Related papers: Gambling and R\'enyi Divergence
In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…
Cricket betting is a multi-billion dollar market. Therefore, there is a strong incentive for models that can predict the outcomes of games and beat the odds provided by bookers. The aim of this study was to investigate to what degree it is…
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
A distortion function, which captures the payoff gap between a player's actual payoff and her true payoff, is introduced and used to analyze games. In our proposed framework, we argue that players' actual payoff functions should be used to…
It is well-known that there are a number of relations between theoretical finance theory and information theory. Some of these relations are exact and some are approximate. In this paper we will explore some of these relations and determine…
We give a criterion under which the expected return on a ticket for certain large lotteries is positive. In this circumstance, we use elementary portfolio analysis to show that an optimal investment strategy includes a very small allocation…
Graphon games have been introduced to study games with many players who interact through a weighted graph of interaction. By passing to the limit, a game with a continuum of players is obtained, in which the interactions are through a…
This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…
We address an open problem on the computability of correlated equilibria in a variant of polymatrix where each player's utility is the maximum of their edge payoffs. We demonstrate that this max-variant game has the polynomial expectation…
Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a…
Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…
We derive a new variational formula for the R\'enyi family of divergences, $R_\alpha(Q\|P)$, between probability measures $Q$ and $P$. Our result generalizes the classical Donsker-Varadhan variational formula for the Kullback-Leibler…
The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…
Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are only trained to minimize the training/test error, they could suffer from…
Coherent sets of desirable gamble sets is used as a model for representing an agents opinions and choice preferences under uncertainty. In this paper we provide some results about the axioms required for coherence and the natural extension…
We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that…
Measuring contributions is a classical problem in cooperative game theory where the Shapley value is the most well-known solution concept. In this paper, we establish the convergence property of the Shapley value in parametric Bayesian…