Paper bidding is the entry point to reviewer assignment at large CS conferences: reviewers declare interest, combined by an optimizer with automated affinity scores. Reviewers who have never met recruit each other online, exchange identifiers, bid on each other's papers, and reciprocate with inflated scores. Existing collusion models assume already-trusted colleagues; open recruitment removes that assumption and the mechanism that made such arrangements work. We give the first game-theoretic model of collusion \emph{formation} in peer review, the \emph{Mutual Bidding Dilemma}: a four-stage game covering recruitment, exchange of identifiers under risk of being reported, unverifiable bidding, and reciprocal reviewing. The model predicts the arrangement cannot form: once assigned a partner's paper, writing the inflated review is pure cost, since the benefit depends on the partner's own decision. Reciprocation is never individually rational, for any payoffs, and the arrangement unwinds. What closes the gap is enforcement, not incentives: authors see their own reviews, deadlines recur every few months, and the group remembers who reciprocated. We derive the condition under which inflation is sustainable, the detection rate above which no partnership survives, and show effort enters both. On a calibrated end-to-end conference simulation, no detector we test exceeds $F_1 = 0.322$ against an attacker who camouflages bids, spreads them around a ring, and manipulates affinity; a two-person arrangement is worth $3.2$ points of acceptance probability; and the harm is distributional, not aggregate: $70$ honest papers are displaced while mean quality moves by only $0.002$, so no summary statistic reveals it. Randomized assignment is the one defense reaching enforcement itself, making a partner who never bid indistinguishable from one who bid and lost.

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