On Information Design with Spillovers

Abstract

An information designer has access to a set of experiments and decides which of these to assign to each of the agents in a directed network. The network encodes informational spillovers: an agent has access to the experiments assigned to him, as well as to others’ experiments that might spill over to him. We study optimal information design (through the assignment of experiments) under a variety of considerations ranging from the mode of spillovers (local vs. global) to lossy information transmission. Our results indicate that in the global spillover case, when each agent follows at most one other agent (i.e., each node has in-degree at most one), the optimal information structure can be obtained in a tractable way. However, the complexity of the problem exhibits a phase transition when some agents follow more than one agent: it becomes NP-hard even when some agents follow two agents, regardless of how simple the communication technology is (characterized in terms of the number of communication thresholds). The tractability under local spillovers has quite a different nature and contrasts with the global spillover case. In this case, we show that the problem is tractable so long as each agent does not follow many agents and the communication technology is simple. However, it becomes intractable with any deviation from these two factors. Finally, we study the implications of our framework for information design in supply chains with spillovers, where a retailer reveals demand-related information to influence upstream investment decisions. We show that by exploiting the special structure of the payoffs in this problem, tractable algorithms can be obtained in even richer settings. We also shed light on how different types of spillovers impact the retailer’s payoff.

Keywords: Information design, information spillovers, communication network, tree decomposition