Results 1  10
of
10
Network Bargaining: Using Approximate Blocking Sets to Stabilize Unstable Instances
"... Abstract. We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos [8], where the set of players corresponds to vertices in a graph G = (V, E) and each edge ij ∈ E represents a possible deal between players i and j. We reformulate the problem as a cooperative g ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos [8], where the set of players corresponds to vertices in a graph G = (V, E) and each edge ij ∈ E represents a possible deal between players i and j. We reformulate the problem as a cooperative game and study the following question: Given a game with an empty core (i.e. an unstable game) is it possible, through minimal changes in the underlying network, to stabilize the game? We show that by removing edges in the network that belong to a blocking set we can find a stable solution in polynomial time. This motivates the problem of finding small blocking sets. While it has been previously shown that finding the smallest blocking set is NPhard [3], we show that it is possible to efficiently find approximate blocking sets in sparse graphs. 1
Distributed bargaining in dyadicexchange networks
 IEEE Transactions on Control of Network Systems
"... AbstractThis paper considers dyadicexchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents ob ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
AbstractThis paper considers dyadicexchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provablycorrect continuoustime algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having the dynamics for finding stable outcomes feeding into the one for finding balanced ones. Our technical approach to establish convergence and robustness combines notions and tools from optimization, graph theory, nonsmooth analysis, and Lyapunov stability theory and provides a useful framework for further extensions. We illustrate our results in a wireless communication scenario where singleantenna devices have the possibility of working as 2antenna virtual devices to improve channel capacity.
Social Exchange Networks With Distant Bargaining
"... Network bargaining is a natural extension of the classical, 2player Nash bargaining solution to the network setting. Here one is given an exchange network G connecting a set of players V in which edges correspond to potential contracts between their endpoints. In the standard model, a player may e ..."
Abstract
 Add to MetaCart
(Show Context)
Network bargaining is a natural extension of the classical, 2player Nash bargaining solution to the network setting. Here one is given an exchange network G connecting a set of players V in which edges correspond to potential contracts between their endpoints. In the standard model, a player may engage in at most one contract, and feasible outcomes therefore correspond to matchings in the underlying graph. Kleinberg and Tardos [STOC’08] recently proposed this model, and introduced the concepts of stability and balance for feasible outcomes. The authors characterized the class of instances that admit such solutions, and presented a polynomialtime algorithm to compute them. In this paper, we generalize the work of Kleinberg and Tardos by allowing agents to engage into more complex contracts that span more than two agents. We provide suitable generalizations of the above stability and balance notions, and show that many of the previously known results for the matching case extend to our new setting. In particular, we can show that a given instance admits a stable outcome only if it also admits a balanced one. Like Bateni et al. [ICALP’10] we exploit connections to cooperative games. We fully characterize the core of these games, and show that checking its nonemptiness is NPcomplete. On the other hand, we provide efficient algorithms to compute core elements for several special cases of the problem, making use of compact linear programming formulations.
Network bargaining with general capacities
"... Abstract. We study balanced solutions for network bargaining games with general capacities, where agents can participate in a fixed but arbitrary number of contracts. We provide the first polynomial time algorithm for computing balanced solutions for these games. In addition, we prove that an instan ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We study balanced solutions for network bargaining games with general capacities, where agents can participate in a fixed but arbitrary number of contracts. We provide the first polynomial time algorithm for computing balanced solutions for these games. In addition, we prove that an instance has a balanced solution if and only if it has a stable one. Our methods use a new idea of reducing an instance with general capacities to a network bargaining game with unit capacities defined on an auxiliary graph. This represents a departure from previous approaches, which rely on computing an allocation in the intersection of the core and prekernel of a corresponding cooperative game, and then proving that the solution corresponding to this allocation is balanced. In fact, we show that such cooperative game methods do not extend to general capacity games, since contrary to the case of unit capacities, there exist allocations in the intersection of the core and prekernel with no corresponding balanced solution. Finally, we identify two sufficient conditions under which the set of balanced solutions corresponds to the intersection of the core and prekernel, thereby extending the class of games for which this result was previously known. 1
Microsoft
, 2012
"... milanv@microsoft.com Microsoft Research, Cambridge, UKAbstract – We examine how the relation between individual and social utility affect the efficiency of gametheoretic solution concepts. We first provide general results for monotone utilitymaximization games, showing that if each player’s utilit ..."
Abstract
 Add to MetaCart
milanv@microsoft.com Microsoft Research, Cambridge, UKAbstract – We examine how the relation between individual and social utility affect the efficiency of gametheoretic solution concepts. We first provide general results for monotone utilitymaximization games, showing that if each player’s utility is at least his marginal contribution to the welfare, then the social welfare in any Strong Nash Equilibrium is at least half of the optimal. The efficiency degrades smoothly as the marginal contribution assumption is relaxed. For nonmonotone utility maximization games, we manage to give efficiency results if the game is also a potential game. We also extend previous results on efficiency of Nash Equilibria for the case when social welfare is submodular. We then focus on Effort Market Games, a general cooperative setting where players exert effort in projects and then the produced value is redistributed to them using some simple local mechanism. Our results for general utility maximization games are instrumental in reasoning about efficiency in Effort Market Games. We show that in a concave environment, splitting locally according to the Shapley value achieves globally at least half of the optimal social welfare at any Nash Equilibrium of the game (our proof is of a smoothness type and hence generalizes also to noregret learning outcomes). We generally characterize the properties that a distribution mechanism has to satisfy to achieve good efficiency. Moreover, we show that equal splitting of the value works well only when the projects have small number of participants. In a convex environment, Nash
Finding small stabilizers for unstable graphs
"... An undirected graph G = (V,E) is stable if its inessential vertices (those that are exposed by at least one maximum matching) form a stable set. We call a set of edges F ⊆ E a stabilizer if its removal from G yields a stable graph. In this paper we study the following natural edgedeletion question ..."
Abstract
 Add to MetaCart
An undirected graph G = (V,E) is stable if its inessential vertices (those that are exposed by at least one maximum matching) form a stable set. We call a set of edges F ⊆ E a stabilizer if its removal from G yields a stable graph. In this paper we study the following natural edgedeletion question: given a graph G = (V,E), can we find a minimumcardinality stabilizer? Stable graphs play an important role in cooperative game theory. In the classic matching game introduced by Shapley and Shubik [19] we are given an undirected graph G = (V,E) where vertices represent players, and we define the value of each subset S ⊆ V as the cardinality of a maximum matching in the subgraph induced by S. The core of such a game contains all fair allocations of the value of V among the players, and is wellknown to be nonempty iff graph G is stable. The stabilizer problem addresses the question of how to modify the graph to ensure that the core is nonempty. We show that this problem is vertexcover hard. We then prove that there is a minimumcardinality stabilizer that avoids some maximum matching of G. We use this insight to give efficient approximation algorithms for sparse graphs and for regular graphs.