When Knowing Early Matters: Gossip, Percolation and Nash Equilibria

TL;DR

This paper analyzes how early information dissemination affects social welfare and individual incentives in networked communication, revealing conditions under which selfish behavior leads to efficient or wasteful outcomes.

Contribution

It introduces a model linking information timing, network structure, and costs, and characterizes Nash equilibria using first passage percolation analysis.

Findings

Nash equilibria can be efficient or wasteful depending on network and cost structure.

Communication speed impacts the efficiency of information spread in equilibrium.

Network topology influences the potential for wasteful or optimal information dissemination.

Abstract

Continually arriving information is communicated through a network of $n$ agents, with the value of information to the $j$'th recipient being a decreasing function of $j/n$, and communication costs paid by recipient. Regardless of details of network and communication costs, the social optimum policy is to communicate arbitrarily slowly. But selfish agent behavior leads to Nash equilibria which (in the $n \to \infty$ limit) may be efficient (Nash payoff $=$ social optimum payoff) or wasteful ($0 < $ Nash payoff $<$ social optimum payoff) or totally wasteful (Nash payoff $=0$). We study the cases of the complete network (constant communication costs between all agents), the grid with only nearest-neighbor communication, and the grid with communication cost a function of distance. The main technical tool is analysis of the associated first passage percolation process or SI epidemic (representing spread of one item of information) and in particular its "window width", the time interval during which most agents learn the item. Many arguments are just outlined, not intended as complete rigorous proofs.