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For a game with positive profit, the optimal proportion of investment required to continue investing without borrowing is uniquely determined by an integral equation for each price. For a game with parallel translated profit, the ratio of…
In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several…
Markov decision processes (MDPs) are a popular model for decision-making in the presence of uncertainty. The conventional view of MDPs in verification treats them as state transformers with probabilities defined over sequences of states and…
The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on…
For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is…
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…
Equity premium, the surplus returns of stocks over bonds, has been an enduring puzzle. While numerous prior works approach the problem assuming the utility of money is invariant across contexts, our approach implies that in efficient…
In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper…
A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a "primitive ontology" (PO), i.e., variables…
The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the…
Peer-prediction is a mechanism which elicits privately-held, non-variable information from self-interested agents---formally, truth-telling is a strict Bayes Nash equilibrium of the mechanism. The original Peer-prediction mechanism suffers…
This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the…
As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing…
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for…
We derive an explicit formula for the probability of ruin of a gambler playing against an infinitely-rich adversary, when the games have payoff given by a general integer-valued probability distribution.
Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from the truthfulness; it is not incorporated in players' utility functions (and doing so…
Decentralized prediction markets (DePMs) allow open participation in event-based wagering without fully relying on centralized intermediaries. We review the history of DePMs which date back to 2011 and includes hundreds of proposals.…