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Today's multiagent systems have grown too complex to rely on centralizedcontrollers, prompting increasing interest in the design of distributedalgorithms. In this respect, game theory has emerged as a valuable tool tocomplement more traditional techniques. The fundamental idea behind thisapproach is the assignment of agents' local cost functions, such that theirselfish minimization attains, or is provably close to, the global objective.Any algorithm capable of computing an equilibrium of the corresponding gameinherits an approximation ratio that is, in the worst case, equal to itsprice-of-anarchy. Therefore, a successful application of the game designapproach hinges on the possibility to quantify and optimize the equilibriumperformance.  Toward this end, we introduce the notion of generalized smoothness, and showthat the resulting efficiency bounds are significantly tighter compared tothose obtained using the traditional smoothness approach. Leveraging thisnewly-introduced notion, we quantify the equilibrium performance for the classof local resource allocation games. Finally, we show how the agents' localdecision rules can be designed in order to optimize the efficiency of thecorresponding equilibria, by means of a tractable linear program.

When Smoothness is Not Enough: Toward Exact Quantification and Optimization of the Price-of-Anarchy