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We consider a basic resource allocation game, where the players' strategyspaces are subsets of $R^m$ and cost/utility functions are parameterized bysome common vector $u\in R^m$ and, otherwise, only depend on the own strategychoice. A strategy of a player can be interpreted as a vector of resourceconsumption and a joint strategy profile naturally leads to an aggregateconsumption vector. Resources can be priced, that is, the game is augmented bya price vector $\lambda\in R^m_+$ and players have quasi-linear overallcosts/utilities meaning that in addition to the original costs/utilities, aplayer needs to pay the corresponding price per consumed unit. We investigatethe following question: for which aggregated consumption vectors $u$ can wefind prices $\lambda$ that induce an equilibrium realizing the targetedconsumption profile?  For answering this question, we revisit a well-known duality-based frameworkand derive several characterizations of the existence of such $u$ and $\lambda$using convexification techniques. We show that for finite strategy spaces orcertain concave games, the equilibrium existence problem reduces to solving awell-structured LP. We then consider a class of monotone aggregative gameshaving the property that the cost/utility functions of players may depend onthe induced load of a strategy profile. For this class, we show a sufficientcondition of enforceability based on the previous characterizations. Wedemonstrate that this framework can help to unify parts of four largelyindependent streams in the literature: tolls in transportation systems,Walrasian market equilibria, trading networks and congestion control incommunication networks.

Pricing in Resource Allocation Games Based on Lagrangean Duality and Convexification