Mind the Gap: Belief-Policy Gaps about an Artificial Bargaining Counterpart in the Ultimatum Game

Abstract This study examines how people form beliefs about an artificial bargaining counterpart and whether misperceiving its observed policy has strategic costs. We elicit incentivised beliefs from 108 university students about a large language model's proposer offers and responder acceptance decisions in an Ultimatum Game and benchmark them against 1,000 simulations per scenario. The average proposer forecast shows no detectable mean bias, but individual point forecasts are heterogeneous. Responder beliefs diverge systematically from the observed acceptance policy: 85.2\% of participants report a weakly monotone acceptance schedule even though the baseline artificial policy is non-monotone. These gaps affect belief-implied best responses: \$500 belongs to the maximizing set for 62.0\% of participants, whereas the baseline policy makes \$250 optimal. Counterfactual best responding to elicited beliefs therefore generates sizeable expected payoff losses. Additional simulations show that the observed artificial policy is sensitive to prompt formulation, decoding temperature, numerical scale, and inference environment. The results connect experimental bargaining with the economics of interacting heterogeneous agents by showing how mismatches between human beliefs and protocol-contingent artificial policies can create payoff-relevant frictions in human--AI interaction.