Game Theory in Urban Birds: A Nash Equilibrium Analysis Using Crows and Pigeons

Abstract

Nash equilibrium, otherwise popularly known as the game theory or Prisoner’s Dilemma is a concept developed by John Nash, a Nobel laureate who was awarded the Nobel Prize for his concept of Game theory. This is a very important concept which has been frequently used in various branches of social sciences, psychology and also in biology. Though the theory or the concept may sound abstract, but has its application in all walks of life, including in our daily activities. The theory has been applied in many situations in social sciences, political scenarios, etc., but the theory has not been extensively studied in biology. Limited studies have been reported on this concept as that of Hawk and dove game, and also to explain certain concepts in behavioural ecology. In the present study, we have modelled the success of two urban bird populations, the crow and the pigeon using the concept of Game theory. According to this concept no player, can gain or change their outcome, by changing their strategy or game alone. In summary it may be said the cooperation is the best way to gain or acquire maximum benefit. This has been explained by modelling the two birds as producers and scroungers. The payoff matrix illustrates that when both the bird’s strategy (s1, s -1) is producers (P,P), then the gain is 4 units each. If the bird’s strategy (s 1, s -1) is that of producer and scrounger (P, S) then the payoff is 2 units each, but if both the bird’s strategy is  (s 1, s -1) is that of scroungers (S, S) then the payoff is 0 each. (null). Suggesting that if both the bird populations, cooperate in their food collecting and eating strategy, there is a greater benefit rather than one acting as a producer, or both acting as scroungers. The success of these two birds, crow and pigeon in highly polluted and populated urban scenario, may be attributed and explained by game theory as proposed by John Nash.