Towards an Extended Evolutionary Game Theory with Survival Analysis and Agreement Algorithms for Modeling Uncertainty, Vulnerability, and Deception

Abstract

Competition , cooperation and communication are the three fundamental relationships upon which natural selection acts in the evolution of life. Evolutionary game theory (EGT) is a 'marriage' between game theory and Darwin's evolution theory; it gains additional modeling power and flexibility by adopting population dynamics theory. In EGT, natural selection acts as optimization agents and produces inherent strategies, which eliminates some essential assumptions in traditional game theory such as rationality and allows more realistic modeling of many problems. Prisoner's Dilemma (PD) and Sir Philip Sidney (SPS) games are two well-known examples of EGT, which are formulated to study cooperation and communication , respectively. Despite its huge success, EGT exposes a certain degree of weakness in dealing with time-, space- and covariate-dependent (i.e., dynamic ) uncertainty , vulnerability and deception . In this paper, I propose to extend EGT in two ways to overcome the weakness. First, I introduce survival analysis modeling to describe the lifetime or fitness of game players . This extension allows more flexible and powerful modeling of the dynamic uncertainty and vulnerability (collectively equivalent to the dynamic frailty in survival analysis). Secondly, I introduce agreement algorithms , which can be the Agreement algorithms in distributed computing (e.g., Byzantine Generals Problem [6][8], Dynamic Hybrid Fault Models [12]) or any algorithms that set and enforce the rules for players to determine their consensus. The second extension is particularly useful for modeling dynamic deception (e.g., asymmetric faults in fault tolerance and deception in animal communication). From a computational perspective, the extended evolutionary game theory (EEGT) modeling, when implemented in simulation, is equivalent to an optimization methodology that is similar to evolutionary computing approaches such as Genetic algorithms with dynamic populations [15][17].