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Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
A casino offers the following game. There are three cups each containing a die. You are being told that the dice in the cups are all the same, but possibly nonstandard. For a bet of \$1, the game master shakes all three cups and lets you…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
We introduce a general framework for continuous-time betting markets, in which a bookmaker can dynamically control the prices of bets on outcomes of random events. In turn, the prices set by the bookmaker affect the rate or intensity of…
There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have…
Dynamic game arises as a powerful paradigm for multi-robot planning, for which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, as real-world robots need to operate and satisfy constraints…
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…
We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
Facing the FRTB, banks need to allocate their capital to each business units or risk positions to evaluate the capital efficiency of their strategies. This paper proposes two computationally efficient allocation methods which are weighted…
This article investigates the influence of luck and strategic considerations on performance of teams participating in the M6 investment challenge. We find that there is insufficient evidence to suggest that the extreme Sharpe ratios…
This paper investigates the robust {non-zero-sum} games in an aggregated {overfunded} defined benefit (abbr. DB) pension plan. The sponsoring firm is concerned with the investment performance of the fund surplus while the participants act…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise…
The decisions that human beings make to allocate time has significant bearing on economic output and to the sustenance of social networks. The time allocation problem motivates our formal analysis of the resource allocation game, where…
In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies.…
We investigate the relation between Bell inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bell…
We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal strategy. This model can be interpreted as trading in an…
Risk and uncertainty will always be a matter of experience, luck, skills, and modelling. Leverage is another concept, which is critical for the investor decisions and results. Adaptive skills and quantitative probabilistic methods need to…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
Hedge has been proposed as an adaptive scheme, which guides an agent's decision in resource selection and distribution problems that can be modeled as a multi-armed bandit full information game. Such problems are encountered in the areas of…