Related papers: Robust Draws in Balanced Knockout Tournaments
The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages,…
Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a $k$-king if it…
The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…
We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…
A decision-maker faces uncertainty governed by a data-generating process (DGP), which is only known to belong to a set of sequences of independent but possibly non-identical distributions. A robust decision maximizes the expected payoff…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
Consider a round-robin tournament on n teams, where a winner must be (possibly randomly) selected as a function of the results from the ${n \choose 2}$ pairwise matches. A tournament rule is said to be k-SNM-${\alpha}$ if no set of k teams…
A long-standing open problem in algorithmic game theory asks whether or not there is a polynomial time algorithm to compute a Nash equilibrium in a random bimatrix game. We study random win-lose games, where the entries of the $n\times n$…
Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…
We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…
The paper develops a new technique to extract a characteristic subset from a random source that repeatedly samples from a set of elements. Here a characteristic subset is a set that when containing an element contains all elements that have…
Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…