Time inconsistency and learning in bargaining games

1. The Problem and Related Literature In our daily lives, we always face decisions to make and alternative actions to choose overtime. Traditional economic analysis expects people behave rationally (take actions maximizing their payoff or utility) and thus behave consistently (following the original contingent plan or strategy) when they make these decisions. In other words, a rational agent's goals (and strategies to achieve them) at different dates cannot be in conflict and he always agrees with his future selves. However, we always suffer from these kinds of conflicts. This is due to the vulnerability of individuals to self-deception, over-optimism, over-confidence, self-control and many other characteristics mentioned in Psychology literature. One way of incorporating some of these characteristics into the decision making analysis is to introduce time-inconsistent preferences. Hyperbolic discounting is often used in economics literature to model time-inconsistency (interchangeably, preference reversals or self-control problem) The literature about time-inconsistency, which attracts more attention recently, mainly takes the characteristic of the agent as given and focuses on how this plays a role in different decision making problems. Some of the existing literature also mentions "time-inconsistent agents' abilities of learning to be less time-inconsistent overtime" at footnotes (see, O'donoghue and Rabin, 2001; Sarafidis, 2004). However, there is no distinct work, as far as we know, focusing on learning capabilities of time-inconsistent agents. The rationale behind time-inconsistent learners is the following: delaying costly tasks forever, which arises as a symptom of self-control, or holding the same belief about one's self is prevented by different forces such as deadlines. One can realize his inconsistent behavior to some extent if he repeatedly fails to follow his plans and/or does not carry out actions in accordance with his beliefs. In other words, he can revise his contingent actions and update his beliefs about himself. While, generically, it is difficult to impose an evolutionary structure on time-inconsistent behavior of agents (e.g., time-inconsistent agents will vanish in the population overtime by evolutionary forces), it is possible to observe learning to be more rational in some specific strategic environments. This paper will not address learning of time-inconsistent agents thoroughly in a general context either, but it introduces learning in a context of bargaining. We present two solution concepts formalized by Sarafidis, 2004, and their applications to bargaining games first without learning (extensions of some arguments in Akin, 2004), then we will allow learning. At each case, we examine whether there …