We survey a research line recently initiated by Mavronicolas et al. [14, 15, 16], concerning a strategic game on a graph G(V,E) with two confronting classes of randomized players: ν attackers who choose vertices and wish to minimize the probability of being caught by the defender, who chooses edges and gains the expected number of attackers it catches. So, the defender captures system rationali...

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. ...

We study a spatial model of party formation in which the set of agendas is the unit circle. We characterize the sets of pure-strategy Nash equilibria under the plurality and proportional rules. In both rules, multiple configurations of parties are possible in Nash equilibrium. We refine our predictions using a new notion called “defection-proof” Nash equilibrium. Under the plurality rule, only ...

In recent work of Hazan and Krauthgamer (SICOMP 2011), it was shown that finding an ε-approximate Nash equilibrium with near-optimal value in a two-player game is as hard as finding a hidden clique of size O(logn) in the random graph G(n,1/2). This raises the question of whether a similar intractability holds for approximate Nash equilibrium without side constraints such as high value. We give ...

In this paper, we investigate a distributed Nash equilibrium seeking problem for a timevarying multi-agent network consisting of two subnetworks. We propose a subgradientbased distributed algorithm to seek a Nash equilibrium of a zero-sum game, where the two subnetworks share the same sum objective function. We show that the proposed distributed algorithm with homogenous stepsize can achieve a ...

The observed choices of a set of players interacting in various related games are said to be Nash rationalizable if there exist preferences for the players that make those choices the pure strategy Nash equilibria for each game. We provide an intuitive characterization of Nash rationalizability under less restrictive conditions than those in the existing literature, and show that this restricte...