Research Ideas: Asymmetric Evolutionary Games with Type-Specific Resource Constraints

Asymmetric conflicts are at the core of most animal conflicts. The most common example of asymmetric conflict is the fight for gaining access to a territory, where one animal protects its territory and another animal, intruder, tries to take the territory from the incumbent animal. In such conflicts, `incumbent' and `attacker' are two roles of the animals and these two roles have different strategies to implement during the conflict. Hence, in the scholarship of Evolutionary Game Theory (EGT), these conflicts are put under the domain of asymmetric conflicts. 

Till date, asymmetric conflicts are seen to be embedded in symmetric games, as it is assumed that strategies are programs set for `roles' and `roles' can be randomly assumed by a random animal at the time of conflict. The random allotment of role to an animal has facilitated the treatment of asymmetric conflict through the theory of standard EGT which is strictly based on symmetric games. 

I propose a different class of games where the assumption of role by a random animal is not random, but dependent on the identity of the animal. In other words, the type of the animal will decide on the roles that the animal is `allowed' to assume. This constraint on the capacity of assuming roles essentially makes the traditional treatment of asymmetric conflict through symmetric games ineffective. Hence, a restructuring of the standard mathematical notion of evolutionary stability will be required in order to study the evolutionary behavior of this class of games.