Abstract
Many natural games have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all results to date on dynamics in games show only convergence to some equilibrium, especially within a polynomial number of steps. In this work we initiate a theory of how well-motivated multiagent dynamics can make use of global information about the game---which might be common knowledge or injected into the system by a helpful central agency---and show that in a wide range of interesting games this can allow the dynamics to quickly reach (within a polynomial number of steps) states of cost comparable to the best Nash equilibrium. We present several natural models for dynamics that can use such additional information and analyze their ability to reach low-cost states for two important and widely studied classes of potential games: network design with fair cost-sharing and party affiliation games (which include consensus and cut games). From the perspective of a...
Highlights
There has been substantial work in the machine learning, game theory, and algorithmic game theory communities on understanding the overall behavior of multi-agent systems in which agents follow natural learning dynamics such as best/better response and no-regret learning
We propose a novel angle on this problem by considering whether providing more information to simple learning algorithms about the game being played can allow natural dynamics to reach such high quality states
As described above we introduce and analyze two models for guiding dynamics to good equilibria, and within these models we prove strong positive results for two classes of games, fair cost sharing and consensus games
Summary
There has been substantial work in the machine learning, game theory, and (more recently) algorithmic game theory communities on understanding the overall behavior of multi-agent systems in which agents follow natural learning dynamics such as (randomized) best/better response and no-regret learning. It is well known that in potential games, best-response dynamics, in which players take turns each making a bestresponse move to the current state of all the others, is guaranteed to converge to a pure-strategy Nash equilibrium [24, 27]. Low-cost solutions might be known because people analyzing the specific instance being played might discover and publish low cost global behaviors In this case, individual players might occasionally test out their parts of these behaviors, using them as extra inputs to their own learning algorithm or adaptive dynamics to see if they do provide benefit to themselves. That model is related to the model we consider here, but is much more rigid because it posits two classes of players (one that follows the given instructions and one that doesn’t) and does not allow players to adaptively decide for themselves. (See Section 1.2 for more discussion)
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