Related papers: Extreme Points and Large Contests
We characterize the extreme points of multidimensional monotone functions from $[0,1]^n$ to $[0,1]$, as well as the extreme points of the set of one-dimensional marginals of these functions. These characterizations lead to new results for…
We study competition among contests in a general model that allows for an arbitrary and heterogeneous space of contest design, where the goal of the contest designers is to maximize the contestants' sum of efforts. Our main result shows…
We characterize the extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Our framework subsumes problems with and without transfers, such as monopoly pricing, principal-optimal bilateral…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…
In this paper our aim is to characterize the set of extreme points of the set of all n-dimensional copulas (n > 1). We have shown that a copula must induce a singular measure with respect to Lebesgue measure in order to be an extreme point…
We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a…
We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
We study $n$-dimensional contests between two players with heterogeneous effort costs, where each dimension (battle) is modeled as a Tullock contest. Prize-allocation rules are identity-independent, budget-balanced, and weakly increasing in…
Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…
Research on distributed machine learning algorithms has focused primarily on one of two extremes - algorithms that obey strict concurrency constraints or algorithms that obey few or no such constraints. We consider an intermediate…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
We study a contest in which $N$ players sequentially draw from a distribution as many times as they want at a fixed cost per draw, with no recall, and the highest accepted value wins a prize. In the unique symmetric equilibrium, the…
The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of…
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this…
We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…
We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify…
We provide an analytic, microscopic analysis of extreme events in an adaptive population comprising competing agents (e.g. species, cells, traders, data-packets). Such large changes tend to dictate the long-term dynamical behaviour of many…