In this paper, we study an experimental "intergenerational" ultimatum bargaining game in which a sequence of non-overlapping generations of players play a stage game for a finite number of periods and are then replaced by other agents who continue the game in their role for a similar length of time. Players in each generation t are allowed to send a message to their successors in generation t+1, advising them on how they should behave. Players also care about the next generation in that their payoffs depend on the payoff achieved by their successor as well as upon their own actions. We have shown in a previous paper that a game of this sort is useful in understanding the evolution of conventions of play in coordination games. In the present paper we find that this intergenerational structure is also very useful in organizing the data in the ultimatum game, and that the intergenerational structure of the game provides many insights into how the terms of trade or sharing contracts emerge endogenously in the ultimatum game. In particular, we argue that the failure of the sub-game-perfect Nash equilibrium prediction for the ultimatum game in our experiment (as in every other experimental study) should be viewed as, roughly, equilibrium behavior, and that the principal motivation of individuals playing this game is a concern for expected payoff maximization, with little or no concern for fairness or equity as such. Advice is the key ingredient in explaining the behavior of subjects in our intergenerational ultimatum game. More specifically, when advice exists it tends to be followed in the sense that it serves as the key variable explaining the offers sent by the Senders in the game. In addition, from examining the written advice offered from one generation of sender to the next, we conclude that subjects, in rationalizing the offers that they suggest to their successors, infrequently rely upon arguments of fairness or backward induction. What are relied on are arguments of simple expected payoff maximization. In fact, even when 50-50 splits, the hallmark of equity offers, are proposed, they are mostly proposed because the sender receivers the probability of having lesser offers accepted to be unacceptably low. Third, behavior is "more conventional" when advice is allowed in that the data of those games allowing advice is more easily organized if one posits that subjects were following conventions than other alternatives. Fourth, in our Intergenerational Ultimatum games Senders appear to "leave money on the table," in that they consistently make offers to their Receivers which are greater than the Receivers' minimum acceptable offers. While this may appear to make the conventions we observe inconsistent with equilibrium behavior, we demonstrate that our observed Sender behavior can be rationalized as being part of a Bayes-Nash equilibrium to a game with incomplete information played over time by Senders and Receivers.

Co-author Andrew Schotter