Two-Person Sequential Bargaining with Boundedly Rational Players

This paper reconsiders Rubinstein’s alternating-offer bargaining game with complete information. We investigate the assumption of lack of common knowledge of rationality. Therefore we define K-step rationalizability and K-step trembling-hand rationalizability for our multi-stage game and we find outcomes which are more suitable than the subgame perfect equilibrium (SPE) for explaining experimental results. Other main results are : (i) K-step trembling-hand rationalizable outcomes exclude perpertual disagreement, but not delay, (ii) the speed of convergence to the SPE of the set of K-step trembling-hand rationalizable outcomes is faster when there is random choice of whe makes the offer, (iii) if players’ preferences display constant costs of delay, then common knowledge of rationality is no more necessary for solving Rubinstein’s bargaining game.