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Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

We extend the classic regret minimization framework for approximating equilibria in normal-form games by greedily weighing iterates based on regrets observed at runtime. Theoretically, our method retains all previous convergence rate…

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

Finding numerical approximations to minimax regret treatment rules is of key interest. To do so when potential outcomes are in {0,1} we discretize the action space of nature and apply a variant of Robinson's (1951) algorithm for iterative…

This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the…

In the field of Artificial Intelligence, traditional approaches to choosing moves in games involve the we of the minimax algorithm. However, recent research results indicate that minimizing may not always be the best approach. In this paper…

We consider a setting in which a principal gets to choose which game from some given set is played by a group of agents. The principal would like to choose a game that favors one of the players, the social preferences of the players, or the…

Paper erroneously re-submitted as duplicte. Readers should look at math-ph/9909004.

The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of…

Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…

This work studies external regret in sequential prediction games with both positive and negative payoffs. External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. In…

Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…

Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.

One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…

We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by $p$, the alphabet size of the Unique Game, gives a trivial $p$-approximation that can…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

In the present article, we have given a corrigendum to our paper ``On (p,q)-analogue of Bernstein operators" published in Applied Mathematics and Computation 266 (2015) 874-882.

We show that there is a polynomial-time approximation scheme for computing Nash equilibria in anonymous games with any fixed number of strategies (a very broad and important class of games), extending the two-strategy result of Daskalakis…