A Delivery Network Creation Game
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Piliouras, Georgios; Vigfusson, Ymir
We study a non-cooperative network creation game where players, represented by nodes, can build edges to other players for a cost of ?, and strive to maintain short paths to other players while minimizing cost. Players incur a penalty of ? for each unreachable node in addition to the charges for constructing edges, and attempt to optimize their accrued cost. The model generalizes previous work such that it provides an abstraction for describing the synthesis of various economic networks. For instance, in a network for the transportation of goods between facilities, the ? cost parameter can intuitively be viewed as the price of establishing a route between facilities, and ? is the value (or incentive) to have access to goods at a remote site. We observe sharp changes in optima as the ? and ? parameters vary. Furthermore, we bound the price of anarchy of the game for all values of ?, ? and n, where n is the number of players. We identify surprising properties in the structure of Nash equilibria. We show that not only do there exist zero-incentive strict Nash equilibria of arbitrarily large size but they also exhibit properties such as constant diameter and resilience to any single-edge deletion. Lastly, we identify the ?rst super-constant lower bound on the price of anarchy in this line of research and prove that it is persistent even if we incorporate in our model coalitions of size up to o(sqrt(n)).
Game theory; Network creation game