The Influence of Fairness in Multi-Issue and Multi-Stage Bargaining: An Evolutionary Simulation

Large discrepancies are often found between game-theoretic predictions for bilateral bargaining games and experiments with humans. Subgame perfection for instance predicts that, in the ultimatum game, the responding agent accepts any division of the bargaining surplus. Experimental studies, on the other hand, show that a human responder often rejects an unequal division [3]. A possible explanation for the occurrence of these discrepancies is that the responder takes into account the "fairness" of the deal and tends to reject "insultingly low" proposals. As a result, an anticipating proposer should take into account these expectations about the responder's behaviour. Lin and Sunder [2] recently proposed a model for the ultimatum game in line with this hypothesis. In their model, the probability of acceptance of a proposal increases with the amount offered to the responder. Such a model, making more realistic assumptions about the agents' behaviour, appears to organise the data from experiments with humans better than the standard approach. We extended Lin and Sunder's approach to multi-issue and multi-stage negotiations and investigated this model using evolutionary algorithms (EAs) [1]. EAs are powerful search algorithms which can be used to model social learning in societies of boundedly-rational agents. A responding agent in our model can evaluate the "fairness" of a proposal in each round or only if the deadline of the negotiations is reached. The computational simulations show that fair deals can evolve in both cases. Results are depending on the fairness settings (which determine the probability of acceptance), but fair deals evolve for most fairness settings if the agents evaluate the fairness of proposals in each round; thus, results are much more robust when the latter approach is used by the agents. We supplement the computational results with a game-theoretical analysis for a simple game.