Consider discrete-time linear distributed averaging dynamics, whereby agents in a network start with uncorrelated and unbiased noisy measurements of a common underlying parameter (state of the world) and iteratively update their estimates following a non-Bayesian rule. Specifically, let every agent update her estimate to a convex combination of her own current estimate and those of her neighbors in the network. As a result of this iterative averaging, each agent obtains an asymptotic estimate of the state of the world, and the variance of this individual estimate depends on the matrix of weights the agents assign to self and to the others. We study a game-theoretic multi-objective optimization problem whereby every agent seeks to choose her self-weight in such a convex combination in a way to minimize the variance of her asymptotic estimate of the state of the unknown parameters. Assuming that the relative influence weights assigned by the agents to their neighbors in the network remain fixed and form an irreducible and aperiodic relative influence matrix, we characterize the Pareto frontier of the problem, as well as the set of Nash equilibria in the resulting game.

翻译：考虑离散时间线性分布平均动态,让网络中的代理开始对一个共同基本参数(世界状况)进行不相干和不偏袒的噪音测量,并根据非巴伊西亚规则反复更新其估计值。具体地说,让每个代理更新其估计值,将其目前估计值与网络中邻居的估计值相混合。由于这一迭代平均值,每个代理获得对世界状况的无症状估计值,而这一个人估计值的差异取决于代理自我分配和他人分配的重量矩阵。我们研究一个游戏理论性多目标优化问题,即每个代理试图在这种螺旋组合中选择其自重,以尽量减少她对未知参数状况的无症状估计值差异。假设代理商对网络中邻居的相对影响权重保持不变,形成一个不可降低的定期相对影响矩阵,我们将该问题的Pareto边界定性为问题,以及由此产生的游戏中的Nash equilibria。