Shaheen Fatima

An agenda-based framework for multi-issue negotiation

This paper presents a new model for multi-issue negotiation under time constraints in an incomplete information setting. The issues to be bargained over can be associated with a single good/service or multiple goods/services. In our agenda-based model, the order in which issues are bargained over and agreements are reached is determined endogenously, as part of the bargaining equilibrium. In this context we determine the conditions under which agents have similar preferences over the implementation scheme and the conditions under which they have conflicting preferences. Our analysis shows the existence of equilibrium even when both players have uncertain information about each other, and each agents information is its private knowledge. We also study the properties of the equilibrium solution and determine conditions under which it is unique, symmetric, and Pareto-optimal.

Multi-issue negotiation under time constraints

This paper presents a new model for multi-issue negotiation under time constraints in an incomplete information setting. In this model the order in which issues are bargained over and agreements are reached is determined endogenously as part of the bargaining equilibrium. We show that the sequential implementation of the equilibrium agreement gives a better outcome than a simultaneous implementation when agents have like, as well as conflicting, time preferences. We also show that the equilibrium solution possesses the properties of uniqueness and symmetry, although it is not always Pareto-optimal.

Multi-issue negotiation with deadlines

This paper studies bilateral multi-issue negotiation between self-interested autonomous agents. Now, there are a number of different procedures that can be used for this process; the three main ones being the package deal procedure in which all the issues are bundled and discussed together, the simultaneous procedure in which the issues are discussed simultaneously but independently of each other, and the sequential procedure in which the issues are discussed one after another. Since each of them yields a different outcome, a key problem is to decide which one to use in which circumstances. Specifically, we consider this question for a model in which the agents have time constraints (in the form of both deadlines and discount factors) and information uncertainty (in that the agents do not know the opponents utility function). For this model, we consider issues that are both independent and those that are interdependent and determine equilibria for each case for each procedure. In so doing, we show that the package deal is in fact the optimal procedure for each party. We then go on to show that, although the package deal may be computationally more complex than the other two procedures, it generates Pareto optimal outcomes (unlike the other two), it has similar earliest and latest possible times of agreement to the simultaneous procedure (which is better than the sequential procedure), and that it (like the other two procedures) generates a unique outcome only under certain conditions (which we define).

Optimal Negotiation of Multiple Issues in Incomplete Information Settings

This paper studies bilateral multi-issue negotiation between self-interested agents. The outcome of such encounters depends on two key factors: the agenda (i.e., the set of issues under negotiation) and the negotiation procedure (i.e., whether the issues are discussed together or separately). Against this background, this paper analyses such negotiations by varying the agenda and negotiation procedure. This analysis is carried out in an incomplete information setting in which an agent knows its own negotiation parameters, but has incomplete information about its opponentýs. We first determine the equilibrium strategies for two negotiation procedures: issue-by-issue and package deal. On the basis of these strategies we determine the negotiation outcome for all possible agenda ¿ procedure combinations and the optimal agenda ¿ procedure combination for each agent. We determine those conditions for which agents have identical preferences over the optimal agenda and procedure and those for which they do not, and for both conditions we show the optimal agenda and procedure.

A linear approximation method for the Shapley value

The Shapley value is a key solution concept for coalitional games in general and voting games in particular. Its main advantage is that it provides a unique and fair solution, but its main drawback is the complexity of computing it (e.g., for voting games this complexity is #p-complete). However, given the importance of the Shapley value and voting games, a number of approximation methods have been developed to overcome this complexity. Among these, Owens multi-linear extension method is the most time efficient, being linear in the number of players. Now, in addition to speed, the other key criterion for an approximation algorithm is its approximation error. On this dimension, the multi-linear extension method is less impressive. Against this background, this paper presents a new approximation algorithm, based on randomization, for computing the Shapley value of voting games. This method has time complexity linear in the number of players, but has an approximation error that is, on average, lower than Owens. In addition to this comparative study, we empirically evaluate the error for our method and show how the different parameters of the voting game affect it. Specifically, we show the following effects. First, as the number of players in a voting game increases, the average percentage error decreases. Second, as the quota increases, the average percentage error decreases. Third, the error is different for players with different weights; players with weight closer to the mean weight have a lower error than those with weight further away. We then extend our approximation to the more general k-majority voting games and show that, for n players, the method has time complexity O(k^2n) and the upper bound on its approximation error is O(k^2/n).

Bargaining with incomplete information

This paper analyses the process and outcomes of competitive bilateral negotiation for a model based on negotiation decision functions. Each agent has time constraints in the form of a deadline and a discounting factor. The importance of information possessed by participants is highlighted by exploring all possible incomplete information scenarios – both symmetric and asymmetric. In particular, we examine a range of negotiation scenarios in which the amount of information that agents have about their opponent’s parameters is systematically varied. For each scenario, we determine the equilibrium solution and study its properties. The main results of our study are as follows. Firstly, in some scenarios agreement takes place at the earlier deadline, while in others it takes place near the beginning of negotiation. Secondly, in some scenarios the price surplus is split equally between the agents while in others the entire price surplus goes to a single agent. Thirdly, for each possible scenario, the equilibrium outcome possesses the properties of uniqueness and symmetry – although it is not always Pareto optimal. Finally, we also show the relative impacts of the opponent’s parameters on the bargaining outcome.

A Comparative Study of Game Theoretic and Evolutionary Models of Bargaining for Software Agents

Most of the existing work in the study of bargaining behavior uses techniques from game theory. Game theoretic models for bargaining assume that players are perfectly rational and that this rationality is common knowledge. However, the perfect rationality assumption does not hold for real-life bargaining scenarios with humans as players, since results from experimental economics show that humans find their way to the best strategy through trial and error, and not typically by means of rational deliberation. Such players are said to be boundedly rational. In playing a game against an opponent with bounded rationality, the most effective strategy of a player is not the equilibrium strategy but the one that is the best reply to the opponent’s strategy. The evolutionary model provides a means for studying the bargaining behaviour of boundedly rational players. This paper provides a comprehensive comparison of the game theoretic and evolutionary approaches to bargaining by examining their assumptions, goals, and limitations. We then study the implications of these differences from the perspective of the software agent developer.

Adaptive task resources allocation in multi-agent systems

In this paper, we present an adaptive organizational policy for multi-agent systems called \acro{trace}. \acro{trace} allows a collection of multi-agent organizations to dynamically allocate tasks and resources between themselves in order to efficiently process an incoming stream of task requests. \acro{trace} is intended to cope with environments in which tasks have time constraints, and environments that are subject to load variations. \acro{trace} is made up of two key elements: the task allocation protocol (\acro{tap}) and the resource allocation protocol (\acro{rap}). The \acro{tap} allows agents to cooperatively allocate their tasks to other agents with the capability and opportunity to successfully carry them out. As requests arrive arbitrarily, at any instant, some organizations could have surplus resources while others could become overloaded. In order to minimize the number of lost requests caused by an overload, the allocation of resources to organizations is changed dynamically by the resource allocation protocol (\acro{rap}), which uses ideas from computational market systems to allocate resources (in the form of problem solving agents) to organizations. We begin by formally defining the task allocation problem, and show that it is \acro{NP}-complete, and hence that centralized solutions to the problem are unlikely to be feasible. We then introduce the task and resource allocation protocols, focussing on the way in which resources are allocated by the \acro{rap}. We then present some experimental results, which show that \acro{trace} exhibits high performance despite unanticipated changes in the environment.

A randomized method for the shapley value for the voting game

The Shapley value is one of the key solution concepts for coalition games. Its main advantage is that it provides a unique and fair solution, but its main problem is that, for many coalition games, the Shapley value cannot be determined in polynomial time. In particular, the problem of finding this value for the voting game is known to be #P-complete in the general case. However, in this paper, we show that there are some specific voting games for which the problem is computationally tractable. For other general voting games, we overcome the problem of computational complexity by presenting a new randomized method for determining the approximate Shapley value. The time complexity of this method is linear in the number of players. We also show, through empirical studies, that the percentage error for the proposed method is always less than 20% and, in most cases, less than 5%.

New Trends in Agent-Based Complex Automated Negotiations

Complex Automated Negotiations represent an important, emerging area in the field of Autonomous Agents and Multi-Agent Systems. Automated negotiations can be complex, since there are a lot of factors that characterize such negotiations. These factors include the number of issues, dependencies between these issues, representation of utilities, the negotiation protocol, the number of parties in the negotiation (bilateral or multi-party), time constraints, etc. Software agents can support automation or simulation of such complex negotiations on the behalf of their owners, and can provide them with efficient bargaining strategies. To realize such a complex automated negotiation, we have to incorporate advanced Artificial Intelligence technologies includes search, CSP, graphical utility models, Bayes nets, auctions, utility graphs, predicting and learning methods. Applications could include e-commerce tools, decision-making support tools, negotiation support tools, collaboration tools, etc. This book aims to provide a description of the new trends in Agent-based, Complex Automated Negotiation, based on the papers from leading researchers. Moreover, it gives an overview of the latest scientific efforts in this field, such as the platform and strategies of automated negotiating techniques.