Related papers: Twenty (simple) questions
Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set aside at least one coin showing heads;…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
The domatic number of a graph is the maximum number of pairwise disjoint dominating sets admitted by the graph. We introduce a game based around this graph invariant. The domatic number game is played on a graph $G$ by two players, Alice…
We introduce the competitive assignment problem, a two-player version of the well-known assignment problem. Given a set of tasks and a set of agents with different efficiencies for different tasks, Alice and Bob take turns picking agents…
Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…
Suppose Alice has a coin with heads probability $q$ and Bob has one with heads probability $p>q$. Now each of them will toss their coin $n$ times, and Alice will win iff she gets more heads than Bob does. Evidently the game favors Bob, but…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
In this paper, we study algorithms for special cases of energy games, a class of turn-based games on graphs that show up in the quantitative analysis of reactive systems. In an energy game, the vertices of a weighted directed graph belong…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
We consider the problem of decentralized 20 questions with noise for multiple players/agents under the minimum entropy criterion in the setting of stochastic search over a parameter space, with application to target localization. We propose…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
We study the problem of generating a random variate $X$ from a finite discrete probability distribution $P$ using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number…