当知道早期的事情：流言，渗滤和纳什均衡
When Knowing Early Matters: Gossip, Percolation and Nash Equilibria
摘要：
连续到达的信息通过$n$代理的网络进行通信，到达第$j$接收者的信息的价值是$j/n$和接收者支付的通信费用的减函数。无论网络和通信成本的细节如何，社会最优策略都是任意缓慢地通信。但自私的代理人行为导致纳什均衡（在$n \to \infty$极限）可能是有效的（纳什收益$=$社会最优收益）或浪费的（$0 < $纳什收益$<$社会最优收益）或完全浪费的（纳什收益$=0$）。我们研究的情况下，完整的网络（所有代理之间的通信成本不变），网格只有最近的邻居通信，和网格的通信成本的函数的距离。主要的技术工具是分析相关的第一通道渗透过程或SI流行病（代表一个信息项的传播），特别是其“窗口宽度”，大多数代理人学习该项目的时间间隔。许多论点只是概述，并不打算作为完整的严格证明。
英文摘要：
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.
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