Article

# Approximate Strong Equilibrium in Job Scheduling Games.

J. Artif. Intell. Res. (JAIR) 01/2009; 36:387-414.
Source: DBLP
0 0
·
0 Bookmarks
·
45 Views
• Source
##### Conference Proceeding: On the Road to -Completeness: 8 Agents in a Singleton Congestion Game.
[hide abstract]
ABSTRACT: In this paper, we investigate the complexity of computing locally optimal solutions for Singleton Congestion Games (SCG), in the framework ofPLS, as defined in Johnson et al. (34). Here, in an instance weighted agents choose links from a set of identical links, such that no agent has an incentive to unilateraly decrease its cost by switching to a different link. The cost of an agent is the load (the sum of the weights of the agents) on the link it chooses. The agents are selfish and try to minimize their individual cost. Agents may form arbitrary, non-fixed coalitions. The cost of a coalition is defined to be the maximum cost of its members. The potential function is defined as the lexicographical order of the agents' cost. In each selfish step of a coalition, the potential function decreases. Thus, a local minimum is a Nash Equilibrium. The neighborhood of a feasible assignment (every agent chooses a link) are all assignments, where the cost of some arbitrary non-fixed coalition of at most k reallocating agents decreases. We call this problem SCG-(k) and show that SCG-(k) isPLS-complete for k 8. On the other hand, for k = 1, it is well known that the solution computed by Graham's LPT-algorithm (22, 29) is locally optimal for SCG-(k), (20, 32). We show our result by tight reduction from the MAXCONSTRAINTASSIGNMENT problem (p;q;r)-MCA, which is an extension of GENERALIZED SATISFIABILITY to higher valued variables. Here, p is the maximum number of variables occuring in a constraint, q is the maximum number of appearances of a variable, and r is the valuedness of the variables. To the best of our knowledge, SCG-(k) is the first problem, which is known to be solvable in polynomial time for a small neighborhood andPLS-complete for a larger, but still constant neighborhood.
Internet and Network Economics, 4th International Workshop, WINE 2008, Shanghai, China, December 17-20, 2008. Proceedings; 01/2008