Non-cooperative Agents Research Articles

Equilibria in Online Games

We initiate the study of scenarios that combine online decision making with interaction between noncooperative agents. To this end we introduce online games that model such scenarios as noncooperative games, and lay the foundations for studying this model. Roughly speaking, an online game captures systems in which independent agents serve requests in a common environment. The requests arrive in an online fashion, and each is designated to be served by a different agent. The cost incurred by serving a request is paid by the serving agent, and naturally the agents seek to minimize the total cost to themselves. Since the agents are independent, it is unlikely that some central authority can enforce a policy or an algorithm (centralized or distributed) on them, and thus, the agents can be viewed as selfish players in a noncooperative game. In this game, the players have to choose as a strategy an online algorithm according to which requests are served. To further facilitate the game-theoretic approach, we suggest the measure of competitive analysis as the players' decision criterion. As the expected result of noncooperative games is an equilibrium, the question of finding the equilibria of a game is of central importance, and thus it is the central issue on which we concentrate in this paper. We study some natural examples for online games; in order to obtain general insights and develop generic techniques, we present an abstract model for the study of online games generalizing metrical task systems. We suggest a method for constructing equilibria in this model and further devise techniques for implementing it.

Simultaneous Workload Allocation and Capacity Dimensioning for Distributed Production Control

Capacity dimensioning in production systems is an important task within strategic and tactical production planning which impacts system cost and performance. Traditionally capacity demand at each worksystem is determined from standard operating processes and estimated production flow rates, accounting for a desired level of utilization or required throughput times. However, for distributed production control systems, the flows across multiple possible production paths are not known a priori. In this contribution, we use methods from algorithmic game-theory and traffic-modeling to predict the flows, and hence capacity demand across worksystems, based on the available production paths and desired output rates, assuming non-cooperative agents with global information. We propose an iterative algorithm that converges simultaneously to a feasible capacity distribution and a flow distribution over multiple paths that satisfies Wardrop's first principle. We demonstrate our method on models of real-world production networks.

Contemporary Computer Supported Collaboration: Systems, Technologies, Algorithms, and Applications

Contemporary Computer Supported Collaboration: Systems, Technologies, Algorithms, and Applications

Self-organization in service discovery in presence of noncooperative agents

Self-organization and cooperation of agents in open societies play an important role in the success of the service discovery process. Self-organization allows agents to deal with dynamic requirements in service demand. Moreover, in distributed environments where service discovery is carried out by agents that only have a partial view of the system, cooperation with neighbors is a key issue in order to locate the required services. However, cooperation is not always present in open agent societies. With this motivation, we present a set of mechanisms that consider self-organization actions and incentives to adapt the structure of the society to the service demand and to promote a cooperative behavior among agents in open societies.

Phase transitions in a coevolving snowdrift game with costly rewiring.

We propose and study a dissatisfied adaptive snowdrift game with a payoff parameter r that incorporates a cost for rewiring a connection. An agent, facing adverse local environment, may switch action without a cost or rewire an existing link with a cost a so as to attain a better competing environment. Detailed numerical simulations reveal nontrivial and nonmonotonic dependence of the frequency of cooperation and the densities of different types of links on a and r. A theory that treats the cooperative and noncooperative agents separately and accounts for spatial correlation up to neighboring agents is formulated. The theory gives results that are in good agreement with simulations. The frequency of cooperation f_{C} is enhanced (suppressed) at high rewiring cost relative to that at low rewiring cost when r is small (large). For a given value of r, there exists a critical value of the rewiring cost below which the system evolves into a phase of frozen dynamics with isolated noncooperative agents segregated from a cluster of cooperative agents, and above which the system evolves into a connected population of mixed actions with continual dynamics. The phase boundary on the a-r phase space that separates the two phases with distinct structural, population and dynamical properties is mapped out. The phase diagram reveals that, as a general feature, for small r (small a), the disconnected and segregated phase can survive over a wider range of a(r).

Minimizing Rosenthal Potential in Multicast Games

A multicast game is a network design game modelling how selfish non-cooperative agents build and maintain one-to-many network communication. There is a special source node and a collection of agents located at corresponding terminals. Each agent is interested in selecting a route from the special source to its terminal minimizing the cost. The mutual influence of the agents is determined by a cost sharing mechanism, which evenly splits the cost of an edge among all the agents using it for routing. In this paper we provide several algorithmic and complexity results on finding a Nash equilibrium minimizing the value of Rosenthal potential. Let n be the number of agents and G be the communication network. We show that for a given strategy profile s and integer k ? 0, there is a local search algorithm which in time nO(k)?|G|O(1) finds a better strategy profile, if there is any, in a k-exchange neighbourhood of s. In other words, the algorithm decides if Rosenthal potential can be decreased by changing strategies of at most k agents. The running time of our local search algorithm is essentially tight: unless FPT = W[1], for any function f(k), searching of the k-neighbourhood cannot be done in time f(k)?|G|O(1). We also show that an equilibrium with minimum potential can be found in 3n?|G|O(1) time.

STRATEGIES FOR COOPERATION EMERGENCE IN DISTRIBUTED SERVICE DISCOVERY

In distributed environments where entities only have a partial view of the system, cooperation is a key issue. In the case of decentralized service discovery in open agent societies, agents only know about the services they provide and who their direct neighbors are. Therefore, they need the cooperation of their neighbors in order to locate the required services. However, cooperation is not always present in open systems. Noncooperative agents pursuing their own goals could refuse to forward queries from other agents to avoid the cost of this action; therefore, the efficiency of the decentralized service discovery could be seriously damaged. In this article, we propose the combination of incentives and local structural changes in order to promote cooperation in the service discovery process. The results show that, even in scenarios where the predominant behavior is not collaborative, cooperation emerges.

Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks

In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed framework the decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows. An efficient decentralized algorithm is given for computing a strongly Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently, we discuss the properties of the introduced game related to the Price of Anarchy and Price of Stability. The paper is concluded with an experimental study.

Dynamic aggregation evolution of competitive societies of cooperative and noncooperative agents

We propose an evolution model of cooperative agent and noncooperative agent aggregates to investigate the dynamic evolution behaviors of the system and the effects of the competing microscopic reactions on the dynamic evolution. In this model, each cooperative agent and noncooperative agent are endowed with integer values of cooperative spirits and noncooperative spirits, respectively. The cooperative spirits of a cooperative agent aggregate and the noncooperative spirits of a noncooperative agent aggregate change via four competing microscopic reaction schemes: the win-win reaction between two cooperative agents, the lose-lose reaction between two noncooperative agents, the win-lose reaction between a cooperative agent and a noncooperative agent (equivalent to the migration of spirits from cooperative agents to noncooperative agents), and the cooperative agent catalyzed decline of noncooperative spirits. Based on the generalized Smoluchowski's rate equation approach, we investigate the dynamic evolution behaviors such as the total cooperative spirits of all cooperative agents and the total noncooperative spirits of all noncooperative agents. The effects of the three main groups of competition on the dynamic evolution are revealed. These include: (i) the competition between the lose-lose reaction and the win-lose reaction, which gives rise to respectively the decrease and increase in the noncooperative agent spirits; (ii) the competition between the win-win reaction and the win-lose reaction, which gives rise to respectively the increase and decrease in the cooperative agent spirits; (iii) the competition between the win-lose reaction and the catalyzed-decline reaction, which gives rise to respectively the increase and decrease in the noncooperative agent spirits.

Promoting cooperation in service-oriented MAS through social plasticity and incentives

In distributed environments where entities only have a partial view of the system, cooperation plays a key issue. In the case of decentralized service discovery in open service-oriented multi-agent systems, agents only know about the services they provide and their direct neighbors. Therefore, they need the cooperation of their neighbors in order to locate the required services. However, cooperation is not always present in open and distributed systems. Non-cooperative agents pursuing their own goals could refuse to forward queries from other agents to avoid the cost of this action; therefore, the efficiency of the decentralized service discovery could be seriously damaged. In this paper, we propose the combination of local structural changes and incentives in order to promote cooperation in the service discovery process. The results show that, even in scenarios where the predominant behavior is not collaborative the cooperation emerges.

A Non-Cooperative Pareto-Efficient Solution to the One-Shot Prisoner’s Dilemma

The Prisoner's Dilemma is a simple model that captures the essential contradiction between individual rationality and global rationality. Although the one-shot Prisoner's Dilemma is usually viewed simple, in this paper we will categorize it into five different types. For the type-4 Prisoner's Dilemma game, we will propose a self-enforcing algorithmic model to help non-cooperative agents obtain Pareto-efficient payoffs. The algorithmic model is based on an algorithm using complex numbers and can work in macro applications.

A Generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination

We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum (Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized decision-making mode.

Worst-case equilibria

In a system where noncooperative agents share a common resource, we propose the price of anarchy, which is the ratio between the worst possible Nash equilibrium and the social optimum, as a measure of the effectiveness of the system. Deriving upper and lower bounds for this ratio in a model where several agents share a very simple network leads to some interesting mathematics, results, and open problems. 2 2 The conference version of this work [Koutsoupias and Papadimitriou (1999) [17]] appeared a decade ago and it has been followed by a large amount of work on the concept of the price of anarchy (as witnessed by the extensive coverage in Nisan et al. (2007) [9]). In this journal version we tried to keep as much as possible the text of the original paper. There are, though, important changes because results that were substantially improved in the meantime are omitted. The other notable change is that here we use the term “price of anarchy” instead of the original term “coordination ratio”. The use of the latter term faded away in the literature, being replaced by the term “price of anarchy” which was first introduced in Papadimitriou (2001) [18].

Securitizing congestion: The congestion call option

We introduce the idea of a European-type congestion call option to value commuting to work along a given path for a given departure time selected by automobile drivers who are modeled as Cournot–Nash non-cooperative agents competing for limited roadway capacity when the alternative of telecommuting exists. We show how to compute flow patterns based on congestion call options and contrast these to traditional user optimized flow patterns. In particular, a numerical example is presented that shows congestion options have the potential to lower the network-wide social costs of congestion.

The build-up of cooperative behavior among non-cooperative selfish agents

We develop a theoretical model in which each individual is, in some ultimate sense, motivated by purely egoistic satisfaction derived from the goods accruing to him, but there is an implicit social contract such that each performs duties for the others in a way that enhances the satisfaction of all. We introduce a state variable that acts as a proxy for social capital of trustworthiness and that we call the stock of cooperation. We show that non-cooperative agents might condition their action on this state variable. Agents build-up the society's stock of cooperation and gradually overcome the free riding problem in a game of private contribution to a public good. We assume that there are neither penalties in the sense of trigger strategies, nor guilt and that each individual is rational.

On the severity of Braess's Paradox: Designing networks for selfish users is hard

We consider a directed network in which every edge possesses a latency function that specifies the time needed to traverse the edge given its congestion. Selfish, noncooperative agents constitute the network traffic and wish to travel from a source vertex s to a destination t as quickly as possible. Since the route chosen by one network user affects the congestion experienced by others, we model the problem as a noncooperative game. Assuming that each agent controls only a negligible portion of the overall traffic, Nash equilibria in this noncooperative game correspond to s– t flows in which all flow paths have equal latency. A natural measure for the performance of a network used by selfish agents is the common latency experienced by users in a Nash equilibrium. Braess's Paradox is the counterintuitive but well-known fact that removing edges from a network can improve its performance. Braess's Paradox motivates the following network design problem: given a network, which edges should be removed to obtain the best flow at Nash equilibrium? Equivalently, given a network of edges that can be built, which subnetwork will exhibit the best performance when used selfishly? We give optimal inapproximability results and approximation algorithms for this network design problem. For example, we prove that there is no approximation algorithm for this problem with approximation ratio less than n / 2 , where n is the number of network vertices, unless P = N P . We further show that this hardness result is the best possible, by exhibiting an ( n / 2 ) -approximation algorithm. We also prove tight inapproximability results when additional structure, such as linearity, is imposed on the network latency functions. Moreover, we prove that an optimal approximation algorithm for these problems is the trivial algorithm: given a network of candidate edges, build the entire network. As a consequence, we show that Braess's Paradox—even in its worst-possible manifestations—is impossible to detect efficiently. En route to these results, we give a fundamental generalization of Braess's Paradox: the improvement in performance that can be effected by removing edges can be arbitrarily large in large networks. Even though Braess's Paradox has enjoyed 35 years as a textbook example, our result is the first to extend its severity beyond that in Braess's original four-node network.

Coordinating Self-interested Planning Agents

We consider planning problems where a number of non-cooperative agents have to work on a joint problem. Such problems consist in completing a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. Since the agents are non-cooperative, they insist on planning independently and do not want to revise their individual plans when the joint plan has to be assembled from the individual plans. We present a general formal framework to study some computational aspects of this non-cooperative coordination problem and we establish some complexity results to identify some of the factors that contribute to the complexity of this problem. Finally, we illustrate our approach with an application to coordination in multi-modal logistic planning.

Population Learning of Cooperative Behavior in a Three-Person Centipede Game

We consider mixed populations (N 1/4 21) of genuine (humans) and arti.cial (robots) agents repeatedly interacting in small groups whose composition is changed randomly from round to round. Our purpose is to study the spread of cooperative or non-cooperative behavior over time in populations playing a 3-person centipede game by manipulating the behavior of the robots (cooperative vs. noncooperative) and their proportion in the population. Our results convey a positive message: adding a handful of cooperative robots increases the propensity of the genuine subjects to cooperate over time, whereas adding a handful of non-cooperative agents does not decrease this propensity. If there are enough hard-core cooperative subjects in the population, they not only negate the behavior of the non-cooperative robots but also induce other subjects to behave more cooperatively.

Bargaining on an Internet Agent-based Market: Behavioral vs. Optimizing Agents

In this paper, we analyze an Internet agent-based market where non-cooperative agents using behavioral rules negotiate the price of a given product in a bilateral and sequential manner. In this setting, we study the optimal decision-making process of a buying agent that enters the market. Our approach is based on i>Negotiation Analysis (Raiffa, 1982; Sebenuis, 1992) and we consider that the optimizing buying agent maximizes her discounted expected utility using subjective probabilities. The optimal decision-making process of the buying agent is treated as a stochastic control problem that can be solved by dynamic programming. Three types of behavioral agents are studied, namely conceder agents, boulware agents and imitative agents. A set of simulations is undertaken in order to predict the average outcome in a negotiation process for different parameters of the optimizing buying agent and for the three possible selling agents' behaviors. Finally, we compare the performance of the optimizing agent with that of behavioral buying agents.

Network games; adaptations to Nash-Cournot equilibrium

We consider nonlinear flow problems involving noncooperative agents, all active in the same network. To find Nash equilibria, we develop an algorithm that lends itself to decentralized computation and parallel processing. The algorithm, which proceeds in terms of iterative strategy adjustments, is, in essence, of subgradient type. One advantage of that type is the ease with which stochastic and nonsmooth data can be accommodated.