基于DARPA网络挑战的博弈模型
A Game-Theoretic Model Motivated by the DARPA Network Challenge
摘要：
在本文中，我们提出了一个博弈论模型来分析类似于2009年\emph{DARPA Network Challenge}，这是由美国国防高级研究计划局（DARPA）组织的探索的作用，互联网和社交网络发挥激励广域合作的事件。挑战是组成一个小组，第一个找到美国各地十个停泊的气象气球的位置。我们考虑一个模型，其中$N$人（谁可以形成组）位于一些拓扑结构与固定的覆盖体积周围的每个人的地理位置。我们考虑各种拓扑的球员可以位于如欧几里德$d$维空间和顶点的图。一个气球被放置在空间中，如果一个小组第一个报告气球的位置，则该小组获胜。团队越大，找到气球的概率越高，但我们假设奖金在团队成员中平均分配。因此，有一个竞争的紧张局势，以保持团队尽可能小。\emph{Risk aversion}是一个人不愿意接受一个不确定回报的交易，而不是另一个更确定的交易，但可能更低，预期回报。在我们的模型中，我们考虑的\emph{isoelastic}效用函数来自阿罗-普拉特测量的相对风险厌恶。主要目的是分析我们模型的纳什均衡中的群体结构。对于$d$维欧几里德空间（$d\geq 1$）和有界度正则图类，我们表明，在任何纳什均衡的\emph{richest}组（具有最大期望效用的人）覆盖了一个恒定的分数的总体积。
英文摘要：
In this paper we propose a game-theoretic model to analyze events similar to the 2009 \emph{DARPA Network Challenge}, which was organized by the Defense Advanced Research Projects Agency (DARPA) for exploring the roles that the Internet and social networks play in incentivizing wide-area collaborations. The challenge was to form a group that would be the first to find the locations of ten moored weather balloons across the United States. We consider a model in which $N$ people (who can form groups) are located in some topology with a fixed coverage volume around each person's geographical location. We consider various topologies where the players can be located such as the Euclidean $d$-dimension space and the vertices of a graph. A balloon is placed in the space and a group wins if it is the first one to report the location of the balloon. A larger team has a higher probability of finding the balloon, but we assume that the prize money is divided equally among the team members. Hence there is a competing tension to keep teams as small as possible. \emph{Risk aversion} is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff. In our model we consider the \emph{isoelastic} utility function derived from the Arrow-Pratt measure of relative risk aversion. The main aim is to analyze the structures of the groups in Nash equilibria for our model. For the $d$-dimensional Euclidean space ($d\geq 1$) and the class of bounded degree regular graphs we show that in any Nash Equilibrium the \emph{richest} group (having maximum expected utility per person) covers a constant fraction of the total volume.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
