Related papers: Evaluating gambles using dynamics
We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…
This paper investigates optimal portfolio strategies in a financial market where the drift of the stock returns is driven by an unobserved Gaussian mean reverting process. Information on this process is obtained from observing stock returns…
The objective is to find a Cellular Automata (CA) rule that can evolve 2D patterns that are optimal with respect to a global fitness function. The global fitness is defined as the sum of local computed utilities. A utility or value function…
We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
From the standpoint of game theory, dominoes is a game that has not received much attention (specially the variety known as draw). It is usually thought that this game is already solved, given general results in game theory. However, the…
In game theory and artificial intelligence, decision making models often involve maximizing expected utility, which does not respect ordinal invariance. In this paper, the author discusses the possibility of preserving ordinal invariance…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
The accumulation of individual fitness or wealth is modelled as a population game in which pairs of individuals are recurrently and randomly matched to play a game over a resource. In addition, all individuals have random access to a…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…
The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries, St. Petersburg paradox, premature profits and growing losses criticized by Livermore are reviewed under an angle of view comparing mathematical expectations with…
A classical portfolio theory deals with finding the optimal proportion in which an agent invests a wealth in a risk-free asset and a probabilistic risky asset. Formulating and solving the problem depend on how the risk is represented and…
In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
We present a stylized model with feedback loops for the evolution of a population's wealth over generations. Individuals have both talent and wealth: talent is a random variable distributed identically for everyone, but wealth is a random…
We propose a set of conservative models in which agents exchange wealth with a preference in the choice of interacting agents in different ways. The common feature in all the models is that the temporary values of financial status of agents…
We study a class of probabilistic cooperative games which can be treated as an extension of the classical cooperative games with transferable utilities. The coalitions have an exogenous probability of being realized. This probability…
An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…
Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that…