The most common form of civil war in the post-World War II period has been a stalemated guerrilla war confined to a rural periphery of a low-income, post-colonial state. Standard contest models of conflict do not capture important and distinctive features of insurgency, and in particular the fact that guerrilla survival depends on their controlling information about who and where they are. I present a game model in which rebel control of territory depends on how many remain uncaptured by government forces. Capture becomes more likely as the rebel movement expands, due to network connections among the rebels. The model explains how and why insurgencies can remain stalemated at low levels of conflict. It also shows that standard explanations for the strong cross-national association between poverty and civil war risk – for example, that poverty makes joining a rebel band a more attractive option or that risk aversion makes the rich more fearful of conflict – are incoherent or strongly incomplete as typically stated. I argue that more plausible explanations for the empirical regularity pose an indirect link, via the association of high income with (a) natural and social terrains inimical to guerrilla hiding, (b) possibly state military capability to conduct more efficient counterinsurgency, and (c) inability to appropriate as large a share of income through house-to-house visits by guerrillas, due in part to the mobility of human capital.