Playing the Wrong Game

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The robustness of multiagent systems can be affected by mistakes or behavioral biases (e.g., risk-aversion, altruism, toll-sensitivity), with some agents playing the ``wrong game.'' This can change the set of equilibria, and may in turn harm or improve the social welfare of agents in the system. We are interested in bounding what we call the biased price of anarchy (BPoA) in populations with diverse agent behaviors, which is the ratio between welfare in the ``wrong'' equilibrium and optimal welfare. We study nonatomic routing games, and derive an externality bound that depends on a key topological parameter of the underlying network called the "parallel width". We then prove a general BPoA bound for games with diverse populations that relies on the network structure and the average bias of all agents in the population.
 
Time permits, I will characterize the graphs whose parallel width is bounded by k, using directed graph embeddings.
 
Joint work with David Parkes. 
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