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We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random…

The sequential multiple testing problem is considered under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$…

We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…

We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be…

This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…

Statistical arbitrage exploits temporal price differences between similar assets. We develop a unifying conceptual framework for statistical arbitrage and a novel data driven solution. First, we construct arbitrage portfolios of similar…

Leveraging planning during learning and decision-making is central to the long-term development of intelligent agents. Recent works have successfully combined tree-based search methods and self-play learning mechanisms to this end. However,…

We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to…

We study repeated multi-player vector-valued games in which a player observes a payoff vector each round and evaluates outcomes through linear scalarizations of those vectors. Different from most prior works, the choice of scalarization is…

We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…

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…

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…

We study the design of optimal incentives in sequential processes. To do so, we consider a basic and fundamental model in which an agent initiates a value-creating sequential process through costly investment with random success. If…

We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…

A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…

We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the…

We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…

We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…

Stackelberg equilibrium is a solution concept that describes optimal strategies to commit: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader's…