We study a two-period model where ex ante inferior choice may tempt the decisionmaker in the second period. Individuals have preferences over sets of alternatives that represent second period choices. Our axioms yield a representation that identifies the individual's commitment ranking, temptation ranking, and cost of self-control. An agent has a preference for commitment if she strictly prefers a subset of alternatives to the set itself. An agent has self-control if she resists temptation and chooses an option with higher ex ante utility. We introduce comparative measures of preference for commitment and self-control and relate them to our representations.
Subgame-perfect equilibria are characterized for a market in which the seller quotes a price each period. Assume zero costs, positive interest rate, continuum of buyers, and some technical conditions. If buyers' valuations are positive then equilibrium is unique, buyers' strategies are stationary, and the price sequence is determinant along the equilibrium path but possibly randomized elsewhere, Otherwise a continuum of stationary equilibria can exist, but at most one with analytic strategies. Coase's conjecture is verified for stationary strategies: reducing the period length drives all prices to zero or the least valuation. Connections to bargaining models are described. Journal qf Economic Literature Classification Number: 022.
The paper develops a reputation based theory of bargaining. The idea is to investigate and highlight the influence of bargaining ''postures'' on bargaining outcomes. A complete information bargaining model a la Rubinstein is amended to accommodate ''irrational types'' who are obstinate, and indeed for tractability assumed to be completely inflexible in their offers and demands. A strong ''independence of procedures'' result is derived: after initial postures have been adopted, the bargaining outcome is independent of the fine details of the bargaining protocol so long as both players have the opportunity to make offers frequently. The latter analysis yields a unique continuous-time limit with a war of attrition structure. In the continuous-time game, equilibrium is unique, and entails delay, consequently inefficiency. The equilibrium outcome reflects the combined influence of the rates of time preference of the players and the ex ante probabilities of different irrational types. As the probability of irrationality goes to zero, delay and inefficiency disappear; furthermore, if there is a rich set of types for both agents, the limit equilibrium payoffs are inversely proportional to their rates of time preference.
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