The formation of 2-pyrone derivatives by the reaction of CO₂ with a model internal alkyne, 2-butyne, in the presence of (cod)₂Ni and a bisphosphine ligand (dppb), was studied using the M06/6-311G(d,p) density functional theory method, which revealed that the reaction takes place in three stages. The first stage is the formation of the 2-butyne complex intermediate (dppb)Ni(η²-MeC≡CMe). There are several pathways for the formation of 2-pyrone complexes from it, and the more favorable two pathways were found among them. In the second stage, the coupling of (dppb)Ni(η²-MeC≡CMe) with 2-butyne or CO₂ produces nickelacyclopentadiene or oxanickelacyclopentenone with the Ni–O bond, respectively. In the third stage, the reaction of CO₂ with nickelacyclopentadiene or that of 2-butyne with oxanickelacyclopentenone produces 2-pyrone Ni complexes. The rate-limiting step is the second, in which nickelacyclopentadiene or oxanickelacyclopentenone is formed. The formation of oxanickelacyclopentenone with the Ni–O bond is kinetically more favorable, while the formation of nickelacyclopentadiene is thermodynamically more favorable. Thus, depending on the experimental conditions, the two pathways are in competition. This supports the mechanisms suggested by Inoue et al. and Hoberg et al., and we discuss the factors that make these mechanisms more favorable.