Related papers: Dominance in the Monty Hall Problem
Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected…
A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than can…
Recent studies have analyzed whether one forecast method dominates another under a class of consistent scoring functions. While the existing literature focuses on empirical tests of forecast dominance, little is known about the theoretical…
This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of…
Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in…
Consider a balls-in-bins process in which each new ball goes into a given bin with probability proportional to f(n), where n is the number of balls currently in the bin and f is a fixed positive function. It is known that these so-called…
This paper develops stochastic optimization problems for describing and analyzing behavioral investors with Markowitz Stochastic Dominance (MSD) preferences. Specifically, we establish dominance conditions in a discrete state-space to…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
The Minority Game (MG) behaves as a stochastically perturbed deterministic system due to the coin-toss invoked to resolve tied strategies. Averaging over this stochasticity yields a description of the MG's deterministic dynamics via mapping…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
Knowing the strategy of an opponent in a competitive environment conveys obvious evolutionary advantages. But this information is costly, and the benefit of being informed may not necessarily offset the additional cost. Here we introduce…
Dominance is usually considered a constant value that describes the relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a focal polymorphic locus. However, the observed dominance can vary with…
We consider a dominance order on positive vectors induced by the elementary symmetric polynomials. Under this dominance order we provide conditions that yield simple proofs of several monotonicity questions. Notably, our approach yields a…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
The prototype of a cyclic dominant system is the so-called rock-scissors-paper game, but similar relation among competing strategies can be identified in several other models of evolutionary game theory. In this work we assume that a…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
We have shown that entanglement assisted stochastic strategies allow access to strategic measures beyond the classically correlated measures accessible through passive common randomness, and thus attain a quantum advantage in decentralised…
Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence…
Like many other voting systems, Majority Judgement suffers from the weaknesses of the underlying mathematical model: Elections as problem of choice or ranking. We show how the model can be enhanced to take into account the complete process…