CSCI 3210: Computational Game Theory Inefficiency of Equilibria - - PDF document
12/5/19 CSCI 3210: Computational Game Theory Inefficiency of Equilibria & Routing Games Ref: Ch 17, 18 [AGT] Mohammad T . Irfan Email: mirfan@bowdoin.edu Web: www.bowdoin.edu/~mirfan 1 Split or steal game u NE outcome vs. socially
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u NE outcome vs. socially best/optimal outcome Payoff matrix
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u Again: NE outcome vs socially optimal outcome Payoff matrix
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u What is the objective function to compare
u Utilitarian u Egalitarian
u How to deal with multiplicity of NE?
u Inefficiency of which NE? u Price of anarchy vs. price of stability
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u PoA =
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u PoS =
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u Calculate PoA and PoS Payoff matrix
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u Calculate PoA and PoS Payoff matrix
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u Consider costs u PoA and PoS will be >= 1 u PoA = PoS when all NE have the same cost
u In general, PoA >= PoS
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u PoA: worst case guarantee in a system of
u PoS: measures benefit of a protocol or
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u Multicommodity flow network
u Directed network with multiple (source, sink) pairs u Each (source, sink) pair is called a commodity u ri amount of traffic for each commodity i
u Each edge e has a delay or cost function ce
u Every car going through an edge gets same delay
u Cost of a path = sum of edge costs
u Note: cost doesn't depend on identity of players u Congestion games
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u Let f be a feasible flow (combining all
u f is equilibrium flow if
u All detours have higher (or equal) delay
equilibrium flow
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u Cost of the whole flow (all red and green)
u Total delay on each edge
s1 s2 t1 t2
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u Price of anarchy for any nonatomic routing
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u Consider large number p; 1 unit of traffic u Equilibrium cost = ? Optimal cost = ? PoA = ?
equilibrium flow PoA à +∞
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u 1 unit of traffic
equilibrium flow and cost? PoA = ?
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u New super highway between v and w
PoA = 4/3
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