A Unified Theory of Implementation

This paper unifies the theories of Nash implementation and Bayesian implementation. Environments considered are such that each agent's characteristics include, in addition to a specification of his private information, a commonly known type parameter, while both attributes are unknown to the designer. Each social choice correspondence (SCC) assigns a commonly known type vector to a social choice set. Conditions that fully characterize an implementable SCC in economic environments where agents are not satiated generalize and merge respective conditions in the complete information model of Danilov (1992) and the incomplete information model of Jackson (1991).Bayesian implementation

A Note on Jackson's Theorems in Bayesian Implementation

This note shows that in an incomplete information situation the closure condition will be satisfied by all social choice sets if and only if the set of states of the society which all agents believeoccur with positive probability satisfies the `connection' condition.It then follows from Jackson''s [1] fundamental theorems that whenever `connection'' is satisfied and there are at least three agents in the society, for the implementability of social choice sets in Bayesian equilibrium the incentive compatibility and Bayesian monotonicity conditions are both necessary and sufficient in economic environments. It also follows that the incentive compatibility and monotonicity-no-veto conditions are sufficient in noneconomic environments.Bayesian implementation incomplete information

A Unified Implementation Theory

This paper unifies the theories of Nash implementation and Bayesian implementation in a single framework. Environments considered are such that each agent's characteristics include, in addition to a specification of his private information, a commonly known type parameter, while both attributes are unknown to the designer. Each social choice correspondence (SCC) assigns a commonly known type vector to a social choice set, a collection of functions mapping private type vectors to allocations. Conditions that fully characterize an implementable SCC in economic environments where agents are not satiated generalize and merge respective conditions in the complete information model of Danilov (1992) and the incomplete information model of Jackson (1991). In noneconomic environments there remains to exist a gap between the necessary and sufficient conditions, like in Jackson (1991). In order to narrow down this gap, we employ Danilov's notion of essential elements and develop a stronger necessary condition, termed essential-generalized-Bayesian monotonicity (EGBM).Bayesian implementation; Nash implementation; mechanism; complete information; incomplete information; social choice correspondence

Effect of Short Term Cold Storage on the Quality of \u3ci\u3eTrichogramma Brassicae, T. Cacoeciae\u3c/i\u3e, and \u3ci\u3eT. Evanescens\u3c/i\u3e (Hymenoptera: Trichogrammatidae)

Trichogramma cacoeciae Marchall, T. brassicae Bezdenko and T. evanescens Westwood (Hymenoptera: Trichogrammatidae) could be useful in biological control programs of agricultural insect pests. The possibility of storing Trichogramma species at low temperatures and the effect of such storage on the quality of the parasitoids and their fecundity were studied. Trichogramma cacoeciae, T. brassicae and T. evanescens pupae were stored 1, 2, 3, and 4 weeks at 4 ± 1 °C in a refrigerator, 60-70% R.H. and full darkness. Parasitoid emergence was 98.80%, 99.33% and 99.60% for T. cacoeciae, T. brassicae and T. evanescens, respectively, after 1 week of storage. Storage at 4 ± 1 °C resulted in a significant decline in parasitoid emergence after 3 weeks. Subsequent trials focused on fitness of stored pupae in terms of percentage of parasitized eggs and longevity of females. Storage at 4 ± 1°C reduced fecundity and longevity of female parasitoids

On the communication complexity of sparse set disjointness and exists-equal problems

In this paper we study the two player randomized communication complexity of the sparse set disjointness and the exists-equal problems and give matching lower and upper bounds (up to constant factors) for any number of rounds for both of these problems. In the sparse set disjointness problem, each player receives a k-subset of [m] and the goal is to determine whether the sets intersect. For this problem, we give a protocol that communicates a total of O(k\log^{(r)}k) bits over r rounds and errs with very small probability. Here we can take r=\log^{*}k to obtain a O(k) total communication \log^{*}k-round protocol with exponentially small error probability, improving on the O(k)-bits O(\log k)-round constant error probability protocol of Hastad and Wigderson from 1997. In the exist-equal problem, the players receive vectors x,y\in [t]^n and the goal is to determine whether there exists a coordinate i such that x_i=y_i. Namely, the exists-equal problem is the OR of n equality problems. Observe that exists-equal is an instance of sparse set disjointness with k=n, hence the protocol above applies here as well, giving an O(n\log^{(r)}n) upper bound. Our main technical contribution in this paper is a matching lower bound: we show that when t=\Omega(n), any r-round randomized protocol for the exists-equal problem with error probability at most 1/3 should have a message of size \Omega(n\log^{(r)}n). Our lower bound holds even for super-constant r <= \log^*n, showing that any O(n) bits exists-equal protocol should have \log^*n - O(1) rounds