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Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…

Using the duality techniques introduced by De Meyer (1996a, 1996b), De Meyer and Marino (2005) provided optimal strategies for both players in finitely repeated games with incomplete information on two sides, in the independent case. In…

We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…

We study a game where one player selects a random function, and the other has to guess that function, and show that with high probability the second player can correctly guess most of the random function. We apply this analysis to…

We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…

Communication is rarely perfect, but rather prone to error of transmission and reception. Often the origin of these errors cannot be properly quantified and is thus imprecisely known. We analyze the impact of an ambiguous noise which may…

This paper considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a…

We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…

We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…

Poker is in the family of imperfect information games unlike other games such as chess, connect four, etc which are perfect information game instead. While many perfect information games have been solved, no non-trivial imperfect…

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…

We examine sequential equilibrium in the context of computational games, where agents are charged for computation. In such games, an agent can rationally choose to forget, so issues of imperfect recall arise. In this setting, we consider…

Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in…

We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider…

This paper develops a theory of learning under ambiguity induced by the decision maker's beliefs about the collection of data correlated with the true state of the world. Within our framework, two classical results on Bayesian learning…

It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with…

The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the…

We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…