Related papers: Optimal strategy in the game Risk or Safety
In the natural generalization of tic-tac-toe to an $n \times n \times n$ board where $n \in \mathbb{N}$, it is known that the first player has a winning strategy if $n \leq 4$ and that either player can force a draw if $n \geq 8$. The…
In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
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…
We consider multiplayer stochastic games in which the payoff of each player is a bounded and Borel-measurable function of the infinite play. By using a generalization of the technique of Martin (1998) and Maitra and Sudderth (1998), we show…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…
We all have preferences when multiple choices are available. If we insist on satisfying our preferences only, we may suffer a loss due to conflicts with other people's identical selections. Such a case applies when the choice cannot be…
Weighted timed games are two-player zero-sum games played in a timed automaton equipped with integer weights. We consider optimal reachability objectives, in which one of the players, that we call Min, wants to reach a target location while…
Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure.…
We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…
The game show Lucky 13 differs from other television game shows in that contestants are required to place a bet on their own knowledge of trivia by selecting a range that contains the number of questions that they answered correctly. We…
The Rock-Scissors-Paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic…
This paper revisits a classical problem of slotted multiple access with success, idle, and collision events on each slot. First, results of a 2-user multiple access game are reported. The game was conducted at the University of Southern…
Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
In this paper, we consider zero-sum repeated games in which the maximizer is restricted to strategies requiring no more than a limited amount of randomness. Particularly, we analyze the maxmin payoff of the maximizer in two models: the…
Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a…