Costly decisions and sequential bargaining

This paper models a near-rational agent who chooses from a set of feasible alternatives, subject to a cost function for precise decision-making. Unlike previous papers in the «control costs» tradition, here the cost of decisions is explicitly interpreted in terms of time. That is, by choosing more slowly, the decision-maker can achieve greater accuracy. Moreover, the timing of the choice is itself also treated as a costly decision. A trade off between the precision and the speed of choice becomes especially interesting in a strategic situation, where each decision maker must react to the choices of others. Here, the model of costly choice is applied to a sequential bargaining game. The game closely resembles that of Perry and Reny (1993), in which making an offer, or reacting to an offer, requires a positive amount of time. But whereas Perry and Reny treat the decision time as an exogenous fixed cost, here we allow the decision-maker to vary precision by choosing more or less quickly, thus endogenizing the order and timing of offers and responses in the game. Numerical simulations of bargaining equilibria closely resemble those of the Binmore, Rubinstein, and Wolinsky (1983) framework, except that the time to reach agreement is nonzero and offers are sometimes rejected. In contrast to the model of Perry and Reny, our numerical results indicate that equilibrium is unique when the space of possible offers is sufficiently finely spaced.