The Price of Optimum in a Matching Game
- Cite this paper as:
- Escoffier B., Gourvès L., Monnot J. (2011) The Price of Optimum in a Matching Game. In: Persiano G. (eds) Algorithmic Game Theory. SAGT 2011. Lecture Notes in Computer Science, vol 6982. Springer, Berlin, Heidelberg
Due to the lack of coordination, it is unlikely that the selfish players of a strategic game reach a socially good state. Using Stackelberg strategies is a popular way to improve the system’s performance. Stackelberg strategies consist of controlling the action of a fraction α of the players. However compelling an agent can be costly, unpopular or just hard to implement. It is then natural to ask for the least costly way to reach a desired state. This paper deals with a simple strategic game which has a high price of anarchy: the nodes of a simple graph are independent agents who try to form pairs. We analyse the optimization problem where the action of a minimum number of players shall be fixed and any possible equilibrium of the modified game must be a social optimum (a maximum matching).
For this problem, deciding whether a solution is feasible or not is not straitforward, but we prove that it can be done in polynomial time. In addition the problem is shown to be APX-hard, since its restriction to graphs admitting a vertex cover is equivalent, from the approximability point of view, to vertex cover in general graphs.
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