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Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple…
The uniform distribution is an important counterexample in game theory as many of the canonical game dynamics have been shown not to converge to the equilibrium in certain cases. In particular none of the canonical game dynamics converge to…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
We address Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize…
We consider a dynamical approach to sequential games. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding restriction…
Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and…
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function…
The aim of this paper is threefold. First, we provide a unified framework, by means of non-trivial examples, to compare the results obtained in simultaneous-move and sequential-move versions of bilateral oligopoly with the Cournot model and…
We study discrete two player all-pay auction with complete information. We provide full characterization of mixed strategy Nash equilibria and show that they constitute a subset of Nash equilibria of discrete General Lotto game. We show…
A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…
We study stochastic effects on the lagging anchor dynamics, a reinforcement learning algorithm used to learn successful strategies in iterated games, which is known to converge to Nash points in the absence of noise. The dynamics is…
This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best…
This paper considers dynamic moral hazard settings, in which the consequences of the agent's actions are not precisely understood. In a new continuous-time moral hazard model with drift ambiguity, the agent's unobservable action translates…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
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 study, we analyse the global stability of the equilibrium in a departure time choice problem using a game-theoretic approach that deals with atomic users. We first formulate the departure time choice problem as a strategic game in…
In economics duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called `leader-follower' model. We give a quantum perspective on Stackelberg…
The all-pay auction, a classic competitive model, is widely applied in scenarios such as political elections, sports competitions, and research and development, where all participants pay their bids regardless of winning or losing. However,…
Cooperative dynamics are central to our understanding of many phenomena in living and complex systems. However, we lack a universal mechanism to explain the emergence of cooperation. We present a novel framework for modelling social dilemma…
We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a…