Related papers: A General Theorem for Non-Simultaneous Hat Guessin…
Lionel Levine's hat challenge has $t$ players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are…
We study the hat chromatic number of a graph defined in the following way: there is one player at each vertex of a loopless graph $G$, an adversary places a hat of one of $K$ colors on the head of each player, two players can see each…
In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based…
Prisoner's Dilemma is a game theory model used to describe altruistic behavior seen in various populations. This theoretical game is important in understanding why a seemingly selfish strategy does persist and spread throughout a population…
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy…
Punishment is a common tactic to sustain cooperation and has been extensively studied for a long time. While most of previous game-theoretic work adopt the imitation learning where players imitate the strategies who are better off, the…
In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a…
Geschke, Lubarsky, and Rahn in ``Choice and the Hat Game''~\cite{choice-and-the-hat-game} generalize the classic hat game puzzle to infinitely-many players and ask whether every model of set theory without choice in which the optimal…
We introduce a two-player game in which one and his/her opponent attempt to pack as many ``prisoners'' as possible on the squares of an n-by-n checkerboard; each prisoner has to be ``protected'' by at least as many guards as the number of…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
The dilemma in cooperation is one of the major concerns in game theory. In a public-goods game, each individual pays a cost for cooperation, or to prevent defection, and receives a reward from the collected cost in a group. Thus, defection…
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger…
We propose a two-agent game wherein a questioner must be able to conjure discerning questions between sentences, incorporate responses from an answerer, and keep track of a hypothesis state. The questioner must be able to understand the…
Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…
The field of Game Theory provides a useful mechanism for modeling many decision-making scenarios. In participating in these scenarios individuals and groups adopt particular strategies, which generally perform with varying levels of…
We analyze the version of the deterministic Hats game. In this paper, we present new constructors, i.e. theorems that allow built winning strategies for the sages on different graphs. Using this technique we calculate the hat guessing…
The Prisoner's Dilemma has been a subject of extensive research due to its importance in understanding the ever-present tension between individual self-interest and social benefit. A strictly dominant strategy in a Prisoner's Dilemma…
Cooperation is usually represented as a Prisoner's Dilemma game. Although individual self-interest may not favour cooperation, cooperation can evolve if, for example, players interact multiple times adjusting their behaviour accordingly to…
We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus.…
The logic of the hide and seek game LHS was proposed to reason about search missions and interactions between agents in pursuit-evasion environments. As proved in literature, having an equality constant in the language of LHS drastically…