Akaki Mamageishvili

Tree Nash Equilibria in the Network Creation Game

In the network creation game with n vertices, every vertex (a player) buys a set of adjacent edges, each at a fixed amount {\alpha} > 0. It has been conjectured that for {\alpha} >= n, every Nash equilibrium is a tree, and has been confirmed for every {\alpha} >= 273n. We improve upon this bound and show that this is true for every {\alpha} >= 65n. To show this, we provide new and improved results on the local structure of Nash equilibria. Technically, we show that if there is a cycle in a Nash equilibrium, then {\alpha} = 41n, then every such Nash equilibrium is a tree.

Multicast Network Design Game on a Ring

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of

Election Security and Economics: It’s All About Eve

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No truthful mechanism can be better than n approximate for two natural problems

43 and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best Nash equilibrium and of a general optimum. Therefore, we answer an open question posed by Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches 2 for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy achieved for a worst-case order of the arrival of the players. We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of

Improved bounds on equilibria solutions in the network design game

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Sophisticated Attacks on Decoy Ballots: A Devil's Menu and the Market for Lemons

43, and provide an upper bound of