Abstract | ||
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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. |
Year | Venue | Field |
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2012 | CoRR | Mathematical economics,Isoelastic utility,Computer science,Expected utility hypothesis,Euclidean space,Network topology,Risk aversion,Nash equilibrium,Bounded function,Stochastic game |
DocType | Volume | Citations |
Journal | abs/1204.6552 | 2 |
PageRank | References | Authors |
0.38 | 8 | 4 |
Name | Order | Citations | PageRank |
---|---|---|---|
Rajesh Hemant Chitnis | 1 | 101 | 8.44 |
MohammadTaghi Hajiaghayi | 2 | 3082 | 201.38 |
Jonathan Katz | 3 | 7579 | 347.97 |
Koyel Mukherjee | 4 | 31 | 5.45 |