Bargaining by Heterogeneously Responsive Individuals

Abstract

I study the process of bargaining over a pie of fixed size under the Nash demand game protocol. Motivated by the argument that the manner in which bargaining unfolds often depends on antecedents, I embed the bargaining process in a recurrent framework where individuals obtain random samples from the demands made in the past and respond to this information in a manner that is dictated by their respective behavioural traits. I pursue two specific issues: firstly, is there a behavioural trait (i.e. manner of responding to past information) that outperforms any other behavioural trait in the bargaining game, and secondly, to assess the evolutionary stability of behavioural traits in the bargaining game. In context of the first question, using a bargaining framework where individuals described by a particular behavioural trait bargain with individuals described by another behavioural trait, I find that a population of 'wildly optimistic' individuals obtains almost the entire pie against a population comprised of 'almost any other' behavioural type. Secondly, using a playing-the-field model of bargaining I find that all behavioural traits are unstable, i.e. there exists no state where all the incumbent behavioural traits always obtain a higher fitness than any mutant behavioural trait.The only state where any behavioural trait can co-exist with any other behavioural trait is when each individual demands exactly half of the pie. This demonstrates the importance of the equal-splitting norm for co-existence of various behavioural traits. I also prove a hardwired behaviour-responsive behaviour equivalence theorem, which shows that the analysis of evolutionary stability of a population comprising of various behavioural traits is equivalent to the analysis of evolutionary stability of an invariant population level strategy profiles.