12,280 research outputs found
Network Topology and Equilibrium Existence in Weighted Network Congestion Games
Every finite noncooperative game can be presented as a weighted network congestion game, and also as a network congestion game with player-specific costs. In the first presentation, different players may contribute differently to congestion, and in the second, they are differently (negatively) affected by it. This paper shows that the topology of the underlying (undirected two-terminal) network provides information about the existence of pure-strategy Nash equilibrium in the game. For some networks, but not for others, every corresponding game has at least one such equilibrium. For the weighted presentation, a complete characterization of the networks with this property is given. The necessary and sufficient condition is that the network has at most three routes that do traverse any edge in opposite directions, or it consists of several such networks connected in series. The corresponding problem for player-specific costs remains open.Congestion games, network topology, existence of equilibrium
Nash equilibria of the pay-as-bid auction with K-Lipschitz supply functions
We model a system of n asymmetric firms selling a homogeneous good in a
common market through a pay-as-bid auction. Every producer chooses as its
strategy a supply function returning the quantity S(p) that it is willing to
sell at a minimum unit price p. The market clears at the price at which the
aggregate demand intersects the total supply and firms are paid the bid prices.
We study a game theoretic model of competition among such firms and focus on
its equilibria (Supply function equilibrium). The game we consider is a
generalization of both models where firms can either set a fixed quantity
(Cournot model) or set a fixed price (Bertrand model). Our main result is to
prove existence and provide a characterization of (pure strategy) Nash
equilibria in the space of K-Lipschitz supply functions.Comment: 6 pages, 5 figures, to appear Proc. of the 22nd International
Federation of Automatic Control World Congress (IFAC 2023
On Linear Congestion Games with Altruistic Social Context
We study the issues of existence and inefficiency of pure Nash equilibria in
linear congestion games with altruistic social context, in the spirit of the
model recently proposed by de Keijzer {\em et al.} \cite{DSAB13}. In such a
framework, given a real matrix specifying a particular
social context, each player aims at optimizing a linear combination of the
payoffs of all the players in the game, where, for each player , the
multiplicative coefficient is given by the value . We give a broad
characterization of the social contexts for which pure Nash equilibria are
always guaranteed to exist and provide tight or almost tight bounds on their
prices of anarchy and stability. In some of the considered cases, our
achievements either improve or extend results previously known in the
literature
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