Social game for building energy efficiency: Incentive design

We present analysis and results of a social game encouraging energy efficient behavior in occupants by distributing points which determine the likelihood of winning in a lottery. We estimate occupants utilities and formulate the interaction between the building manager and the occupants as a reversed Stackelberg game in which there are multiple followers that play in a non-cooperative game. The estimated utilities are used for determining the occupant behavior in the non-cooperative game. Due to nonconvexities and complexity of the problem, in particular the size of the joint distribution across the states of the occupants, we solve the resulting the bilevel optimization problem using a particle swarm optimization method. Drawing from the distribution across player states, we compute the Nash equilibrium of the game using the resulting leader choice. We show that the behavior of the agents under the leader choice results in greater utility for the leader.