Related papers: BONUS! Maximizing Surprise
Motivated by a problem posed by Aldous, our goal is to find the maximal-entropy win-martingale: In a sports game between two teams, the chance the home team wins is initially $x_0 \in (0,1)$ and finally 0 or 1. As an idealization we take a…
In a sponsored search auction the advertisement slots on a search result page are generally ordered by click-through rate. Bidders have a valuation, which is usually assumed to be linear in the click-through rate, a budget constraint, and…
When selling many goods with independent valuations, we develop a distributionally robust framework, consisting of a two-player game between seller and nature. The seller has only limited knowledge about the value distribution. The seller…
Unusually large prize pools in lotteries like Mega Millions and Powerball attract additional bettors, which increases the likelihood that multiple winners will have to share the pool. Thus, the expected value of a lottery ticket decreases…
A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to…
A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
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…
Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the na\"ive estimate of…
This paper examines games with strategic complements or substitutes and incomplete information, where players are uncertain about the opponents' parameters. We assume that the players' beliefs about the opponent's parameters are selected…
The primary contribution of this paper resides in devising constant-factor approximation guarantees for revenue maximization in two-sided matching markets, under general pairwise rewards. A major distinction between our work and…
We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number…
Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament…
We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no…
We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…
We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…
In this paper, we propose a model which simulates odds distributions of pari-mutuel betting system under two hypotheses on the behavior of bettors: 1. The amount of bets increases very rapidly as the deadline for betting comes near. 2. Each…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…