We analyze the simplest Condorcet cycle with three players and three alternatives within a strategic bargaining model with recognition probabilities and costless delay. Mixed consistent subgame perfect equilibria exist whenever the geometric mean of the agents' risk coefficients, ratios of utility differences between alternatives, is at most one. Equilibria are generically unique, Pareto efficient, and ensure agreement within finite expected time. Agents propose best or second-best alternatives. Agents accept best alternatives, may reject second-best alternatives with positive probability, and reject otherwise. For symmetric recognition probabilities and risk coefficients below one, agreement is immediate and each agent proposes his best alternative.