A computational model for incomplete contracts

This work aims at connecting developments in the theory of agency and implicit contracts with research on bounded rationality and agent based computational models. These are two related areas as implicit contracts are justified on the basis of bounded rationality, which additionally is one of the justifications of computational agent based models. INTRODUCTION: THE BASIC SETUP The paper develops a general framework, in which a population of individuals face a long-term (which we shall interpret as longer than a one-shot game) contractual relationship. In this, two types of agents, buyers and sellers, exchange a commodity for a given price according to a set of specified characteristics in a private contract. We do not need to specify what is exchanged (a good or a service) but rather the institutional setting in which exchange takes place. In order to analyse it we will resort to numerical simulations. Agreeing on a exchange implies accepting the conditions of a contract. In order to do so agents must account for different facts, which in brief are: 1. The difficulty of including all possible contingencies in a contract. This makes that the more specific is the agreement, the more costs it has for both parties. Transaction costs become prohibitive when all possible future states are to be anticipated and covered by the contract. This justifies the fact that most contractual agreements are based on incomplete contracts which rely on the bounded rational behavior of economic agents and reduce transaction costs. 2. Information asymmetries. Sellers have private information about the inherent properties of the good/service they sell. The quality of the product is an example but it does not exhaust all the possibilities, which can include timing of delivery, or effort by the seller (in case of a service) to mention some. 3. Costly monitoring of the contract. Both the buyer and the seller may be interested in monitoring the performance of the contract. While in a world of perfect information this is just unnecessary, monitoring becomes an important part of long term contracts in a setting in which any of the previous characteristics arise. For instance, with asymmetric information buyers may be interested in verifying the characteristics of the commodity; in case of an incomplete contract both parties may be interested in solving any contingency that may happen while the contract is in force. Broadly speaking incomplete contracts arise as the outcome of boundedly rational individuals interacting in markets of imperfect and asymmetric information. Both aspects are relevant to the literature on agent based computational economics and is within this framework that we develop the computational model. COMPUTATIONAL EXPERIMENTS In order to study the emergent properties of a population of buying and selling agents, which shall be engaged in long-terms contracts, we propose to undertake computational simulations of a model with the previously mentioned characteristics. Moreover we want to study the effect of the different institutional settings in the outcomes. This is a significant part of the work as institutional design may be of interest by itself. In brief, simulations are based on the following three-stage game: 1. At stage 1 buyers and sellers are paired. The buyer proposes a contract to the agent. The contract shall be a complete one (suppose that such a contract may exist) or incomplete. In case of an incomplete contract, the buyer may define a monitoring mechanism to verify it. 2. At stage 2 sellers accept or reject the contract. In the former case the game continues until stage three. In the latter it ends and both receive a utility of 0. 3. At stage 3 the exchange takes place. In case of a complete contract there are no further steps to take. In case of an incomplete contract buyers shall monitor its performance. At the end of this stage both agents receive individual payoffs. The seller receives the payment set in the contract minus the investment made in order to supply this amount. The buyer receives its valuation of the commodity minus the cost of either monitoring the incomplete contract, or the cost of making a complete contract. This three steps are repeated a number T of times. The evolutionary nature allows for analysing different institutional setups and its impact in the outcomes of the game. Among other we may include: modification of costs of making contracts, establishing public information about sellers/buyers, allowing information networks among agents, introducing heterogeneous terms for the contracts, or allowing for a third party enforcement of the contracts (law enforcement) to mention some. It is the evolutionary process guiding the adaptive agents that will ultimately lead to an equilibrium in the population.