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In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
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…
In a guessing game, players guess the value of a random real number selected using some probability density function. The winner may be determined in various ways; for example, a winner can be a player whose guess is closest in magnitude to…
The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to…
Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…
We study a complementarity game with multiple populations whose members' offered contributions are put together towards some common aim. When the sum of the players' offers reaches or exceeds some threshold K, they each receive K minus…
We propose a generic mechanism for incentivizing behavior in an arbitrary finite game using payments. Doing so is trivial if the mechanism is allowed to observe all actions taken in the game, as this allows it to simply punish those agents…
This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed…
Decentralized optimization of distributed stochastic differential systems has been an active area of research for over half a century. Its formulation utilizing static team and person-by-person optimality criteria is well investigated.…
We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…
Multi-player multi-armed bandit is an increasingly relevant decision-making problem, motivated by applications to cognitive radio systems. Most research for this problem focuses exclusively on the settings that players have \textit{full…
Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the…
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…
In the Penney-Ante game, Player I chooses a head/tail string of a predetermined length $n\ge3$. Player II, upon seeing Player I's choice, chooses another head/tail string of the same length. A coin is then tossed repeatedly and the player…
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource.…
We study how disagreement influences team performance in a dynamic game with positive production externalities. Players can hold different views about the productivity of the available production technologies. This disagreement results in…
We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…
In this paper, we study the average case complexity of the Unique Games problem. We propose a natural semi-random model, in which a unique game instance is generated in several steps. First an adversary selects a completely satisfiable…