We present an average-case complexity analysis for the zerofinding problem for functions from C([0, 1]), r > 2 , which change sign at the endpoints. This class of functions is equipped with a conditional r-folded Wiener measure. We prove that the average-case complexity of computing an «-approximation is of order log log( 1 /e), and that a hybrid secant-bisection method with a suitable adaptive...

Agents vote to choose a fair mixture of public outcomes; each agent likes or dislikes each outcome. We discuss three outstanding voting rules. The Conditional Utilitarian rule, a variant of the random dictator, is Strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar Random Priority rul...

We study the problem of stochastic stability for evolutionary dynamics under logit choice rule. consider general classes coordination games, symmetric or asymmetric, with an arbitrary number strategies, which satisfies marginal bandwagon property (i.e., there is positive feedback to coordinate). Our main result that most likely escape paths from a status quo convention consist series identical ...

We augment the mechanism used in Nash implementation with a political process that collects the opinions of a subset of individuals with a fixed probability distribution. The outcome is a function of only the collected opinions. We show that the necessary – and sometimes sufficient – condition for implementation by a specific political process can be either weaker or stronger than Maskin monoto...

This paper studies Nash implementation when the outcomes of the mechanism can be renegotiated among the agents but the planner does not know the renegotiation function that they will use. We characterize the social objectives that can be implemented in Nash equilibrium when the same mechanism must work for every admissible renegotiation function. The constrained Walrasian correspondence, the co...

For discontinuous games Simon and Zame (1990) introduced a new approach to the existence of equilibria. To obtain the required continuity, they convert the original discontinuous payoff function into an upper semicontinuous payoff correspondence; graphically, this corresponds to a “vertical interpolation” to close the discontinuity gap at the discontinuity points. The resulting payoff indetermi...

We consider the mechanism design problem when agents’ types are multidimensional and continuous, and their valuations are interdependent. If there are at least three agents whose types satisfy a weak correlation condition, then for any decision rule and any ε > 0 there exist balanced transfers that render truthful revelation a Bayesian ε-equilibrium. A slightly stronger correlation condition en...

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...

The paper introduces the category of algebraic axioms and investigates when a social rule of decision-making can be uniquely characterized with such axioms. The first result shows that every set of axioms that characterize a given rule is equivalent to a set of three algebraic axioms. The second result suggests a method for constructing an algebraic proof of uniqueness via finding an appropriat...