Descriptive theories of bargaining. An experimental analysis of two- and three-person characteristic function bargaining (Q1188675)

This monograph is devoted to the experimental analysis of bargaining in 2- and 3-person games, given in the characteristic function form. From the mathematical viewpoint 2-person cooperative games are trivial: all these games are equivalent to giving v(i) to each player and dividing the remaining sum of money \(v=v(12)-v(1)-v(2)\) between them. Therefore due to the symmetry considerations the natural solution is to divide v into two halves v/2. However, experiments organized by the author show that people prefer the ``proportional division'', i.e. they divide v into two parts proportional to v(1) and v(2). The main difference between this proportional division and real payoffs is due to the fact that people normally prefer round numbers. For 3-person games a natural generalization of this proportional division method is formulated, and it also turns out to be experimentally the best fit for the real decisions. From all the already known concepts of decision the best fit is the core (for the games that have a core, and for which this core is sufficiently big). A nontrivial mathematical technique is developed to compare the experimental behaviour of different theories; the necessity for such techniques stems from the fact that if real payoffs are outside the set, predicted by a theory, it is bad for a theory; but if all experimental payoffs are inside this set it does not necessarily mean that this theory is a good fit, because it may turn out that real payoffs fill only a tiny portion of that set. So one must take the size of the predicted set into consideration when comparing the difference concepts of a solution.