Social Norms, Bounded Rationality and Optimal Contracts by Suren Basov

Author:Suren Basov
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

where

The first term in expression for γ L captures the fraction of low types that choose the contract designed for them, while the second term captures the fraction of high types who choose the contract designed for the low types.

Note that if the monopolist offers exactly the same contract as would have been offered to the rational consumers exactly half of low types would have dropped out and exactly half of high types would have chosen to behave as if they were low types. Therefore, though the degree of irrationality is assumed to be small, the losses would have been of order of , rather than . Basov (2009) shows that the monopolist will instead choose to create slack in the previously binding constraints of order of . The high type will still be served efficiently, and the low-type quality will also be the same up to terms of order of . Therefore, in the main approximation with respect to λ the monopolist offers the same qualities, she would have offered to the rational consumers, but adjusts the tariffs by terms of order of . This implies that the probability of a wrong choice by both types of the consumers is of order Therefore, using the optimal two contract menu the monopolist earns lower profits against nearly rational consumers than she would have earned against the fully rational ones and the magnitude of the loss is

Note that this outcome cannot be implemented by tariff of type defined over a connected product line , since under bounded rationality the distribution of choices will have a continuous rather than binary support. Therefore, two mechanisms equivalent under full rationality will be no longer equivalent under bounded rationality.

It can be shown that using continuous tariffs will decrease the profits of the monopolist comparatively to a binary menu. Next I am going to ask: can the monopolist improve her profits using more elaborate mechanism? I argue that the answer is yes, if there are no complexity costs. In particular, in this case it is possible to achieve profits, which are exponentially close to the profits under the assumption of full rationality.

Let us consider the following message game: the set of all possible massages is divided into three groups. The default group consists of just a single message; the low group consists of m L messages and the high group of m H messages. The consumer is asked to send a message and is not assigned any good if she sends the default message, is offered the contract devised for the low-type rational consumers if she sends the message belonging to the low group and the contract devised for the high-type rational consumers if she sends the message belonging to the high group. The probability that the low-type consumer will by mistake choose to not participate is 1/m l , while the probability that the high type will accidentally choose the problem designed for the low type is m l /(m l + m H ).

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