We study graphical games where the payoff function of each player satisfies one of four types of symmetry in the actions of his neighbors. We establish that deciding the existence of a pure Nash equilibrium is NP-hard in general for all four types. Using a characterization of games with pure equilibria in terms of even cycles in the neighborhood graph, as well as a connection to a generalized s...

In this paper, a detailed survey is presented for the analysis and control of networked evolutionary games via matrix method. The algebraic form firstly recalled. Then, some existing results on are summarized. Furthermore, several generalized forms reviewed, including with time delay, bankruptcy mechanism, time-varying networks, random Boolean games. computational complexity general still chall...

We evaluated 22 patients with epileptic seizures in which the seizures were triggered by various games or game-related materials. Based on whether spontaneous seizure coexisted or not, these 22 patients were divided into two groups. Ten patients who experienced seizures exclusively while playing or watching specific games were referred to as Group I, while 12 patients that had both game-induced...

In this work, we study the generalized Nash equilibrium (GNE, see Definition 1 ) seeking problem for monotone noncooperative games with set constraints and shared affine inequality constraints. A novel projected gradient-based regularized penalized dynam...

What happens when you play Chess and Tic-Tac-Toe at the same time? What about Mancala, Othello and Checkers? Playing multiple games together as a Combined Game introduces an entirely new, infinite set of games to analyze and play. We use traditional Game Theory tools to examine combined pairs of small, well-solved games, yielding information on the optimal strategies for playing each combined g...

The purpose of this paper is to prove a new topological fixed point theorem by using the connectedness property, and next existence of equilibria in generalized games are established as applications.

We define generalized extensive-form games which allow for asymmetric awareness of actions. We extend Pearce’s (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties, and prove existence.

We provide a general mechanism to design online learning algorithms based on a minimax analysis within a drifting-games framework. Different online learning settings (Hedge, multi-armed bandit problems and online convex optimization) are studied by converting into various kinds of drifting games. The original minimax analysis for drifting games is then used and generalized by applying a series ...

We propose a parametric family of measures of fairness in allocations of TU-cooperative games. Their definition is based on generalized Rényi Entropy, is related to the Cowell-Kuga generalized entropy indices in welfare economics, and aims to parallel the spirit of the notion of price of anarchy in the case of convex TU-cooperative games. Since computing these indices is NP-complete in general,...

Risk aversion in game theory is usually modeled using expected utility, which was criticized early on, leading to an extensive literature on generalized utility. In this paper we are the first apply ?–? analysis of (static) games. widely accepted finance literature; it allows us study effect uncertainty endogenous game, i.e., mixed equilibria. particular, look at case linear utility functions a...