Luca Anderlini

INCOMPLETE CONTRACTS AND COMPLEXITY COSTS

This paper investigates, in a simple risk-sharing framework, the extent to which the incompleteness of contracts could be attributed to the complexity costs associated with the writing and the implementation of contracts. We show that, given any measure of complexity in a very general class, it is possible to find simple contracting problems such that, when complexity costs are explicitly taken into account, the contracting parties optimally choose an incomplete contract which coincides with the ‘default’ division of surplus. Optimal contracts with complexity costs are constrained efficient in our model. We therefore interpret our results as saying that, in the absence of a strategic role for complexity costs, their effect is entirely determined by their size relative to the size of payoffs.

Costly Bargaining and Renegotiation

We identify the inefficiencies that arise when negotiation between two parties takes place in the presence of transaction costs. First, for some values of these costs it is efficient to reach an agreement but the unique equilibrium outcome is one in which agreement is never reached. Secondly, even when there are equilibria in which an agreement is reached, we find that the model always has an equilibrium in which agreement is never reached, as well as equilibria in which agreement is delayed for an arbitrary length of time. Finally, the only way in which the parties can reach an agreement in equilibrium is by using inefficient punishments for (some of) the opponents deviations. We argue that this implies that, when the parties are given the opportunity to renegotiate out of these inefficiencies, the only equilibrium outcome which survives is the one in which agreement is never reached, regardless of the value of the transaction costs.

Some notes on Church's thesis and the theory of games

This paper considers games in normal form played by Turing Machines. The machines are fed as input all the relevent information and then are required to play the game. Some ‘impossibility’ results are derived for this set-up. In particular, it is shown that no Turing Machine exists which will always play the correct strategy given its opponents choice. Such a result also generalizes to the case in which attention is restricted to economically optimizing machines only. The paper also develops a model of knowledge. This allows the main results of the paper to be interpreted as stemming out of the impossibility of always deciding whether a player is rational or not in some appropriate sense.

Cooperation and Effective Computability

A common interest game is a game in which there exists a unique pair of payoffs which strictly Pareto dominates all other payoffs. The authors consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game. They show that, if supergame strategies are restricted to be computable within Churchs thesis, the only pair of payoffs that survives any computable tremble with sufficiently large support is the Pareto-efficient pair. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future. Copyright 1995 by The Econometric Society.

Structural Stability Implies Robustness to Bounded Rationality

The introduction of a small amount of bounded rationality into a model sometimes has little effect and sometimes has a dramatic impact on predicted behavior. We call a model robust to bounded rationality if small deviations from rationality result only in small changes in the equilibrium set. We also say that a model is structurally stable if the equilibrium set (given fully rational agents) varies continuously with the parameter values of the model. It is easy to see that when the equilibrium set is discontinuous, bounded rationality can have a very large impact on behavior in the neighborhood of the discontinuity. We go further and show that it is only at such discontinuities that bounded rationality can have large effects. It follows that a model is robust to bounded rationality if and only if it is structurally stable. Thus, we can characterize which models will be robust to bounded rationality and which will not, independently of the exact form that the bounded rationality takes. Journal of Economic Literature Classification Numbers: C69, C79, D51, E19.

Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’

Summary.We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication.When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to “whitewash” the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a “neutral historian” who verifies the truthfulness of others’ reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs.We also analyze a centralized communication protocol in which history leaves a “footprint” that can only hidden by the current cohort by a unanimous “coverup.” We show that in this case the set of payoffs that are sustainable in equilibrium coincides with the weakly renegotiation proof payoffs of the standard repeated game.

Legal institutions, innovation, and growth

We analyze the relationship between legal institutions, innovation and growth. We compare a rigid (law set ex-ante) legal system and a exible one (law set after observing current technology). The exible system dominates in terms of welfare, amount of innovation and output growth at intermediate stages of technological development - periods when legal change is needed. The rigid system is preferable at early stages of technological development, when (lack of) commitment problems are severe. For mature technologies the two legal systems are equivalent. We nd that rigid legal systems may induce excessive (greater than rst-best) R&D investment and output growth.

Communication in Dynastic Repeated Games: 'Whitewashes' and 'Coverups'

We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication.

Cooperation and computability in n-player games

Abstract A Common Interest game is a game that has a unique vector of payoffs that strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such an n -player Common Interest game. We restrict supergame strategies to be computable within Church’s thesis, and we introduce computable trembles on these strategies. If the trembles have sufficiently large support, the only equilibrium vector of payoffs that survives is the Pareto-efficient one. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future. The players take turns to reveal their cooperative intentions, and the result is proved by backwards induction on the set of players. We also show that our equilibrium selection result fails when there are a countable infinity of players.

Costly Contingent Contracts

We identify and investigate the basic ?hold-up? problem which arises whenever each party to a contingent contract has to pay some ex-ante cost for the contract to become feasible. We then proceed to show that, under plausible circumstances, a ?contractual solution? to this hold-up problem is not available. This is because a contractual solution to the hold-up problem typically entails writing a ?contract over a contract? which generates a fresh set of ex-ante costs, and hence is associated with a new hold-up problem. We conclude the paper investigating two applications of our results to a static and to a dynamic principal-agent model.