We study a persuasion game à la Kamenica and Gentzkow (2011) where players are ambiguity averse with maxmin expected utility (Gilboa and Schmeidler, 1989). With no prior ambiguity, a Sender may choose to use ambiguous communication devices. Our main result characterizes the value of optimal ambiguous persuasion, which is often higher than what is feasible under Bayesian persuasion. We characterize posteriors that are potentially plausible when they are generated by ambiguous devices. One way to construct an optimal ambiguous communication device is by using synonyms, messages that lead to the same posteriors, in which Sender can hedge himself against ambiguity while inducing actions from Receiver that would not be possible under standard Bayesian persuasion. We also show that the use of synonyms are a necessary * We are grateful to the Editor, Marciano Siniscalchi, and two anonymous referees for very constructive comments and suggestions that have significantly improved the paper. We are also grateful to Pierre

The influence of cultural industry competitiveness on economic growth is analyzed by using grey relational degree method. Then, the influence of cultural industry on the three industries is analyzed and compared in the same way. On this basis, further from the cultural industry, the impacts of core layer, outer layer, and related layer on economic growth were compared and analyzed. Finally, the economic growth model is used to measure the impact of investment, labor, and innovation in cultural industry on economic growth. The results show that cultural industry has a great influence on economic growth. The cultural industry has an obvious driving effect on the tertiary industry. The correlative layer of cultural industry has the greatest influence on economic growth. Cultural industry innovation has a huge pulling effect on economic growth. The SPSS software was used to process the data, and the data indicators were screened. Finally, the grey relational degree model was constructed. Then, the improved diamond model was used to select the influential factors of the development of cultural industry, and the main influencing factors were found out through the grey relational degree analysis. This paper analyzes the factors affecting economic benefits and puts forward countermeasures. The results show that it is of great significance to pay attention to the development of cultural manufacturing industry in cultural industry and promote cultural innovation to promote economic growth.