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We analyze the conditions under which the emergence of frequently observedechelon formation can be explained solely by the maximization of energysavings. We consider a two-dimensional multi-agent echelon formation, whereeach agent receives a benefit that depends on its position relative to theothers, and adjusts its position to increase this benefit. We analyze theselfish case where each agent maximizes its own benefit, leading to aNash-equilibrium problem, and the collaborative case in which agents maximizethe global benefit of the group. We provide conditions on the benefit functionunder which the frequently observed echelon formations cannot be Nashequilbriums or group optimums.  We then show that these conditions are satisfied by the conventionally usedfixed-wing wake benefit model. This implies that energy saving alone is notsufficient to explain the emergence of the migratory formations observed, basedon the fixed-wing model. Hence, either non-aerodynamic aspects or a moreaccurate model of bird dynamics should be considered to construct suchformations.

Are energy savings the only reason for the emergence of bird echelon formation?