In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount α > 0. It has been conjectured that for α ≥ n, every Nash equilibrium is a tree, and has been confirmed for every α ≥ 273 · n. We improve upon this bound and show that this is true for every α ≥ 65 · n. To show this, we provide new and improved results on the local structur...

We study the complexity of computing Nash equilibria in games where players arranged as the vertices of a graph play a symmetric 2-player game against their neighbours. We call this a pairwise interaction game. We analyse this game for n players with a fixed number of actions and show that (1) a mixed Nash equilibrium can be computed in constant time for any game, (2) a pure Nash equilibrium ca...

We do a game-theoretic analysis of leader election, under the assumption that each agent prefers to have some leader than to have no leader at all. We show that it is possible to obtain a fair Nash equilibrium, where each agent has an equal probability of being elected leader, in a completely connected network, in a bidirectional ring, and a unidirectional ring, in the synchronous setting. In t...

The problem of finding Nash equilibria is one of the fundamental problems in Algorithmic Game Theory, and has made a nice connection between Game Theory and Computer Science [9]. While Nash [10] introduced the concept of Nash equilibrium and proved every game has a mixed Nash equilibrium, finding a Nash equilibrium in reasonable time seems to be essential. The Nash equilibrium can be used as a ...

We consider a strategic game with two classes of confronting randomized players on a graph G(V,E): ν attackers, each choosing vertices and wishing to minimize the probability of being caught, and a defender, who chooses edges and gains the expected number of attackers it catches. The Price of Defense is the worst-case ratio, over all Nash equilibria, of the optimal gain of the defender over its...

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of Nash equilibrium. Specifically, we examine the conditions under which subjects playing the game of Chicken will condition their behavior on private third–party recommendations drawn from publicly– announced distributions. We find that when recommendations are given...

We introduce a new solution concept for short-sighted players engaging in a repeated interaction: a Belief-based equilibrium (BBE). In a BBE, players optimize myopically given their beliefs which are not necessarily correct, but are not contradicted by the data. We show that, if the stage game has a unique correlated equilibrium then the play of a BBE resembles a Nash equilibrium play. However,...

We study optimal tolls for network congestion games where players aim to route certain amount of traffic between various source destination pairs. We consider weighted atomic users, unsplittable traffic and arbitrary nondecreasing latency functions. Users are selfish and want to follow routes that minimize their respective latencies. We focus on pure Nash equilibria. A Nash equilibrium profile ...

1. We proved that in any game for which there exists a jointly-differentially private algorithm for computing an approximate Nash equilibrium, there exists a corresponding mediated game in which “good behavior” (using the mediator, truthfully reporting your type to it, and then faithfully following its suggestion) forms an ex-post Nash equilibrium, and that the resulting play forms a Nash equil...

The division of a cake by two players is modelled by means of a silent game oí timing. It is shown that this game has a unique Nash equilibrium. The strategies of the Nash equilibrium are explicitly given. KEYWOR~s: Nash equilibrium, Game of timing. 'The author is financally supported by the Netherland Organisation for Scientific R,esearch (NWO). I thank Peter Borm, Eric van Damme, Feico Drost,...