Partially-Specified Large Games

Abstract

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Essential collections for equilibrium concepts

“…We borrow the name of structural robustness from Kalai (2005Kalai ( , 2006, where similar changes in the underlying games are considered and used to study the robustness of Nash equilibria in large games.…”

“…The discussion above says that after any change in the game that does not affect the essential collection for SE, Γ, and b, the outcome of b remains a SE outcome in the modified game; no further calculation is needed, regardless of the actual payoffs of the modified game. On the other hand, suppose that b is just a WPBE but not a SE, then, since the latter changes might have affected the corresponding essential collection for WPBE (which is J u l y 6 , 2 0 1 1 S u b m i s s i o n 5.2.2 Partially-specified games As also discussed in Kalai (2005Kalai ( , 2006, the idea of structural robustness is very related to the possibility of dealing with partially-specified games. Let G p = (Γ, h) be a partially-specified game, i.e., it lacks of a full description of Γ or some payoffs are unknown.…”

Computing Equilibria in Anonymous Games

“…Anonymous games comprise a broad and well studied class of games (see e.g. [4,5,16] for recent work on this subject by economists) which are of special interest to the Algorithmic Game Theory community, as they capture important aspects of auctions and markets, as well as of Internet congestion.…”

Approximate Nash equilibria in anonymous games

“…Once a problem of interest is shown to be intractable, more modest goals are pursued: One seeks to solve important special cases of the problem, or to solve them approximately. That is what we accomplish in this paper: we identify a very broad and significant special class of games, the anonymous games studied in the past (see [Mil96,Blo99,Blo05,Kal05] and the definition below), and develop algorithms for finding approximate Nash equilibria in such games. By "approximate Nash equilibrium" we mean a strategy profile in which each player cannot improve her lot by more than a fixed amount denoted .…”

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AbstractWe study from an algorithmic viewpoint anonymous games [Mil96,Blo99,Blo05,Kal05]. In these games a large population of players shares the same strategy set and, while players may have different payoff functions, the payoff of each depends on her own choice of strategy and the number of the other players playing each strategy (not the identity of these players).

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