not appear to influence the decisions of 2/3 of the population, almost 90 percent of the remaining 1/3 of the population plays a less risky strategy when choosing for a group than when playing only for herself.