Most algorithmic studies on multi-agent information design so far have focused on the restricted situation with no inter-agent externalities; a few exceptions investigated truly strategic games such as zero-sum games and second-price auctions but have all focused only on optimal public signaling. This paper initiates the algorithmic information design of both \emph{public} and \emph{private} signaling in a fundamental class of games with negative externalities, i.e., singleton congestion games, with wide application in today's digital economy, machine scheduling, routing, etc. For both public and private signaling, we show that the optimal information design can be efficiently computed when the number of resources is a constant. To our knowledge, this is the first set of efficient \emph{exact} algorithms for information design in succinctly representable many-player games. Our results hinge on novel techniques such as developing certain "reduced forms" to compactly characterize equilibria in public signaling or to represent players' marginal beliefs in private signaling. When there are many resources, we show computational intractability results. To overcome the issue of multiple equilibria, here we introduce a new notion of equilibrium-\emph{oblivious} hardness, which rules out any possibility of computing a good signaling scheme, irrespective of the equilibrium selection rule.
翻译:到目前为止,关于多试剂信息设计的大多数算法研究都侧重于有限的情况,没有代理外差因素;少数例外调查了真正战略性的游戏,如零和游戏和第二价格拍卖,但都只侧重于最佳公共信号。本文启动了计算信息设计法设计,包括: emph{public} 和\emph{public} 私人,在带有负面外差的基本游戏类别中发出信号,即单吨拥堵游戏,在当今的数字经济中广泛应用,机器时间安排,路由等。对于公共和私人信号,我们显示在资源数量不变时,最佳信息设计可以有效计算。据我们所知,这是第一套高效的计算信息设计计算法,简洁地代表许多玩家游戏。我们的结果取决于一些新技术,如开发某些“诱导形式”,在公共信号中或代表玩家在私人信号中的边际信仰,我们在这里展示的是可计算性规则。我们在这里展示的是可计算性,这是计算性规则的可变性结果。 不论多重平衡性概念的多重平衡性,无论是何为难的。