Karl Sigmund applies mathematics to the evolution of cooperation. His work in evolutionary game theory examines how strategies spread when their success depends on interactions with other individuals.[ref]
https://www.leopoldina.org/en/members/member-list/detail/karl-sigmund. Leopoldina research profile; evolutionary game theory, replicator dynamics and cooperation
With Martin A. Nowak, Sigmund developed a 1998 model of indirect reciprocity: an individual may help someone because that person's previous behaviour has established a favourable reputation, even if the same pair never meets again. The analysis combined mathematical conditions for stability with computer simulations of changing strategy frequencies.[ref]
For example, A helps B, C learns of the act, and C later helps A. The return to A passes through another individual instead of requiring repayment by B. The scientific question is which information and decision rules allow such behaviour to persist against alternatives that avoid the cost of helping. A reputation mechanism makes those rules explicit; it does not establish that every apparently generous action is explained by the same process.[ref]
Evolution of indirect reciprocity by image scoring by Martin A. Nowak and Karl Sigmund. Model of reputation-based donor decisions without repeated pair encounters
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Karl Sigmund is an Austrian mathematician and theoretical biologist known for his work in various fields, including evolutionary biology, game theory, and mathematical ecology. He has made significant contributions to understanding evolutionary strategies and the dynamics of populations. Sigmund has also contributed to the mathematical modeling of social behaviors and the application of game theory to biology, among other topics.