The robustness of the independent private value model in Bayesian mechanism design

Summary. In a Bayesian model of group decision-making, dependence among the agents' types has been shown to have a beneficial effect on the design of incentive compatible mechanisms that achieve the efficient choice associated with complete information. This effect is shown here to depend as much upon the use of large monetary transfers among the agents as it does upon dependence: if the transfers are bounded in magnitude, then nonexistence in the case of independence of an efficient, incentive compatible, ex ante budget-balanced and interim individually rational mechanism is robust to the introduction of a small amount of dependence among types. This robustness result supports the use of the simplifying assumption of independence in mechanism design. Received: October 28, 1996; revised version: May 28, 1997     

Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games

We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects’ learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model.     

Role of linking mechanisms in multitask agency with hidden information

We investigate the adverse selection problem where a principal delegates multiple tasks to an agent. We characterize the virtually implementable social choice functions by using the linking mechanism proposed by Jackson and Sonnenschein (2007) [20] that restricts the message spaces. The principal does not require any incentive wage schemes and can therefore avoid any information rent and welfare loss. We show the resemblance between the functioning of this message space restriction and that of incentive wage schemes. We also extend the results of the single-agent model to the multi-agent model.     

Strategy-proof and individually rational social choice functions for public good economies

Summary This note is to inform about a mistake in my paper (Serizawa, 1996). In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, non-exploitative and non-bossy if and only if it is a scheme of semi-convex cost sharing determined by the minimum demand principle. I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.I thank Professor Rajat Deb, who kindly pointed out my mistake.     

Shotgun mechanisms for common-value partnerships: The unassigned-offeror problem

Shotgun clauses are commonly included in the business agreements of partnerships and limited liability companies (LLCs), but the role of offeror typically remains unassigned. In a common-value, one-sided asymmetric information setting, unequal and inefficient outcomes occur with an unassigned offeror. Experimental results are aligned with our theory.     

After you—endogenous sequencing in voluntary contribution games

We examine contributions to a public good when some donors do not know the true value of the good. If donors in such an environment determine the sequence of moves, two contribution orders may arise as equilibria. Either the uninformed and informed donors contribute simultaneously or the informed contribute prior to the uninformed. Sequential moves result in a larger provision of the public good, because the follower mimics the action of the leader, and in accounting for this response the leader chooses to contribute when it is efficient to do so. An experimental investigation of the game shows that the donors predominantly choose to contribute sequentially, and that the resulting contributions are larger than those of the simultaneous-move game. Although the gain from sequential moves is smaller when the sequence is set exogenously, our results suggest that the involved parties would benefit from having sequential moves imposed upon them.     

Deterministic versus stochastic mechanisms in principal-agent models

This paper shows that, contrary to what is generally believed, decreasing concavity of the agent's utility function with respect to the screening variable is not sufficient to ensure that stochastic mechanisms are suboptimal. The paper demonstrates, however, that they are suboptimal whenever the optimal deterministic mechanism exhibits no bunching. This is the case for most applications of the theory and therefore validates the literature's usual focus on deterministic mechanisms.     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Interlinkage and Generous Tit‐for‐Tat Strategy

We investigate an infinitely‐repeated prisoners' dilemma with imperfect monitoring and consider the possibility that the interlinkage of the players' distinct activities enhances implicit collusion. We show a necessary and sufficient condition for the existence of a generous tit‐for‐tat Nash equilibrium. Such an equilibrium, if it exists, is unique. This equilibrium achieves approximate efficiency when monitoring is almost perfect, where the discount factors are fixed.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Bargaining in a non-stationary environment

We study an alternating offers bargaining model in which the set of possible utility pairs evolves through time in a non-stationary, but smooth manner. In general, there exists a multiplicity of subgame perfect equilibria. However, we show that in the limit as the time interval between two consecutive offers becomes arbitrarily small, there exists a unique subgame perfect equilibrium. Furthermore, we derive a powerful characterization of the unique (limiting) subgame perfect equilibrium payoffs. We then explore the circumstances under which Nash's bargaining solution implements this bargaining equilibrium. Finally, we extend our results to the case when the players have time-varying inside options.     

ECONOMIC NETWORKING AND STABILITY

Abstract. In this paper we discuss finite economies with the presence of transaction costs and with decreasing, constant or increasing returns. In general such an economy may have no general equilibrium existence and may even have an empty core. We analyse the trading networks of such an economy, introducing the concepts of locally stable network structure, un‐dominated locally stable network structures and most stable network structures. We point out that the set of most stable network structures could be treated as a solution concept for the empty core economies both in theoretical analysis and in application.     

Credible assignments can improve efficiency in laboratory public goods games

This paper reports an experiment investigating how assignments improve economic efficiency in a modified version of the standard voluntary-contributions mechanism. The experiment uses a non-binding message that makes common information assignments in the repeated game. A credible assignment is one actually followed by the participants. It turns out to be difficult to credibly assign the symmetric efficient outcome in four person cohorts, but we did discover one assignment that was credible in the last match of the evolutionary repeated game.     

Introduction to Incompleteness and Uncertainty in Economics

This introduces the symposium on incompleteness and uncertainty in economics.     

Strategy-proof assignment on the full preference domain

We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.     

Almost budget-balanced VCG mechanisms to assign multiple objects

Subsidy-free VCG mechanisms assign p identical objects to n agents. The efficiency loss is the largest ratio of budget surplus to efficient surplus, over all profiles of non-negative valuations. The smallest efficiency loss satisfies . If is bounded away from , converges to zero exponentially in n.Participation is voluntary in the optimal mechanism achieving if p=1, but not if p?2. Among voluntary mechanisms, the optimal efficiency loss is not significantly larger than if . But it does not converge to zero in n if .     

The impact of changing skill levels on optimal nonlinear income taxes

The impact of changing an individual's skill level on the solution to a finite population version of the Mirrlees optimal nonlinear income tax problem with quasilinear-in-leisure preferences is investigated. It is shown that it is possible to sign the directions of change in everyone's optimal consumptions and optimal marginal tax rates in response to such a change.     

Optimal nonlinear income taxation with a finite population

In the standard optimal income taxation problem, tax payments depend only on each consumer's own actions. Piketty [J. Econ. Theory 61 (1993) 23-41] shows that, if one individual's tax schedule depends on others’ actions and the government knows the exact ability distribution, it can implement any undistorted allocation as the unique revelation game outcome. If some individuals misreveal their types, Piketty's mechanism may assign infeasible allocations. We require that tax schedules must balance the government budget for every possible vector of revelations. When individuals reveal their type by simple announcements, all undistorted allocations can be still implemented, even with off-equilibrium feasibility constraints.     

Large market games with demand uncertainty

We consider a market game with a continuum of consumers, where the measure of each type is stochastic. Nature selects the set of active consumers, who make bids and offers on ?−1 spot market trading posts. Existence of type-symmetric Nash equilibrium is proven. When facing price uncertainty, best responses are unique, and a Nash equilibrium to the sell-all game is typically not a Nash equilibrium to the original game. Under plausible circumstances, consumers strictly prefer to be on one side of the market.     

Adverse selection problems without the Spence-Mirrlees condition

This paper studies a class of one-dimensional screening problems where the agent's utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agent's unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agent's marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution.