Profit sharing in unique Nash equilibrium: Characterization in the two-agent case

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent’s labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker’s (Econometrica, 1992) characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property. We also show that the familiar stand alone test characterizes the class of fixed-path methods (Friedman, Economic Theory, 2002) under our incentives criterion.Joint production, serial rule, decreasing serial rule, strategyproofness.

Accelerating MCMC via Parallel Predictive Prefetching

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential future steps of the chain in parallel. The approach can accelerate computation of the target distribution of a Bayesian inference problem, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores

Strategyproof Profit Sharing: A Two-Agent Characterization

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent's labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker's (Econometrica, 1992) characterization of their serial mechanism as the unique cost -sharing rule satisfying the same incentives property. We also show that the familiar stand alone test characterizes the class of fixed-path methods (Friedman, Economic Theory, 2002) under our incentives criterion.

Secure Implementation: Strategy-Proof Mechanisms Reconsidered

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept in social choice theory. However, the concept of strategy-proofness has serious drawbacks. First, announcing one's true preference may not be a unique dominant strategy, and using the wrong dominant strategy may lead to the wrong outcome. second, almost all strategy-proof mechanisms have a continuum of Nash equilibria, most of which produce the wrong outcome. Third, experimental evidence shows that most of the strategy-proof mechanisms do not work well. We argue that a possible solution to this dilemma is to require double implementation in Nash equilibrium and in dominant strategies, which we call secure implementation. We characterize environments where secure implementation is possible, and compare it with dominant strategy implementation. An interesting example of secure implementation is a Groves mechanism when preferences are single-peaked.

Secure Implementation

Strategy-proofness, requiring that truth-telling is a dominant strategy, is a standard concept in social choice theory. However, this concept has serious drawbacks. In particular, many strategy-proof mechanisms have multiple Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in Nash equilibrium and in dominant strategies, i.e., secure implementation. We characterize securely implementable social choice functions, and compare our results with dominant strategy implementation. In standard quasi-linear environments with divisible private or public goods, there exist Pareto efficient (non-dictatorial) social choice functions that can be securely implemented. But in the absence of side-payments, secure implementation is incompatible with Pareto efficiency.

Strategyproof Profit Sharing in Partnerships: Improving upon Autarky

Several producers decide to form a partnership, to which they contribute both capital and labor. We propose a group-strategyproof mechanism under which no single agent is tempted to secede from the partnership: the inverse marginal product proportions (or IMPP) mechanism. The IMPP mechanism combines aspects of common ownership with the requirement that private property rights be respected: when an agent decides to stop exploiting her own capital, the latter is shared between the remaining agents in proportion to the productivity of their own capital. The IMPP is in fact the only fixed-path method (as introduced in Friedman, 2002) to satisfy autarkic individual rationality; its path is uniquely determined by the capital contributions of the agents. Thus, our results provide one of the first economic motivation for the asymmetry of fixed-path methods.

Joint estimation of multiple related biological networks

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Distributed Bayesian Probabilistic Matrix Factorization

Matrix factorization is a common machine learning technique for recommender systems. Despite its high prediction accuracy, the Bayesian Probabilistic Matrix Factorization algorithm (BPMF) has not been widely used on large scale data because of its high computational cost. In this paper we propose a distributed high-performance parallel implementation of BPMF on shared memory and distributed architectures. We show by using efficient load balancing using work stealing on a single node, and by using asynchronous communication in the distributed version we beat state of the art implementations

Secure implementation

Strategy-proofness, requiring that truth-telling be a dominant strategy, is a standard concept in social choice theory. However, this concept has serious drawbacks. In particular, many strategy-proof mechanisms have multiple Nash equilibria, some of which produce the wrong outcome. A possible solution to this problem is to require double implementation in Nash equilibrium and in dominant strategies, i.e., secure implementation. We characterize securely implementable social choice functions and investigate the connections with dominant strategy implementation and robust implementation. We show that in standard quasi-linear environments with divisible private or public goods, there exist surplus-maximizing (non-dictatorial) social choice functions that can be securely implemented.Nash implementation, robust implementation, secure implementation, strategy-proofness