{
  "@context": "https://w3id.org/codemeta/3.0",
  "@type": "SoftwareSourceCode",
  "name": "Claim Verification: \u201cConsider a sector with N \u2265 2 symmetric firms, each endowed with L task-positions. Each firm i chooses an automation rate \u03b1\u1d62 in [0,1], paying wage w per human-staffed task and cost c per automated task, with integration friction cost (k/2) \u00b7 L \u00b7 \u03b1\u1d62\u00b2 where k > 0. Aggregate sectoral demand is D = A + \u03bb \u00b7 w \u00b7 L \u00b7 [N - (1-\u03b7) \u03a3\u2c7c \u03b1\u2c7c], where A > 0 is exogenous demand, \u03bb  (0,1] is workers' marginal propensity to consume from wages, and \u03b7  [0,1) is the fraction of displaced wage income recovered through reemployment. Each firm's revenue is D/N (equal market shares). Define s = w - c > 0 and  = \u03bb(1-\u03b7)w > 0. Each firm i maximizes \u03c0\u1d62 = D/N - wL(1-\u03b1\u1d62) - cL\u03b1\u1d62 - (k/2)L\u03b1\u1d62\u00b2. The Nash equilibrium automation rate is \u03b1NE = (s - /N)/k. The cooperative optimum is \u03b1CO = (s - )/k. The difference \u03b1NE - \u03b1CO =  \u00b7 (1 - 1/N)/k is strictly positive.\u201d \u2014 Proved",
  "description": "Verdict: PROVED",
  "version": "1.18.0",
  "dateCreated": "2026-04-16",
  "license": "https://spdx.org/licenses/MIT",
  "codeRepository": "https://github.com/yaniv-golan/proof-engine",
  "url": "https://proofengine.info/proofs/consider-a-sector-with-n-2-symmetric-firms-each-endowed-with-l-task-positions/",
  "author": [
    {
      "@type": "Organization",
      "name": "Proof Engine"
    }
  ]
}