Voice, Thomas, Polukarov, Maria, Byde, Andrew and Jennings, Nicholas R.
(2009)
On the Impact of Strategy and Utility Structures on CongestionAverse Games
At Proc. 5th Int Workshop on Internet and Network Economics (WINE09), Italy.
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Description/Abstract
Recent results regarding games with congestionaverse utilities (or, congestionaverse gamesCAGs) have shown they possess some very desirable properties. Specifically, they have pure strategy Nash equilibria, which may be found by a polynomial time algorithm. However, these results were accompanied by a very limiting assumption that each player is capable of using any subset of its available set of resources. This is often unrealisticfor example, resources may have complementarities between them such that a minimal number of resources is required for any to be useful. To remove this restriction, in this paper we prove the existence and tractability of a pure strategy equilibrium for a much more general setting where each player is given a matroid over the set of resources, along with the (upper and lower) bounds on the size of a subset of resources to be selected, and its strategy space consists of all elements of this matroid that fit in the given size range. (This, in particular, includes the possibility of having a full matroid, or having a set of bases of a matroid.) Moreover, we show that if a player strategy space in a given CAG does not satisfy these matroid properties, then a pure strategy equilibrium need not exist, and in fact the determination of whether or not a game has a pure strategy Nash equilibrium is NPcomplete. We further prove analogous results for each of the congestionaverse conditions on utility functions, thus showing that current assumptions on strategy and utility structures in this model cannot be relaxed anymore.
Item Type: 
Conference or Workshop Item
(Paper)

Venue  Dates: 
Proc. 5th Int Workshop on Internet and Network Economics (WINE09), Italy, 20091201

Organisations: 
Agents, Interactions & Complexity 
ePrint ID: 
267875 
Date : 
Date  Event 

December 2009  Published 

Date Deposited: 
16 Sep 2009 18:48 
Last Modified: 
17 Apr 2017 18:40 
Further Information:  Google Scholar 
URI: 
http://eprints.soton.ac.uk/id/eprint/267875 
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