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Intrinsic Robustness of the Price of Anarchy
 STOC'09
, 2009
"... The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium ..."
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The price of anarchy (POA) is a worstcase measure of the inefficiency of selfish behavior, defined as the ratio of the objective function value of a worst Nash equilibrium of a game and that of an optimal outcome. This measure implicitly assumes that players successfully reach some Nash equilibrium. This drawback motivates the search for inefficiency bounds that apply more generally to weaker notions of equilibria, such as mixed Nash and correlated equilibria; or to sequences of outcomes generated by natural experimentation strategies, such as successive best responses or simultaneous regretminimization. We prove a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective. First, we identify a “canonical sufficient condition ” for an upper bound of the POA for pure Nash equilibria, which we call a smoothness argument. Second, we show that every bound derived via a smoothness argument extends automatically, with no quantitative degradation in the bound, to mixed Nash equilibria, correlated equilibria, and the average objective function value of regretminimizing players (or “price of total anarchy”). Smoothness arguments also have automatic implications for the inefficiency of approximate and BayesianNash equilibria and, under mild additional assumptions, for bicriteria bounds and for polynomiallength bestresponse sequences. We also identify classes of games — most notably, congestion games with cost functions restricted to an arbitrary fixed set — that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worstcase upper bound on the POA, even for the smallest set of interest (pure Nash equilibria). Byproducts of our proof of this result include the first tight bounds on the POA in congestion games with nonpolynomial cost functions, and the first
DIRECT: A Scalable Approach for Route Guidance in Selfish Orienteering Problems
"... We address the problem of crowd congestion at venues like theme parks, museums and world expos by providing route guidance to multiple selfish users (with budget constraints) moving through the venue simultaneously. To represent these settings, we introduce the Selfish Orienteering Problem (SeOP) th ..."
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We address the problem of crowd congestion at venues like theme parks, museums and world expos by providing route guidance to multiple selfish users (with budget constraints) moving through the venue simultaneously. To represent these settings, we introduce the Selfish Orienteering Problem (SeOP) that combines two well studied problems from literature, namely Orienteering Problem (OP) and Selfish Routing (SR). OP is a single agent routing problem where the goal is to minimize latency (or maximize reward) in traversing a subset of nodes while respecting budget constraints. SR is a game between selfish agents looking for minimum latency routes from source to destination along edges of a network available to all agents. Thus, SeOP is a multiagent planning problem where agents have selfish interests and in