Evolutionary game theory of scarce resources


Keywords:
Mathematical modelling
Cellular automata
Evolution
Evolutionary games
Complex systems
Emergence


The principles of Darwinian evolution were discovered long ago but their consequences for networks of randomly interacting organisms are still actively researched. Some generic features of evolution, such as speciation, convergence, cooperativity etc., can be modelled by Evolutionary Game Theory (EGT). In EGT, the complex competitive processes of life are modelled by simple agents playing a simple game. They reproduce and die according to the game’s outcome, and their offspring inherit imperfect copies of the parent’s strategy.


In this project, a student will investigate the application of EGT to various paradigmatic models, in the regime where the opportunities to exploit natural resources are rare compared with the rate of birth and death. In recent work [1], it was shown that this regime can lead to the evolution of risk-aversion and can thereby explain the evolution of altruism - a phenomenon that has long been studied in the literature but is still not fully understood. That recent investigation [1] included the discovery of a generally-applicable theorem, but was applied to only one game (the ultimatum game) of the many standard paradigms in the EGT literature.


(i) The student will further test the new theorem to understand whether the results are generalisable to other standard games in the non-standard regime of scarce resources. This will involve analytical calculations for simple cases and some numerical simulations involving very large numbers of agents.

(ii) The student will investigate a novel hybrid model, designed to investigate how rare, high-value events influence the evolution of strategies for common, low-value interactions. This will model whether rare events in an organism's evolutionary history, such as famines and gluts, can account for day-to-day altruism.

(iii) The student will have the opportunity to interact with colleagues (both theorists and experimentallists) within the UK and internationally. This will potentially allow the student to explore the relationship between the abstract mathematical models and real microbial populations.

References

[1] R M L Evans, 'Pay-off scarcity causes evolution of risk-aversion and extreme altruism', Sci. Rep 8:16074 (2018)

See also https://physicsbloke.blogspot.com/2018/11/evolutionary-games-and-altruism-in-face.html