Generalized predator-prey model and its application in cooperative games in call centers

Abstract

The Predator-Prey (Collection Agent-Debtor) model is defined for two players. However, from the perspective of Game Theory, it can be generalized to N-players, here strategic allies appear, with totally different behaviors. Where for three players: the variables 0 ≤ x(t) ≤ 1, 0 ≤ y(t) ≤ 1, 0 ≤ z(t) ≤ 1 will go on to represent probabilities, and will converge to unity in cooperative equilibrium, in an optimal time totally different from the infinite value as follows: lím _t→t*<<∞ x(t) = 1, lím _t→t*<<∞ y(t)  = 1, lím _t→t*<<∞ z(t) = 1. Using the information from a call center transformed into text in order to find the behavior patterns of debtors and collection agents, we obtain competitive and cooperative equilibria. In summary, we technically demonstrate that human intelligence does not need infinite time to find the optimum between debtors and agents, represented by tranquility and the cessation of conflict (debtor-collection agent balance). Finally, it is always possible to find a solution to a debt dispute. Furthermore, from the perspective of banks, cooperatives and collection companies, we have achieved their objective by achieving cooperative behavior from debtors in the face of unresolved conflicts that had legal outcomes, with lawsuits and coercive measures.