Related papers: Probabilistic vs deterministic gamblers
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
We give a general method for constructing a deterministic strategy of Reality from a randomized strategy in game-theoretic probability. The construction can be seen as derandomization in game-theoretic probability.
Muchnik's paradox says that enumerable betting strategies are not always reducible to enumerable strategies whose bets are restricted to either even rounds or odd rounds. In other words, there are outcome sequences x where an effectively…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
Unlike Martin-L\"of randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and…
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…
The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical…
Toral (2002) considered an ensemble of N\geq2 players. In game B a player is randomly selected to play Parrondo's original capital-dependent game. In game A' two players are randomly selected without replacement, and the first transfers one…
In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, numerous modern forecasting methods are still designed to create deterministic forecasts. Transforming…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
Randomness in the sense of Martin-L\"of can be defined in terms of lower semicomputable supermartingales. We show that such a supermartingale cannot be replaced by a pair of supermartingales that bet only on the even bits (the first one)…
It is known that if two players achieve a superclassical score at a nonlocal game $G$, then their outputs are certifiably random - that is, regardless of the strategy used by the players, a third party will not be able to perfectly predict…
We consider extensive form win-lose games over a complete binary-tree of depth $n$ where players act in an alternating manner. We study arguably the simplest random structure of payoffs over such games where 0/1 payoffs in the leafs are…
We distinguish finitarily between algorithmic verifiability, and algorithmic computability, to show that Goedel's 'formally' unprovable, but 'numeral-wise' provable, arithmetical proposition [(Ax)R(x)] can be finitarily evidenced as:…
We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y…
Consider a binary decision making process where a single machine learning classifier replaces a multitude of humans. We raise questions about the resulting loss of diversity in the decision making process. We study the potential benefits of…
We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event $\mathcal A$ such that if…