A non-cooperative foundation for the continuous Raiffa solution

This paper provides a non-cooperative foundation for (asymmetric generalizations of) the continuous Raiffa solution. Specifically, we consider a continuous-time variation of the classic Ståhl–Rubinstein bargaining model, in which there is a finite deadline that ends the negotiations, and in which each player’s opportunity to make proposals is governed by a player-specific Poisson process, in that the rejecter of a proposal becomes proposer at the first next arrival of her process. Under the assumption that future payoffs are not discounted, it is shown that the expected payoffs players realize in subgame perfect equilibrium converge to the continuous Raiffa solution outcome as the deadline tends to infinity. The weights reflecting the asymmetries among the players correspond to the Poisson arrival rates of their respective proposal processes

Non-cooperative Support for the Asymmetric Nash Bargaining solution

Our work contributes to the game-theoretic analysis of bargaining by providing additional non-cooperative support to the well-known Nash bargaining solution. In particular, in the present paper we study a model of non-cooperative multilateral bargaining with a very general proposer selection protocol and set of feasible payoffs. In each period of the bargaining game, one out of n players is recognized as the proposer according to an irreducible Markov process. The proposer offers a particular element of the convex set of feasible payoffs. If all players accept the offer, it is implemented. If a player rejects the offer, with some probability the negotiations break down and with the remaining probability the next period starts. We show that subgame perfect equilibria in stationary strategies exist and we fuly characterize the set of such equilibria. Our main result is that in the limit, as the exogenous risk of breakdown goes to zero, stationary subgame perfect equilibrium payoffs converge to the weighted Nash bargaining solution with the stationary distribution of the Markov proposer selection process as the weight vector.operations research and management science;

A classification of bargaining solutions by evolutionary origin

For games of contracting under perturbed best response dynamics, varying the perturbations along two dimensions (uniform vs. logit, directed vs. undirected) gives four possibilities. Three of these select differing major bargaining solutions as stochastically stable. The fourth possibility yields a new bargaining solution which exhibits significant nonmonotonicities and demonstrates the interplay of two key drivers of evolutionary selection: (i) the ease of making errors; (ii) the ease of responding to errors

Channel assignment and routing in cooperative and competitive wireless mesh networks

This thesis was submitted for the degree of Docter of Philosophy and awarded by Brunel University.In this thesis, the channel assignment and routing problems have been investigated for both cooperative and competitive Wireless Mesh networks (WMNs). A dynamic and distributed channel assignment scheme has been proposed which generates the network topologies ensuring less interference and better connectivity. The proposed channel assignment scheme is capable of detecting the node failures and mobility in an efficient manner. The channel monitoring module precisely records the quality of bi-directional links in terms of link delays. In addition, a Quality of Service based Multi-Radio Ad-hoc On Demand Distance Vector (QMR-AODV) routing protocol has been devised. QMR-AODV is multi-radio compatible and provides delay guarantees on end-to-end paths. The inherited problem of AODV’s network wide flooding has been solved by selectively forwarding the routing queries on specified interfaces. The QoS based delay routing metric, combined with the selective route request forwarding, reduces the routing overhead from 24% up to 36% and produces 40.4% to 55.89% less network delays for traffic profiles of 10 to 60 flows, respectively. A distributed channel assignment scheme has been proposed for competitive WMNs, where the problem has been investigated by applying the concepts from non-cooperative bargaining Game Theory in two stages. In the first stage of the game, individual nodes of the non-cooperative setup is considered as the unit of analysis, where sufficient and necessary conditions for the existence of Nash Equilibrium (NE) and Negotiation-Proof Nash Equilibrium (N-PNE) have been derived. A distributed algorithm has been presented with perfect information available to the nodes of the network. In the presence of perfect information, each node has the knowledge of interference experience by the channels in its collision domain. The game converges to N-PNE in finite time and the average fairness achieved by all the nodes is greater than 0.79 (79%) as measured through Jain Fairness Index. Since N-PNE and NE are not always a system optimal solutions when considered from the end-nodes prospective, the model is further extended to incorporate non-cooperative end-users bargaining between two end user’s Mesh Access Points (MAPs), where an increase of 10% to 27% in end-to-end throughput is achieved. Furthermore, a non-cooperative game theoretical model is proposed for end-users flow routing in a multi-radio multi-channel WMNs. The end user nodes are selfish and compete for the channel resources across the WMNs backbone, aiming to maximize their own benefit without taking care for the overall system optimization. The end-to-end throughputs achieved by the flows of an end node and interference experienced across the WMNs backbone are considered as the performance parameters in the utility function. Theoretical foundation has been drawn based on the concepts from the Game Theory and necessary conditions for the existence of NE have been extensively derived. A distributed algorithm running on each end node with imperfect information has been implemented to assess the usefulness of the proposed mechanism. The analytical results have proven that a pure strategy Nash Equilibrium exists with the proposed necessary conditions in a game of imperfect information. Based on a distributed algorithm, the game converges to a stable state in finite time. The proposed game theoretical model provides a more reasonable solution with a standard deviation of 2.19Mbps as compared to 3.74Mbps of the random flow routing. Finally, the Price of Anarchy (PoA) of the system is close to one which shows the efficiency of the proposed scheme.The Higher Education Commission of Pakistan and the University of Engineering and Technology, Peshawar