Evolutionary Games

In the context of evolutionary biology, the two basic notions of game theory, namely strategy and payoff, have to be re-interpreted. A strategy is not a deliberate course of action, but an inheritable trait and the payoff is the average reproductive success. The ‘players’ are members of a population, all competing for a larger share of descendants. If several variants of a trait occur in a population, then natural selection leads to an increase in the frequency of those variants with higher fitness. If the success of a trait does not depend on its frequency, this will eventually lead to the fixation of the optimal variant. But if the success of a trait is frequency-dependent, then its increase may lead to a composition of the population where other variants do better; this can be analyzed through game theory . This is similar to what happens in population ecology. If the prey is abundant, predators will increase for a while. But this increase reduces the abundance of prey and eventually leads to a decrease of the predators.

Examples

Evolutionary game theory studies the behavior of large populations of agents who repeatedly engage in strategic interactions. Changes in behavior in these populations are driven either by natural selection via differences in birth and death rates, or by the application of decision rules by individual agents. In that sense, evolutionary game theory merges population ecology with game theory .

The evolution of cooperation through reciprocation i.e the prisoner’s dilemma game is a particularly extensive chapter of evolutionary game theory. Many species engage in interactions that seem to be of the prisoner’s dilemma type. Recently, a prisoner’s dilemma type of interaction has been uncovered for an RNA phage — a virus that reproduces inside a bacterium . When competitive interactions among viruses were studied in the RNA phage at high and low multiplicities of infection (that is, at high and low ratios of infecting phage to host cells), it was found that at high multiplicities, many phages infect and reproduce in the same host cell. Whereas at low multiplicities, the viruses reproduce mainly as clones. An unexpected result of this study was that phage grown at high rates of co-infection increased in fitness initially, but then evolved to lowered fitness.  These data conform to the evolution of lowered fitness in a population of defectors. Generally, any form of associative interaction favors cooperation .

Similarly, Gibbons and colleagues presented a model for evolving coordination in a simulated world of agents playing the prisoner’s dilemma . The agents inhabit a simple grid-like world where each cell on the grid can host one agent. Each agent may interact with agents located in a neighboring cell. Each agent may also view agents located in this neighborhood and can move to an adjacent cell.

Additionally, each agent is represented by a genotype comprising seven bits. The first bit determines how the agent will interact in the game: cooperate or defect. The remaining bits determine how an agent will move. If an agent encounters a cooperator, they have a set of potential actions. These actions are as follows: remain where they are, move randomly, follow the cooperator or flee from it. Similarly, these potential actions are mirrored when an agent encounters a defector. The final two bits are used to determine actions for when an agent encounters both a defector and a cooperator. The actions are: flee from both; follow both; follow the cooperator and flee from the defector and the converse action (flee from the cooperator and follow the defector). During simulation, each potential action of an agent is determined by the genotype. Each interaction involves pairs of agents participating in the Prisoner’s Dilemma. After several iterations, the accumulated score is taken as a measure of fitness. Agents for the next generation are initially selected based on this fitness score —the higher the better. Agents are also subject to mutation (at predefined rates) to allow for more diversity in the population. 

Overall, the same behaviors evolved across all scenarios: agents evolved to move toward cooperators and to flee from defectors. This was true for both cooperators and defectors as both gained in fitness from interacting with cooperators and both achieved reduced fitness from defector interactions. When a cooperator encountered a  cooperator, they learned to ‘follow’ each other and coordinated their movements to gain high rewards for increased interactions involving mutual cooperation. When a cooperator encountered a defector, the ‘flee’ behavior quickly dominated for the cooperator in an attempt to avoid exploitation by those who defect. When a cooperator encountered both cooperators and defectors, they quickly evolved to follow cooperators and flee from defectors. This led to agents that cooperate and cluster together resulting in a form of emergent coordination. The results show that by allowing agents to evolve both their actions and their movements, both cooperation and coordination can be induced in an artificial world. The agents’ behaviors lead to an emergent form of coordination for cooperators who attempt to follow each other while fleeing defectors which increases their frequency of cooperative interactions. This model and experiment show that coordinated movement is indeed evolved.

Citations

Gibbons, M., O’Riordan, C., & Griffith, J. (2014). Evolution of Coordinated Behaviour in Artificial Life Simulations. Proceedings of the International Conference on Theory and Practice in Modern Computing. https://womencourage.acm.org/archive/2015/pdf/papers/paper_3a.pdf
Sigmund, K., & Nowak, M. A. (1999). Evolutionary game theory. Current Biology, 9(14), R503–R505. https://www.cell.com/current-biology/pdf/S0960-9822(99)80321-2.pdf
Turner, P. E., & Chao, L. (1999). Prisoner’s dilemma in an RNA virus. Nature, 398(6726), 441–443. https://doi.org/10.1038/18913