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In this paper, we introduce a novel equilibrium concept, called the equilibrium cycle, which seeks to capture the outcome of oscillatory game dynamics. Unlike the (pure) Nash equilibrium, which defines a fixed point of mutual best…
This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…
We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L\'{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform…
We study a game between two firms in which each provide a service based on machine learning. The firms are presented with the opportunity to purchase a new corpus of data, which will allow them to potentially improve the quality of their…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model…
In this paper, we consider a novel $M$-ary sequential hypothesis testing problem in which an adversary is present and perturbs the distributions of the samples before the decision maker observes them. This problem is formulated as a…
In the paper [Hainaut, D. and Colwell, D.B., {\rm A structural model for credit risk with switching processes and synchronous jumps}, The European Journal of Finance 22(11) (2016): 1040-1062], the authors exploit a synchronous-jump…
In this paper, we address the inverse problem in the case of linear-quadratic discrete-time dynamic non-cooperative games. Given feedback laws of players that are known to be a Nash equilibrium pair for a discrete-time linear system, we…
We consider the classic motion planning problem defined over a roadmap in which a vehicle seeks to find an optimal path from a source to a destination in presence of an attacker who can launch attacks on the vehicle over any edge of the…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the…
This paper introduces risk-revising players to a class of games with incomplete information. These players enter the game with ex ante risk preferences represented by coherent risk measures and develop time-consistent interim revisions of…
In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system's long term…
We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the case where players deviate from it. We then pivot to the study of a large class of adaptive strategies and…
We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture…
The main goal of this paper is to study a stochastic game connected to a system of forward backward stochastic differential equations (FBSDEs) involving delay and so-called noisy memory. We derive suffcient and necessary maximum principles…