Social Shaping of Linear Quadratic Multi-Agent Systems

In this paper, we study multi-agent systems with distributed resource allocation at individual agents. The agents make local resource allocation decisions including, in some cases, trading decisions — incurring income or expenditure subject to the resource price and system-level resource availability. The agents seek to maximize their individual payoffs, which accrue from both resource allocation income and expenditure. We define a social shaping problem for the system and show that the optimal price is always below a prescribed socially resilient price threshold. By exploring optimality conditions for each agent, we express resource allocation decisions in terms of piece-wise linear functions with respect to the price for unit resource. We further establish a tight range for the coefficients of the linear-quadratic utilities, under which optimal pricing is proven to be always socially resilient.