With the evolution of Artificial intelligence (AI), emotional artificial intelligence service agents (AISA) have become common in service industry. However, how artificial empathy of AISA contributes to customer acceptance remains an open question. This study draws on Anthropomorphism Theory and Customer AI Experience Theory to examine whether and how artificial empathy has influence on customer acceptance of AISA. Evidence from three experiments (N=1057) designed by the Experimental vignette method (EVM) shows that: (1) artificial empathy including perspective-taking, empathic concern and emotional contagion has a positive impact on customer acceptance of AISA (study 1); (2) customer AI experience (emotional experience quality, social experience activation and social experience quality) mediates the relationship between artificial empathy and customer acceptance of AISA (study 2); (3) artificial empathy for hedonic (vs. utilitarian) services leads to a stronger effect on customer acceptance of AISA (study 3). This paper enriches our understanding of artificial empathy and provides practical guidance for practitioners strategically managing AISA services in AI-enabled marketing interactions.