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Game contingent claims (GCCs) generalize American contingent claims by allowing the writer to recall the option as long as it is not exercised, at the price of paying some penalty. In incomplete markets, an appealing approach is to analyze…
This paper investigates Nash equilibrium (NE) seeking problems for noncooperative games over multi-players networks with finite bandwidth communication. A distributed quantized algorithm is presented, which consists of local gradient play,…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
In the framework of finite games in extensive form with perfect information and strict preferences, this paper introduces a new equilibrium concept: the Perfect Prediction Equilibrium (PPE). In the Nash paradigm, rational players consider…
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…
In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…
A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is presented, the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems.…
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…
This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like…
In this paper, we consider the competitive diffusion game, and study the existence of its pure-strategy Nash equilibrium when defined over general undirected networks. We first determine the set of pure-strategy Nash equilibria for two…
Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks…
Frequent violations of fair principles in real-life settings raise the fundamental question of whether such principles can guarantee the existence of a self-enforcing equilibrium in a free economy. We show that elementary principles of…
We consider games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach.…
We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players' actions cannot anticipate future values of their types. Such games go under…
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…
We consider a dynamical approach to game in extensive forms. 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…
We revisit in this paper the relation between evolution of species and the mathematical tool of evolutionary games, which has been used to model and predict it. We indicate known shortcoming of this model that restricts the capacity of…
Many distributed systems can be modeled as network games: a collection of selfish players that communicate in order to maximize their individual utilities. The performance of such games can be evaluated through the costs of the system…
Many economic interventions are designed as marginal changes in incentives. Yet in environments shaped by coordination, institutional persistence, and path dependence, such reforms often leave behavior largely unchanged. This paper studies…
A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to…