Related papers: Analysis of the gift exchange problem
We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we…
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven…
Consider the following one player game. A deck containing $m$ copies of $n$ different card types is shuffled uniformly at random. Each round the player tries to guess the next card in the deck, and then the card is revealed and discarded.…
Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new…
The Ultimatum Game is a famous sequential, two-player game intensely studied in Game Theory. A proposer can offer a certain fraction of some amount of a valuable good, for example, money. A responder can either accept, in which case the…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
On the blockchain, NFT games have risen in popularity, spawning new types of digital assets. We present a simplified version of well-known NFT games, followed by a discussion of issues influencing the structure and stability of generic…
As interaction between autonomous agents, communication can be analyzed in game-theoretic terms. Meaning game is proposed to formalize the core of intended communication in which the sender sends a message and the receiver attempts to infer…
Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any…
We consider the following game. A deck with $m$ copies of each of $n$ distinct cards is shuffled in a perfectly random way. The Guesser sequentially guesses the card from top to bottom. After each guess, the Guesser is informed whether the…
We introduce two-player games which build words over infinite alphabets, and we study the problem of checking the existence of winning strategies. These games are played by two players, who take turns in choosing valuations for variables…
For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…
The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at site of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma…
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…
We study secretary problems in settings with multiple agents. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision…
In the distributional Twenty Questions game, Bob chooses a number $x$ from $1$ to $n$ according to a distribution $\mu$, and Alice (who knows $\mu$) attempts to identify $x$ using Yes/No questions, which Bob answers truthfully. Her goal is…
Game theory is fundamental to understanding cooperation between agents. Mainly, the Prisoner's Dilemma is a well-known model that has been extensively studied in complex networks. However, although the emergence of cooperation has been…
In this note we discuss a theory of combinatorial games that involve transmitting the moves through a noisy channel that can introduce errors during the transmission. Players are aware of this interference and incorporate this variable into…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
Given a set of $p$ players we consider problems concerning envy-free allocation of collections of $k$ pieces from a given set of goods or chores. We show that if $p\le n$ and each player can choose $k$ pieces out of $n$ pieces of a cake,…