We initiate the study of  congestion games with variable demands  where the (variable) demand has to be assigned to exactly one subset of resources. The players' incentives to use higher demands are stimulated by non-decreasing and concave utility functions. The payoff for a player is defined as the difference between the utility of the demand and the associated cost on the used resources. Although this class of non-cooperative games captures many elements of real-world applications, it has not been studied in this generality, to our knowledge, in the past.   We study the fundamental problem of the existence of  pure Nash equilibria  (PNE for short) in congestion games with variable demands. We call a set of cost functions  C consistent  if every congestion game with variable demands and cost functions in  C  possesses a PNE. We say that  C  is  FIP consistent  if every such game possesses the α-Finite Improvement Property for every α > 0. Our main results provide a complete characterization of consistency of cost functions revealing structural differences to congestion games with  fixed  demands (weighted congestion games), where in the latter even inhomogeneously exponential functions are FIP consistent.   Finally, we study consistency and FIP consistency of cost functions in a slightly different class of games, where every player experiences the same cost on a resource (uniform cost model). We give a characterization of consistency and FIP consistency showing that only homogeneously exponential functions are consistent while no functions are FIP consistent.
['Tobias Harks', 'Max Klimm']
Congestion games with variable demands