Diffusion control games with rank-based rewards

• Applicant: Professor Dr. Stefan Ankirchner
• Subject Area: Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 448228684

• Final Report Year: 2025

Final Report Abstract

The general aim of the project was to contribute to the understanding of how interaction and rank-based rewards impact the dynamic risk choices of economic agents. To this end, the project has analyzed a symmetric game where the players can dynamically control the diffusion intensity of individual state processes and where the terminal reward of each player depends on the rank of her state process at a given finite time horizon. The project has put a focus on two special cases of the game: first, the zero-sum 2-player game version, and second the mean-field version of the game. In both cases we have found Nash equilibria in closed form. In particular, it has been shown that the mean-field equilibrium provides an approximate equilibrium for games with a large number of players.

Publications

• A simple random walk game. HAL-03607763v1
  S. Ankirchner, H. Bernburg & J. Wendt
  
• Diffusion control and games. Dissertationsschrift, Friedrich Schiller-Universität Jena
  J. Wendt
  
• Large Ranking Games with Diffusion Control. Mathematics of Operations Research, 49(2), 675-696.
  Ankirchner, Stefan; Kazi-Tani, Nabil; Wendt, Julian & Zhou, Chao
  
• Mean-field ranking games with diffusion control. Mathematics and Financial Economics, 18(2-3), 313-331.
  Ankirchner, S.; Kazi-Tani, N.; Wendt, J. & Zhou, C.
  
• The Role of Correlation in Diffusion Control Ranking Games. SIAM Journal on Control and Optimization, 62(3), 1465-1489.
  Ankirchner, Stefan; Kazi-Tani, Nabil & Wendt, Julian
  
• A Sharp Upper Bound for the Expected Interval Occupation Time of Brownian Martingales. Journal of Theoretical Probability, 38(4).
  Ankirchner, Stefan & Wendt, Julian
  
• Two-Player Diffusion Control Games with Private Information. Applied Mathematics & Optimization, 92(2).
  Wendt, Julian