Equilibrium, evolutionary stability and gradient dynamics

TL;DR: A form of "dynamic" fictitious and gradient play strategy update mechanisms that use derivative action in processing opponent actions and, in some cases, can lead to behavior converging to Nash equilibria in previously nonconvergent situations are introduced.

TL;DR: This paper proposes an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players’ actions, and exploits incremental passivity properties and shows that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors.

TL;DR: In this paper, the authors consider the problem of distributed Nash equilibrium seeking over networks, a setting in which players have limited local information (i.e., instantaneous all-to-all player communication) and consider how to modify this gradient-play dynamics in the case of partial or networked information between players.

TL;DR: This paper proposes Nash equilibrium seeking dynamics based on gradient-play, augmented with a dynamic internal-model based component, which is a reduced-order observer of the disturbance, which shows convergence to the Nash equilibrium irrespective of disturbances.

TL;DR: In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.

TL;DR: In this article, the authors consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game, thus, over time, the strategy mix should evolve to some type of optimal or stable state.

TL;DR: Harsanyi and Selten as mentioned in this paper proposed rational criteria for selecting one particular uniformly perfect equilibrium point as the solution of any non-cooperative game, and applied this theory to a number of specific game classes, such as unanimity games, bargaining with transaction costs; trade involving one seller and several buyers; two-person bargaining with incomplete information on one side, and on both sides.