Related papers: Tied Pools and Drawn Games
2.5 player parity games combine the challenges posed by 2.5 player reachability games and the qualitative analysis of parity games. These two types of problems are best approached with different types of algorithms: strategy improvement…
Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…
We introduce a simple one-parameter game derived from a model describing the properties of a directed polymer in a random medium. At his turn, each of the two players picks a move among two alternatives in order to maximize his final score,…
We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a)…
Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Ranking athletes by their performance in competitions and tournaments is common in every popular sport and has significant benefits that contribute to both the organization and strategic aspects of competitions. Although rankings are…
National teams from different continents can play against each other only in afew sports competitions. Therefore, a reasonable aim is maximising the number of intercontinental games in world cups, as done in basketball and football, in…
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…
Hedonic diversity games are a variant of the classical Hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has…
The solution of parity games over pushdown graphs (Walukiewicz '96) was the first step towards an effective theory of infinite-state games. It was shown that winning strategies for pushdown games can be implemented again as pushdown…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
The Bradley-Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such…
The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…