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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Incomplete information network game ： ウィキペディア英語版 Incomplete information network game Network games of incomplete information represent strategic network formation when agents do not know in advance their neighbors, i.e. the network structure and the value stemming from forming links with neighboring agents. In such a setting, agents have prior beliefs about the value of attaching to their neighbors; take their action based on their prior belief and update their belief based on the history of the game.〔Song Y. and M. van der Schaar (2015) “Dynamic Network Formation with Incomplete Information“, Economic Theory, June 2015, Volume 59, Issue 2, pp. 301-331.〕 While games with a fully known network structure are widely applicable, there are many applications when players act without fully knowing with whom they interact or what their neighbors’ action will be.〔Marit, J. and Y. Zenou (2014) “Network Games with Incomplete Information”, NBER Working paper DP10290.〕 For example, people choosing major in college can be formalized as a network game with imperfect information: they might know something about the number of people taking that major and might infer something about the job market for different majors, but they don’t know with whom they will have to interact, thus they do not know the structure of the network.〔Jackson M.O. (2008), Social and Economic Networks, Princeton, NJ: Princeton University Press.〕 == Game theoretic formulation == In this setting,〔 players have private and incomplete information about the network and this private information is interpreted as player's own type (here, private knowledge of own degree). Conditional on their own degree, players form beliefs about the degrees of their neighbors. The equilibrium concept of this game is Bayesian Nash Equilibrium. The strategy of a player is a mapping from the player's degree to the player's action. Let $\backslash textstyle\; \backslash sigma\_\; \backslash in\; ()$ be the probability that a player of degree d chooses action 1. For most degrees (d) the action will be either 0 or 1, but in some cases mixed strategy might occur. The degrees of i's neighbor are drawn from a degree distribution $\backslash textstyle\; \backslash tilde$, where $\backslash textstyle\; \backslash tilde(d)=\backslash frac$ approximates the distribution over a neighbors' degree from the configuration model with respect to a degree sequence represented by P. Given $\backslash textstyle\; \backslash tilde$, the probability that a neighbor takes action 1 is: $\backslash textstyle\; p\_\backslash sigma=\backslash sum\_\; \backslash sigma(d)\; \backslash tilde(d)$. Asymptotically, the belief that exactly m out of the d neighbors of player i choose action 1 follows a binomial distribution $\backslash textstyle\backslash \; p\_^(1-p\_)^$. Thus, the expected utility of player i of degree $\backslash textstyle\; \backslash \; d\_i$ who takes action $\backslash textstyle\; \backslash \; x\_i$ is given by: $\backslash textstyle\backslash \; U\_(x\_i,p\_)=\backslash sum\_^\; u\_(x\_i,m)\; p\_^(1-p\_)^$, where $\backslash textstyle\backslash \; u\_$ is the payoff corresponding to a game played on a certain network structure, in which players choose their strategies knowing how many links they will have but not knowing which network will be realized, given the incomplete information about the link formation of neighbors. Assuming independence of neighbors' degrees, the above formulation of the game does not require knowledge of the precise set of players. The network game is specified by defining a utility $\backslash textstyle\backslash \; u\_d$ for each d and a distribution of neighbor's degrees $\backslash textstyle\; \backslash tilde$. The Bayesian equilibrium of this network game is a strategy $\backslash textstyle\; \backslash sigma(d)$ such that for each d, if $\backslash textstyle\; \backslash sigma(d)>0$, then $\backslash textstyle\backslash \; U\_d(1,p\_)\; \backslash geq\; U\_d(0,p\_)$, and if , then $\backslash textstyle\backslash \; U\_d(1,p\_)\; \backslash leq\; U\_d(0,p\_)$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Incomplete information network game」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.