Comparison Between Public and Private Signals in Network Congestion Games
摘要
This paper addresses an information design problem in a non-atomic network congestion game, where agents seek to move from their origins to their destinations through the fastest path. The information designer, who observes the true state of the world, sends signals to the agents to minimize the expected total travel time (ETTT). We explore two types of signaling policies: public policies and private i.i.d. policies. A public policy provides the same signal to all agents, while private i.i.d. policies can assign different signals to each agent, drawn from the pre-committed distribution. While the best i.i.d. policy consistently archives the lower ETTT, the best public policy is much easier to compute, utilizing a convexification approach. When each cost function is a sum of (i) an affine function of its share and (ii) state-dependent terms, perfect disclosure of the true state proves optimal among all public policies, achieving ETTT at most 4/3 times that of the best private i.i.d. policy. Finally, we introduce a deep neural network model to approximate the optimal private i.i.d. policy.