  We study techniques to incentivize self-interested agents to form socially
desirable solutions in scenarios where they benefit from mutual coordination.
Towards this end, we consider coordination games where agents have different
intrinsic preferences but they stand to gain if others choose the same strategy
as them. For non-trivial versions of our game, stable solutions like Nash
Equilibrium may not exist, or may be socially inefficient even when they do
exist. This motivates us to focus on designing efficient algorithms to compute
(almost) stable solutions like Approximate Equilibrium that can be realized if
agents are provided some additional incentives. Our results apply in many
settings like adoption of new products, project selection, and group formation,
where a central authority can direct agents towards a strategy but agents may
defect if they have better alternatives. We show that for any given instance,
we can either compute a high quality approximate equilibrium or a near-optimal
solution that can be stabilized by providing small payments to some players. We
then generalize our model to encompass situations where player relationships
may exhibit complementarities and present an algorithm to compute an
Approximate Equilibrium whose stability factor is linear in the degree of
complementarity. Our results imply that a little influence is necessary in
order to ensure that selfish players coordinate and form socially efficient
solutions.
