  Autonomous agents can adopt socially-aware behaviors to reduce social costs,
mimicking the way animals interact in nature and humans in society. We present
a new approach to model socially-aware decision-making that includes two key
elements: bounded rationality and inter-agent relationships. We capture the
interagent relationships by introducing a novel model called a relationship
game and encode agents' bounded rationality using quantal response equilibria.
For each relationship game, we define a social cost function and formulate a
mechanism design problem to optimize weights for relationships that minimize
social cost at the equilibrium. We address the multiplicity of equilibria by
presenting the problem in two forms: Min-Max and Min-Min, aimed respectively at
minimization of the highest and lowest social costs in the equilibria. We
compute the quantal response equilibrium by solving a least-squares problem
defined with its Karush-Kuhn-Tucker conditions, and propose two projected
gradient descent algorithms to solve the mechanism design problems. Numerical
results, including two-lane congestion and congestion with an ambulance,
confirm that these algorithms consistently reach the equilibrium with the
intended social costs.
