Renegotiable Options Fail to Prevent Hold-Up Between Two Profit-Maximizing Frontier LLM Agents

Abstract

Do contract terms that protect investment between people also protect it between profit-maximizing language-model agents? In the hold-up problem, a seller can adapt a unit to one buyer at a cost before the price is set. Once that cost is sunk, the buyer can offer almost nothing and the seller will still accept, so a seller who foresees this does not adapt. One remedy is an option: the buyer may buy at a fixed price. In theory the option stops working if the buyer can let it lapse and offer its own price instead. Yet in a laboratory experiment by Hoppe and Schmitz, this renegotiable option raised human investment from 41.5% of pairs without a contract to 67.2%. We had Claude Opus 5.5 and GPT-6.1 Sol, each told to maximize its side's profit, play a one-shot game with the same strategic structure under their four contract regimes and a reference-price control. The agents did what game theory predicts: under the renegotiable option no seller adapted, and under the option that rules out this renegotiation every seller did. In a second experiment in which sellers no longer stated their expected revenue before deciding, removing the profit instruction left investment unchanged under no contract and both options. When we changed the numbers so that the buyer would exercise the option even without adaptation, adapting only added cost, and no seller adapted: the agents did not simply adapt whenever an option was offered or whenever its price covered the cost. Under our protocol, a contract term that raised investment between people did not protect it between agents.