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Economical Graph Discovery
"... Abstract: Consider a weighted nvertex, medge graph G with designated source s and destination t. The topology of G is known, while the edge weights are hidden. Our goal is to discover either the edge weights in the graph or a shortest (s, t)path. This is done by means of agents that traverse diff ..."
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Abstract: Consider a weighted nvertex, medge graph G with designated source s and destination t. The topology of G is known, while the edge weights are hidden. Our goal is to discover either the edge weights in the graph or a shortest (s, t)path. This is done by means of agents that traverse different (s, t)paths in multiple rounds and report back the total cost they incurred. Various cost models are considered, differing from each other in their approach to congestion effects. We seek bounds on the number of rounds and the number of agents required to complete the discovery of the edge weights or a shortest path. A host of results concerning such bounds for both directed and undirected graphs are established. Among these results, we show that: (1) for undirected graphs, all edge weights can be discovered within a single round consisting of m agents; (2) discovering a shortest path in either undirected or directed acyclic graphs requires at least m − n + 1 agents; and (3) the edge weights in a directed acyclic graphs can be discovered in m rounds with m + n − 2 agents under congestionaware cost models. Our study introduces a new setting of graph discovery under uncertainty and provides fundamental understanding of the problem.
Learning Equilibria in Repeated Congestion Games
"... While the class of congestion games has been thoroughly studied in the multiagent systems literature, settings with incomplete information have received relatively little attention. In this paper we consider a setting in which the cost functions of resources in the congestion game are initially unk ..."
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While the class of congestion games has been thoroughly studied in the multiagent systems literature, settings with incomplete information have received relatively little attention. In this paper we consider a setting in which the cost functions of resources in the congestion game are initially unknown. The agents gather information about these cost functions through repeated interaction, and observations of costs they incur. In this context we consider the following requirement: the agents ’ algorithms should themselves be in equilibrium, regardless of the actual cost functions and should lead to an efficient outcome. We prove that this requirement is achievable for a broad class of games: repeated symmetric congestion games. Our results are applicable even when agents are somewhat limited in their capacity to monitor the actions of their counterparts, or when they are unable to determine the exact cost they incur from every resource. On the other hand, we show that there exist asymmetric congestion games for which no such equilibrium can be found, not even an inefficient one. Finally we consider equilibria with resistance to the deviation of more than one player and show that these do not exist even in repeated resource selection games.
BestResponse Mechanisms (Extended Abstract)
"... Under many protocols — in computerized settings and in economics settings — participants repeatedly “best respond ” to each others ’ actions until the system “converges ” to an equilibrium point. We ask when such myopic “local rationality ” implies “global rationality”, i.e., when is it best for a p ..."
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Under many protocols — in computerized settings and in economics settings — participants repeatedly “best respond ” to each others ’ actions until the system “converges ” to an equilibrium point. We ask when such myopic “local rationality ” implies “global rationality”, i.e., when is it best for a player, given that the others are repeatedly bestresponding, to also repeatedly bestrespond? We exhibit a class of games where this is indeed the case. We identify several environments of interest that fall within our class: models of the Border Gateway Protocol (BGP) [9], that handles routing on the Internet, and of the Transmission Control Protocol Protocol (TCP) [7], and also stableroommates [5] and costsharing [12, 13], that have been extensively studied in economic theory.