Volume 3, Issue 1

This paper considers the robustness of optimal decisions in a model of monopoly and a model of competitive equilibrium in a securities market. Robustness, defined as payoffs being continuous with respect to perturbations in the underlying model, fails to hold for either model. Decision rules are made robust by appropriately "smoothing" the problem, and by decreasing the weight given to small details of belief that can cause large changes in optimal payoffs.

This paper develops a theoretical framework for analyzing incentive schemes under bounded rationality. It starts from a standard principal-agent model and then superimposes an assumption of boundedly rational behavior on the part of the agent. Boundedly rational behavior is modeled as an explicit optimization procedure, which combines gradient dynamics with imitation and experimentation. The results predict the underprovision of optimal incentives and deviation from a standard sufficient statistics result from the agency literature. It also allows us to address the question of creating the optimal incentives in a multicultural environment.

In common value models, it is possible that the full information efficiency and the incentive constraint require the quantity of full and asymmetric information to move in opposite directions with the type. This conflict is called non-responsiveness. Most of those models share the features that when there is conflict, the optimal contract is pooling otherwise it is separating. In this note, we will show that, in fact, the robustness of the links between the conflict and separating contracts is not a general consequence of the common value models: it depends crucially on the assumption made in all those models that the principal's marginal benefit from trade with full information is not distorted by the presence of informational rents.

This paper constructs a model of an exchange economy in which bankruptcy arises in a manner similar to what we observe. Compared to related models, this model is a more realistic representation of some markets in which intertemporal assets are traded. Using standard and natural assumptions, it is shown that every economy represented by this model has an equilibrium. Therefore, bankruptcy can co-exist with smoothly functioning competitive markets in fairly general economies. Examples highlight some welfare effects of bankruptcy.

A one-period, simultaneous-offers bargaining game is analyzed in which, for each player, there is a small probability that his or her proposal will not reach the other player. The unique pure strategy equilibrium offers are identical to those of the Rubinstein (1982) infinite-horizon, alternating-offers bargaining game. This provides a novel interpretation of Rubinstein's result, as well as a new non-cooperative implementation of the Nash Bargaining Solution.

The paper studies monopoly pricing of a vertically differentiated durable good in a two-period model. It provides an explanation for seemingly unusual practice of a firm selling a "degraded good," arguing that the presence of Coasian dynamics may lead to the sale of the degraded good that is not less costly to produce than a high-quality good. The main finding is that when the firm can identify previous customers only if they voluntarily reveal their past purchases, it sells the degraded good along with the high-quality good in the first period. When the firm sells an upgrade of the degraded good, the price of the high-quality good cannot be "too low" in the second period, since otherwise the upgrading customers would pretend to be new customers. Thus the firm can enhance first-period sales while mitigating consumers' incentive to wait until the next period.

Stiglitz (1977) established three well-known features of monopoly insurance markets subject to adverse selection: (i) at least one market segment is served, despite the informational asymmetry; (ii) there is always some screening of risk classes; and (iii) efficiency is sacrificed to achieve screening. We modify Stiglitz’s model, replacing his expected utility assumption on consumer behavior with a version of Quiggin’s (1982) rank-dependent utility model that has received strong experimental support. We show that none of the conclusions (i)—(iii) is robust to this revision. In particular, asymmetric information need not lead to any loss in efficiency.

We study an incomplete contract model where both contracting parties can invest, and the investments have both self- and cross-effects. We analyze the performance of non-contingent contracts, message games, option contracts and property rights. We find that the first best is implemented if (i) the cross effects are negative or weaker than self-effects; (ii) the strength of cross-effects relative to self-effects is symmetric across parties. If either of these conditions is violated, even message contingent revelation mechanisms fail to provide efficient incentives. For this case, we obtain a number of results characterizing the second best. We find that property rights outperform contracts and partially relax the symmetry constraint. In either first best or second best, the stronger the cross-effects, the lower the value of contracting. The optimal allocation of property rights assigns ownership to the party with stronger cross-effects.

We analyze how communication and voting interact when there is uncertainty about players' preferences. We consider two players who vote on forming a partnership with uncertain rewards. It may or may not be worthwhile to team up. Both players want to make the right decision but differ in their attitudes toward making an error. Players' preferences are private information and each player is partially informed about the state of the world. Before voting, players can talk to each other.We completely characterize the equilibria and show that the main role of communication is to provide a double check: When there is a conflict between a player's preferences and her private information about the state, she votes in accordance with her private information only if it is confirmed by the message she receives from her opponent. In a scenario where only one of the players is allowed to talk, the benefits of communication are independent of the identity of the sender.

This paper investigates the possibility of signal jamming in games with multiple informed parties whose interests are conflicting. The possibility that signal jamming occurs in equilibrium depends on the observability of individual signals. Paradoxically, if the receiver can observe individual signals perfectly, signal jamming can occur in equilibrium, while it cannot occur if the receiver can observe only the one-dimensional signal synthesized from the senders' individual actions.

A common theme in the theory of demand aggregation is that market demand can acquire properties which are not always individually present among the agents who make up that market, a phenomenon we call heteroiosis in this paper. This paper focusses on the well known result that with a suitable distribution of demand behavior (arising perhaps from the underlying distribution of preferences), market demand can become an approximately linear function of income or even take on approximately Cobb-Douglas properties. We highlight the mathematical arguments underpinning these models and show that in the right context, it is possible to carry the arguments further and achieve exact, rather than just approximate, results: exact Cobb-Douglas market demand or exact linearity of market demand with respect to income.

This paper presents a very general linear production model which nevertheless shows an extremely regular behaviour. We can ensure the solvability of the associated equilibrium systems for quantities and prices and the nonsubstitution property, allowing for joint production and non-square systems. We also discuss the application of this model to the measurement of productivity differences. The assumptions we use are intuitive and very mild (e.g. they are necessary for the type of solvability we require). Proofs are simple and rely on geometrical arguments (the separation theorems), rather than on the use of the theory of determinants.

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected in the long run under the best-response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size, the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest response is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for any given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exist only in local interaction settings and favor the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theory.

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability.In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D; these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete-information games is consistent with Harsanyi's, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis.In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.

This paper characterizes the equilibrium sets of common agency games with direct externalities between principals when they compete with nonlinear prices. Direct externalities arise when the contracting variable of one principal directly affects the other principal's payoff. First, we characterize the set of pure-strategy, symmetric equilibria under complete information of an intrinsic common agency game. This set of equilibria is large because of the presence of price-output offers by the principals that are unchosen by the agent in equilibrium. Equilibria exist in which principals offer out-of-equilibrium price-output choices to the agent and induce aggressive, low-price behavior corresponding to marginal-cost pricing in the extreme case. We then show that this equilibrium set of outputs is robust to the possibility that agent refuses any of the offered contracts; the case of delegated agency. Second, we introduce asymmetric information in order to rationalize existing nonlinear pricing contracts. The introduction of asymmetric information has the effect of restricting the set of equilibrium outputs of the intrinsic common agency game.

We study trading models when the distribution of signals such as costs or values is not known to traders or the mechanism designer when the profit-maximizing trading procedure is designed. We present adaptive mechanisms that simultaneously elicit this information (market research) while maintaining incentive compatibility and maximizing profits when the set of traders is large (market design). First, we study a monopoly pricing model where neither the seller nor the buyers know the distribution of values. Second, we study a model with a broker intermediating trade between a large number of buyers and sellers with private information about their valuations and costs. We show that when the set of traders becomes large our adaptive mechanisms achieve the same expected profits for the monopolist and the broker as when the distribution of signals is common knowledge.