Here is a very quick and incomplete list. Some papers are less directly related, e.g., “Contests for status” is not about innovation contests per se, but if we know that a large appeal from inducement prizes comes from status (as the report also points out), we might still learn something from the paper.
Edit: added *s to indicate papers more directly related.
*Taylor, C. R. (1995). Digging for golden carrots: An analysis of research tournaments. The American Economic Review, 872-890.
Moldovanu, B., & Sela, A. (2001). The optimal allocation of prizes in contests. American Economic Review, 91(3), 542-558.
*Che, Y. K., & Gale, I. (2003). Optimal design of research contests. American Economic Review, 93(3), 646-671.
Yildirim, H. (2005). Contests with multiple rounds. Games and Economic Behavior, 51(1), 213-227.
Moldovanu, B., & Sela, A. (2006). Contest architecture. Journal of Economic Theory, 126(1), 70-96.
Moldovanu, B., Sela, A., & Shi, X. (2007). Contests for status. Journal of political Economy, 115(2), 338-363.
*Ding, W., & Wolfstetter, E. G. (2011). Prizes and lemons: procurement of innovation under imperfect commitment. The RAND Journal of Economics, 42(4), 664-680.
*Fu, Q., Lu, J., & Lu, Y. (2012). Incentivizing R&D: Prize or subsidies?. International Journal of Industrial Organization, 30(1), 67-79.
Halac, M., Kartik, N., & Liu, Q. (2017). Contests for experimentation. Journal of Political Economy, 125(5), 1523-1569.
*Letina, I., & Schmutzler, A. (2019). Inducing variety: A theory of innovation contests. International economic review, 60(4), 1757-1780.
*Gross, D. P. (2020). Creativity under fire: The effects of competition on creative production. Review of Economics and Statistics, 102(3), 583-599.
*Benkert, J. M., & Letina, I. (2020). Designing dynamic research contests. American economic journal: Microeconomics, 12(4), 270-89.
*Che, Y. K., Iossa, E., & Rey, P. (2021). Prizes versus contracts as incentives for innovation. The Review of Economic Studies, 88(5), 2149-2178.
*Lemus, J., & Marshall, G. (2021). Dynamic tournament design: Evidence from prediction contests. Journal of Political Economy, 129(2), 383-420.
*Erkal, N., & Xiao, J. (2021). Scarcity of ideas and optimal prizes in innovation contests. Available at SSRN.
*Chen, B., Chen, B., & Knyazev, D. (2022). Information disclosure in dynamic research contests. The RAND Journal of Economics, 53(1), 113-137.
This seems like a great effort, and I do not want to be overly critical. I would just like to point out that the report overlooks quite a few papers from economics (as distinct from management), which look at strategic behavior in innovation contests, optimal design of innovation contests, and empirical evaluations of existing contests. Since the report states in the intro that one of the main goals is the review of the existing literature, this seemed like an important point.