Fairness and efficiency are important aspects that influence cooperation in social dilemmas. During a repeated interaction, they have the potential to serve as competing goals for the decision maker. The ability to balance between fairness and efficiency depends, among other things, on available information regarding mutual accountability for the outcomes in an interaction. In this paper, we examine how information regarding mutual interdependencies influences the interplay between fairness and efficiency in repeated Chicken Game. We distinguish between three possible types of fair behavior: mutual cooperation, alternating cooperation, and mutual destruction. Our results show that the first two types of fairness are positively correlated with the availability of social information. In contrast, mutual destructive fairness is not sensitive to the availability of information and is generally avoided. We also find that without information regarding mutual interdependencies, unfairness increases in parallel with efficiency. When social information is available, however, increases in fairness is coupled with a decrease in efficiency, and the best compromise between fairness and efficiency is reached when mutual interdependencies are learned through repeated experiences. We highlight the significance of our results for fair and efficient interaction in repeated social interactions.