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.     

Market games with differential information and infinite dimensional commodity spaces: The core

Summary We provide an alternative proof of the existence of core allocations in exchange economies with differential information and infinite dimensional commodity spaces. We also identify a critical feature of information sharing rules that ensures nonemptiness of the core. In essence, the only condition we require on the sharing rules is that profitable insider trading be prohibited. In the absence of insider trading, balancedness is guaranteed and core nonemptiness follows.I thank Dan Arce, Erik Balder, Myrna Wooders, and Nicholas Yannelis for helpful comments. This paper is a greatly revised version of my paper entitled. A Variational Problem Arising in Market Games with Differential Information, written in August of 1991.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

Exchange in a general market with indivisible goods

We show how to restrict trades in exchange markets with heterogeneous indivisible goods so that the resulting restricted exchange markets, the fixed deal exchange markets, have a unique core allocation. Our results on fixed deal exchange markets generalize classical results on the Shapley-Scarf housing market, in which each agent owns one good only. Furthermore, we define the class of fixed deal exchange rules for general exchange markets, and prove that these are the only exchange rules that satisfy strategyproofness, individual rationality, and a weak form of efficiency.     

Approximate cores of games and economies with clubs

We introduce the framework of parameterized collections of games with and without sidepayments and provide three nonemptiness of approximate core theorems. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results. A fundamental new mathematical result, the partition-balancing effect of large numbers, which promises to have further applications, is contained in Appendix A.     

Limited observability as a constraint in contract design

Limited observability is the assumption that economic agents can only observe a finite amount of information. Given this constraint, contracts among agents are necessarily finite and incomplete in comparison to the ideal complete contract that we model as infinite in detail. We consider the extent that finite contracts can approximate a complete contract. The objectives of the paper are: (i) to identify properties of agents’ preferences that determine whether or not finiteness of contracts causes significant inefficiency; (ii) to evaluate the performance of finite contracts against the ideal optimal contract in a bilateral bargaining model.     

Virtual utility and the core for games with incomplete information

The core is extended to games with incomplete information. The feasible set is characterized by incentive-compatible mechanisms. Blocking is organized at the interim stage by an incentive-compatible mediation plan. Membership of the blocking coalition itself may be determined randomly by the blocking mediator. Nonemptiness of an interim fine core is proven for games with a balanced structure, independent types, and sidepayments. An offer of severance payments may be needed to inhibit blocking. Core allocations are characterized in terms of virtual-utility scales that generalize the weighted-utility scales of the inner core. Mechanisms that achieve core allocations are coalitionally durable.     

Non-existence of monotone equilibria in games with correlated signals

Participation in economic games such as auctions is typically costly, which means that players (potential bidders) must consider whether to participate. Such decisions may be no less crucial than how to bid, and yet the literature has been mostly concerned with bidding, assuming an exogenously given number of bidders; see Krishna [Auction Theory, Academic Press, New York, 2002]. Landsberger and Tsirelson [Correlated signals against monotone equilibria, preprint SSRN 222308, Social Science Research Network Electronic Library, May 2000. Available online: http://papers.ssrn.com/abstract=222308] have shown that fundamental results established in symmetric auction theory with correlated signals, such as the existence of a monotone equilibrium, may not hold if participation decisions are part of equilibrium. The major goal of this paper is to illustrate and explain this result that may be considered counter intuitive given the emphasis placed on monotone equilibria in the auction literature.     

Characterizations of bargaining solutions in production economies with unequal skills

In production economies with unequal skills, this paper characterizes bargaining solutions by using axioms on allocation rules rather than axioms on classical bargaining solutions. We introduce a new axiom, consistency w.r.t. technological innovations, so that the non-welfaristic characterizations of bargaining solutions in the production economies are provided. By the characterizations, we can classify the three bargaining solutions (the Nash, the Kalai-Smorodinsky, and the Egalitarian solutions) from the viewpoint of responsibility and compensation discussed by Dworkin.     

Mediation, arbitration and negotiation

We compare three common dispute resolution processes - negotiation, mediation, and arbitration - in the framework of Crawford and Sobel [V. Crawford, J. Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431-1451]. Under negotiation, the two parties engage in (possibly arbitrarily long) face-to-face cheap talk. Under mediation, the parties communicate with a neutral third party who makes a non-binding recommendation. Under arbitration, the two parties commit to conform to the third party recommendation. We characterize and compare the optimal mediation and arbitration procedures. Both mediators and arbitrators should optimally filter information, but mediators should also add noise to it. We find that unmediated negotiation performs as well as mediation if and only if the degree of conflict between the parties is low.