Related papers: Evaluating gambles using dynamics
We introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies…
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…
A perfectly rational decision-maker chooses the best action with the highest utility gain from a set of possible actions. The optimality principles that describe such decision processes do not take into account the computational costs of…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…
We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…
The capitalization-weighted total relative variation $\sum_{i=1}^d \int_0^\cdot \mu_i (t) \mathrm{d} \langle \log \mu_i \rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $\mu_i (\cdot)$…
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
This paper shows how we can combine logical representations of actions and decision theory in such a manner that seems natural for both. In particular we assume an axiomatization of the domain in terms of situation calculus, using what is…
Motivated by cost of computation in game theory, we explore how changing the utilities of players (changing their complexity costs) affects the outcome of a game. We show that even if we improve a player's utility in every action profile,…
Prediction markets are useful for estimating probabilities of claims whose truth will be revealed at some fixed time -- this includes questions about the values of real-world events (i.e. statistical uncertainty), and questions about the…
Algorithms are often used to produce decision-making rules that classify or evaluate individuals. When these individuals have incentives to be classified a certain way, they may behave strategically to influence their outcomes. We develop a…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this…
This paper proposes a mathematical model for the coevolution of actions and opinions for a population facing a social dilemma. In particular, we assume each person participates in a Public Goods Game (PGG), with their action being to…
A decision maker's utility depends on her action $a\in A \subset \mathbb{R}^d$ and the payoff relevant state of the world $\theta\in \Theta$. One can define the value of acquiring new information as the difference between the maximum…
Effectivity functions are the basic formalism for investigating the semantics game logic. We discuss algebraic properties of stochastic effectivity functions, in particular the relationship to stochastic relations, morphisms and congruences…
We initiate a novel direction in randomized social choice by proposing a new definition of agent utility for randomized outcomes. Each agent has a preference over all outcomes and a {\em quantile} parameter. Given a {\em lottery} over the…