Presentation on theme: "Noam Nisan, Michael Schapira, Gregory Valiant, and Aviv Zohar."— Presentation transcript:
Noam Nisan, Michael Schapira, Gregory Valiant, and Aviv Zohar
Motivation Equilibrium is the basic object of study in game theory. Question: How is an equilibrium reached? In a truly satisfactory answer each player’s rule of behavior is simple and “locally rational” repeated best-response repeated better-response regret-minimization
Motivation Repeated best-response is often employed in practice e.g., Internet routing We ask: “When is such locally-rational behavior really rational?”
Repeated best-response is not always best. *the game is solvable through elimination of dominated strategies. 2,12,10,00,0 3,03,01,11,1
Overview of Results We identify a small class of games for which: 1. Repeated best-response converges (quickly) from any initial point. 2. It is a rational choice in the long run (an equilibrium). While small, this class covers several important examples: Internet Routing, Cost Sharing, Stable Roommates, Congestion Control.
Never Best Response (NBR) Strategies 0-202 3-15-10 3-3 121
NBR-Solvability Def: A game G is NBR-solvable (under some tie- breaking rule) if there exists a sequence of eliminations of NBR strategies from the game that leaves each player with only a single strategy. There must be such a sequence for every type configuration of the players.
Example: Congestion Control A crude model of TCP congestion control. [Godfrey, Schapira, Zohar, Shenker – SIGMETRICS 2010] A protocol responsible for scaling back transmission rate in cases of congestion. The network is represented by a graph with capacities on the edges. 2 3 2 1 1 4 3
Each player is a pair of source & target nodes, connected by a simple path, and has some maximal rate of transmission. Actions of players: selecting transmission rate (up to limit). Utility: amount of flow that reaches destination. 2 3 2 1 1 4 3 ST
Flow is handled as if routers use Fair Queuing: Capacity on each link is equally divided between players that use the link. Unused capacity by some player is divided equally among others 9 2 7 C e =9 3.5 2
Adjusting rate to fit bottleneck capacity: equivalent to best reply (with certain tie breaking rules) 2 3 2 4 3 3 4 1 1 1 2 2
Results for Congestion Control Thm: The Congestion Control Game with routers that follow Fair-Queueing is NBR- Solvable with a clear outcome.
Eliminate all transmission rates below e* for them. If they all transmit at least e*, none will manage to get more through. Eliminate all rates above e*. Repeat with the residual graph and remaining players. CeCe
Results for Congestion Control Thm: The Congestion Control Game with routers that follow Fair-Queueing is NBR-Solvable with a clear outcome. Corollaries: Best-response is incentive compatible Converges fast regardless of topology TCP’s actual behavior in this setting can be seen as probing for the best-response.
Other Games Matching Uncorrelated markets, interns and hospitals Cost-sharing games BGP – interdomain routing in the internet. See the paper for more details and references! 1 2 3 4 d
Open Questions: Explore other dynamics (e.g., regret minimization) and other equilibria (e.g., mixed Nash, correlated). Find an exact characterization of games where repeated best-response is rational.