Looking for Bidding Teammates: A Game-Theoretic Model of Stranger Collusion in Peer Review

Paper bidding is the entry point to reviewer assignment at large machine learning conferences: reviewers declare interest in submissions, and an optimizer combines those bids with automated affinity scores. Reviewers who have never met now recruit each other on public social platforms, exchange submission identifiers, bid on each other's papers, and reciprocate with inflated scores. Existing collusion models take the group as given and assume its members already trust one another. We give the first game-theoretic model of collusion formation in peer review: a four-stage game over recruitment, identifier exchange under the risk of being reported, bidding neither party can verify, and reciprocal reviewing. The model predicts the arrangement cannot form, because the benefit at stake is delivered by the partner's separate decision, so reciprocation is never individually rational for any payoffs and the game unravels to the recruitment post. What closes the gap is enforcement rather than incentives: authors always see the reviews of their own paper, deadlines recur, and the group remembers who reciprocated. We give the sustainability condition and the detection rate above which no partnership survives, and show review-writing effort enters both, so cheap machine-assisted reviewing enlarges the sustainable set with no change in detection or sanctions. In a calibrated end-to-end conference simulation no detector we test exceeds $F_1=0.322$ against an attacker who camouflages bids, distributes them around a ring, and manipulates affinity; a two-person arrangement is worth $3.2$ percentage points of acceptance probability; and the harm is distributional rather than aggregate, with $70$ honest papers displaced while mean accepted quality moves by $0.002$. Randomized assignment is the one defense reaching the enforcement itself, making a partner who never bid indistinguishable from one who bid and lost.