Dagstuhl Seminar Proceedings. 05011 - Computing and Markets
Doi
Abstract
This talk will survey two graphical models which the authors have proposed
for compactly representing single-shot, finite-action games in which a large
number of agents contend for scarce resources.
The first model considered is Local-Effect Games (LEGs). These games often
(but not always) have pure-strategy Nash equilibria. Finding a potential
function is a good technique for finding such equilibria. We give a complete
characterization of which LEGs have potential functions and provide the
functions in each case; we also show a general case where pure-strategy
equilibria exist in the absence of potential functions.
Action-graph games (AGGs) are a fully expressive game representation which
can compactly express both strict and context-specific independence between
players\u27 utility functions, and which generalize LEGs. We present algorithms
for computing both symmetric and arbitrary equilibria of AGGs, based on a
continuation method proposed by Govindan and Wilson. We analyze the worst-
case cost of computing the Jacobian of the payoff function, the exponential-
time bottleneck step of this algorithm, and in all cases achieve exponential
speedup. When the indegree of G is bounded by a constant and the game is
symmetric, the Jacobian can be computed in polynomial time