NDLI: Equilibria and Efficiency Loss in Games on Networks

Content Provider	IEEE Xplore Digital Library
Author	Davis, J.R. Goldman, Z. Hilty, J. Koch, E.N. Liben-Nowell, D. Sharp, A. Wexler, T. Zhou, E.
Copyright Year	2009
Abstract	Social networks are the substrate upon which we make and evaluate many of our daily decisions: our costs and benefits depend on whether---or how many of, or which of---our friends are willing to go to that restaurant, choose that cellular provider, already own that gaming platform. Much of the research on the ``diffusion of innovation,'' for example, takes a game-theoretic perspective on strategic decisions made by people embedded in a social context. Indeed, multiplayer games played on social networks, where the network's nodes correspond to the game's players, have proven to be fruitful models of many natural scenarios involving strategic interaction. In this paper, we embark on a mathematical and general exploration of the relationship between 2-person strategic interactions (a ``base game'') and a ``networked'' version of that same game. We formulate a generic mechanism for superimposing a symmetric 2-player base game $M$ on a social network $G$: each node of $G$ chooses a single strategy from $M$ and simultaneously plays that strategy against each of its neighbors in $G$, receiving as its payoff the sum of the payoffs from playing~$M$ against each neighbor. We denote the \emph{networked game} that results by~$\gamenet{M}{G}$. We are broadly interested in the relationship between properties of~$M$ and of~$\gamenet{M}{G}$: how does the character of strategic interaction change when it is embedded in a social network? We focus on two particular properties: the (pure) price of anarchy and the existence of pure Nash equilibria. We show tight results on the relationship between the price of anarchy in~$M$ and $\gamenet{M}{G}$ in coordination games. We also show that, with some exceptions when $G$ is bipartite, the existence or absence of pure Nash equilibria (and even the guaranteed convergence of best-response dynamics) in $M$ and $\gamenet{M}{G}$ are not entailed in either direction. Taken together, these results suggest that the process of superimposing $M$ on a graph is a nontrivial operation that can have rich, but bounded, effects on the strategic environment.
Starting Page	82
Ending Page	89
File Size	1013749
Page Count	8
File Format	PDF
ISBN	9781424453344
DOI	10.1109/CSE.2009.45
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-08-29
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Technological innovation Social network services Humans social networks game theory Educational institutions Mobile handsets Convergence Jacobian matrices Cellular networks price of anarchy Veins Nash equilibria Computer networks coordination games
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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