To　reveal　the　causes　of　unlawful　behaviours　between　special　equipment　quality　supervision　institutions　and　third-party　special　equipment　inspection　institutions,　an　evolutionary　game　model　was　developed.　Since　the　expected　payoff　matrix　frequently　used　in　general　game　model　cannot　accurately　describe　the　influence　of　the　risk　expectations,　the　prospect　value　function　was　proposed　to　build　the　revenue　perception　matrix　of　the　model.　Then,　the　evolutionary　characteristics　were　analysed　through　replicator　dynamics　equations.　Accordingly,　the　evolutionary　stable　strategies　were　obtained　based　on　the　Jacobian　matrix.　Moreover,　the　dynamic　evolution　phase　diagrams　were　formulated　to　describe　the　behaviours.　Finally,　numerical　simulation　examples　were　conducted　to　investigate　the　evolutionary　path　and　the　evolutionarily　stable　strategies.　Results　show　that　the　probability　of　the　third-party　special　equipment　inspection　institution　choosing　the　passive　performance　strategy　is　negatively　correlated　with　the　expected　risk　value.　The　supervision　probability　of　the　quality　supervision　institution　is　directly　proportional　to　the　social　benefits.　In　addition,　the　supervision　probability　is　dependent　on　the　penalty　risks,　and　the　initial　population　scale.