Michael Wooldridge

University of Oxford | OX · Department of Computer Science

For cooperative games with externalities, the problem of optimally partitioning a set of players into disjoint exhaustive coalitions is called coalition structure generation, and is a fundamental computational problem in multi-agent systems. Coalition structure generation is, in general, computationally hard and a large body of work has therefore i...

Within the area of multi-agent systems, normative systems are a widely used framework for the coordination of interdependent activities. A crucial problem associated with normative systems is that of synthesising norms that effectively accomplish a coordination task and whose compliance forms a rational choice for the agents within the system. In t...

We study concurrent games with finite-memory strategies where players are given a Buchi and a mean-payoff objective, which are related by a lexicographic order: a player first prefers to satisfy its Buchi objective, and then prefers to minimise costs, which are given by a mean-payoff function. In particular, we show that deciding the existence of a...

The existence of (Nash) equilibria with undesirable properties is a well-known problem in game theory, which has motivated much research directed at the possibility of mechanisms for modifying games in order to eliminate undesirable equilibria, or induce desirable ones. Taxation schemes are a well-known mechanism for modifying games in this way. In...

Norms have been extensively proposed as coordination mechanisms for both agent and human societies. Nevertheless, choosing the norms to regulate a society is by no means straightforward. The reasons are twofold. First, the norms to choose from may not be independent (i.e, they can be related to each other). Second, different preference criteria may...

The fields of economic theory and artificial intelligence (AI) share many common interests and notions such as utility, probability, and reasoning about other actors in the environment. This common ground has given rise to a wide body of literature at the interface of economic theory and AI whose scope includes algorithmic aspects of cooperative an...

In this paper, we investigate a noncooperative sequential bargaining game for allowing a group of agents agents to partition themselves into non-overlapping coalitions. We focus on the issue of how a player's position on the bargaining agenda affects his power. We also analyse the relationship between the distribution of the power of individual pla...

In this work we build on these models to look at social influence from a strategic perspective. We do so by introducing a new class of games, called games of influence. Specifically, a game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or...

In this work we build on these models to look at social influence from a strategic perspective. We do so by introducing a new class of games, called games of influence. Specifically, a game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or...

We introduce a novel notion of expressiveness for temporal logics that is based on game theoretic properties of multi-agent systems. We focus on iterated Boolean games, where each agent i has a goal γi, represented using (a fragment of) Linear Temporal Logic (LTL). The goal γi captures agent i's preferences: the models of γi represent system behavi...

Reactive Modules is a high-level modelling language for concurrent , distributed, and multi-agent systems, which is used in a number of practical model checking tools. Reactive Modules Games are a game-theoretic extension of Reactive Modules, in which agents in a system are assumed to act strategically in an attempt to satisfy a temporal logic form...

We address the problem of how a set of agents can decide to share a resource, represented as a unit-sized pie. The pie can be generated by the entire set but also by some of its subsets. We investigate a finite horizon non-cooperative bargaining game, in which the players take it in turns to make proposals on how the resource should for this purpos...

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the infor...

We develop a logic for reasoning about semi-public environments, i.e. environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning...

The coalition structure generation problem is a natural abstraction of one of the most important challenges in multi-agent systems: How can a number of agents divide themselves into groups in order to improve their performance? More precisely, the coalition structure generation problem focuses on partitioning the set of agents into mutually disjoin...

Although the notion of social capital has been extensively studied in various bodies of the literature , there is no universally accepted definition or measure of this concept. In this article, we discuss a new approach for measuring social capital which builds upon cooperative game theory. The new approach not only turns out to be a natural tool f...

Reactive Modules is a high-level specification language for concurrent and multi-agent systems, used in a number of practical model checking tools. Reactive Modules Games is a game-theoretic extension of Reactive Modules, in which concurrent agents in the system are assumed to act strategically in an attempt to satisfy a temporal logic formula repr...

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's...

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a...

In the Complete Set Partitioning problem we are given a finite set of elements where every subset is associated with a value, and the goal is to partition this set into disjoint subsets so as to maximise the sum of subset values. This abstract problem captures the Coalition Structure Generation problem in cooperative games in characteristic functio...

Most normative systems make use of explicit representations of norms (namely, obligations, prohibitions, and permissions) and associated mechanisms to support the self-regulation of open societies of self-interested and autonomous agents. A key problem in research on normative systems is that of how to synthesise effective and efficient norms. Manu...

This column discusses extensive form games and shows how backward induction can be used to analyze such games. It also discusses some of the apparent paradoxes that can arise when using backward induction to analyze games.

One key problem is that of identifying the key members of the organization using information about the terrorist network's topology: this capability would enable security agencies to focus severely limited resources on just those key members. many standard measures of centrality from the field of social network analysis can be used. Centrality meas...

On-line norm synthesis is a widely used approach to facilitate coordination in MASs. In [2] we introduced NormLab, a computational framework to support research on on-line norm synthesis. That framework provides functionalities to model, simulate and analyse norm synthesis algorithms in an agent-based simulation environment. Here we present several...

Norms have been extensively studied to coordinate multi-agent systems, and the literature has investigated two general approaches to norm synthesis: off-line (synthesising norms at design-time) and on-line (run-time synthesis). On-line synthesis is generally recognised to be appropriate for open systems, where aspects of the system remain unknown a...

Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as model...

In this paper, the authors consider some of the main ideas underpinning attempts to build automated negotiators--computer programs that can effectively negotiate on our behalf. If we want to build programs that will negotiate on our behalf in some domain, then we must first define the negotiation domain and the negotiation protocol. Defining the ne...

Many multiagent settings require a collection of agents to partition themselves into coalitions. In such cases, the agents may have conflicting preferences over the possible coalition structures that may form. We investigate a noncooperative bargaining game to allow the agents to resolve such conflicts and partition themselves into non-overlapping...

We address the problem of how a group of agents can decide to share a resource, represented as a unit-sized pie. We investigate a finite horizon non-cooperative bargaining game, in which the players take it in turns to make proposals on how the resource should be allocated, and the other players vote on whether or not to accept the allocation. Voti...

We introduce and investigate formal quantitative measures of inconsistency between the beliefs of agents in multi-agent systems. We start by recalling a well-known model of belief in multi-agent systems, and then, using this model, present two classes of inconsistency metrics. First, we consider metrics that attempt to characterise the overall degr...

Event structures form a canonical model of concurrent behaviour which has a natural game-theoretic interpretation. This game-based interpretation was initially given for zero-sum concurrent games. This paper studies an extension of such games on event structures to include a much wider class of game types and solution concepts. The extension permit...

When the performance of a team of agents exceeds our expectations or fall short of them, we often explain this by saying that there was some synergy in the team---either positive (the team exceeded our expectations) or negative (they fell short). Our aim in this article is to develop a formal and principled way of measuring synergies, both positive...

An increasing number of businesses and organisations rely on existing users for finding new users or spreading a message. One of the widely used "refer-a-friend" mechanisms offers an equal reward to both the referrer and the invitee. This mechanism provides incentives for direct referrals and is fair to the invitee. On the other hand, multi-level m...

We address the issue of manipulating games through communication. In the specific setting we consider (a variation of Boolean games), we assume there is some set of environment variables, the values of which are not directly accessible to players; the players have their own beliefs about these variables, and make decisions about what actions to per...

Much previous research has investigated explicit, machine-process-able norms as a means to facilitate coordination in open multi-agent systems. This research can typically be classified as considering either offline design (norms are synthesised at design time) or online design. Online synthesis techniques aim to construct norms for a system while...

MAS research has investigated norms as a means to coordinate open multi-agent systems (MAS). This has spurred a strand of research on on-line norm synthesis algorithms for MASs. However, to the best of our knowledge, currently there is no computational framework to support the development and study of on-line norm synthesis. Here we present NORMLAB...

We introduce and formally study games in which the goals of players relate to the epistemic states of players in the game. For example, one player might have a goal that another player knows a certain proposition, while another player might have as a goal that a certain player does not know some proposition. The formal model we use to study epistem...

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central notion to the Shapley value - be defined in a variety of ways, but it is also not obvious which axiomatization...

We study a recently developed centrality metric to identify key players in terrorist organisations due to Lindelauf et al. [2013]. This metric, which involves computation of the Shapley value for connectivity games on graphs proposed by Amer and Gimenez [2004], was shown to produce substantially better results than previously used standard centrali...

Iterated games are well-known in the game theory literature. We study iterated Boolean games. These are games in which players repeatedly choose truth values for Boolean variables they have control over. Our model of iterated Boolean games assumes that players have goals given by formulae of Linear Temporal Logic (LTL), a formalism for expressing p...

This work is motivated by the following concern. Suppose we have a game exhibiting multiple Nash equilibria, with little to distinguish them except that one of them can be verified while the others cannot. That is, one of these equilibria carries sufficient information that, if this is the outcome, then the players can tell that an equilibrium has...

The concept of program equilibrium, introduced by Howard (Theory and Decision 24(3):203–213, 1988) and further formalised by Tennenholtz (Game Econ Behav 49:363–373, 2004), represents one of the most ingenious and potentially far-reaching applications of ideas from computer science in game theory to date. The basic idea is that a player in a game s...

We present a logic for reasoning about choice. Choice ctl (c-ctl) extends the well-known branching-time temporal logic ctl with choice modalities, “\(\Diamond\)” and “□”. An example c-ctl formula is \(\Diamond\) AF happy, asserting that there exists a choice that will lead to happiness. c-ctl is related to both stit logics and temporal cooperation...

Key concepts are described from the area now known as evolutionary game theory, while also introducing some important applications of these concepts.

Normative systems (norms) have been widely proposed as a tech-nique for coordinating multi-agent systems. The automated synthe-sis of norms for coordination remains an open and complex prob-lem, which we tackle in this paper. We propose a novel mechanism called IRON (Intelligent Robust On-line Norm synthesis mecha-nism), for the on-line synthesis o...

We study settings in which a central authority must appoint a number of committees, where each committee is tasked with making a specific decision via a given voting rule. Each voter has their own individual preferences, and the center desires the decisions to be made in a certain way. The overall problem is whether the center can design the commit...

Here, the authors discuss matching problems and how the Gale-Shapley algorithm solves them, while also explaining some matching techniques.

This article investigates the conjecture that agents who make decisions in scenarios where trust is important can benefit from the use of a social structure, representing the social relationships that exist between agents. We propose techniques that can be used by agents to initially build and then progressively update such a structure in the light...

I begin by arguing that the notion of economic equilib-rium is an important analytical tool with which to understand the behaviour of today's networked computer systems. This is because the behaviours that such systems exhibit are in part a function of the preferences and desires of system participants; this gives such sys-tems the flavour of an ec...

One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities. In particular, when externalities occur, a direct translation of Shapley's axioms does not imply a unique value. In this paper we study the marginality approach to this problem, based on the idea of an alpha-parametrized definit...

Given the current level of international interest in game theory and its applications in AI and computer science, it seems worth pausing to consider whether game theory actually works. This article considers the evidence available in support of the two most common interpretations of game theory: the descriptive interpretation, which considers game...

Logic can be a powerful tool for reasoning about multiagent systems. First of all, logics provide a language in which to specify properties-properties of an agent, of other agents, and of the environment. Ideally, such a language then also provides a means to implement an agent or a multiagent system, either by somehow executing the specification,...

The last decade has been witness to a rapid growth of interest in logics intended to support reasoning about the interactions between knowledge and action. Typically, logics combining dynamic and epistemic components contain ontic actions (which change the state of the world, e.g., switching a light on) or epistemic actions (which affect the inform...

Boolean games are a compact and expressive class of games, based on propositional logic. However, Boolean games are computationally complex: checking for the existence of pure Nash equilibria in Boolean games is Εp/2-complete, and it is co-NP-complete to check whether a given outcome for a Boolean game is a pure Nash equilibrium. In this paper, we...

Cooperative game theory studies situations in which agents can benefit by working together. This article outlines the key concepts of cooperative game theory, and discusess the challenges that arise in applying these in AI applications.

The Banzhaf index is a well known and widely used index for measuring the power a player has in a voting game. However, the problem of computing this index is computationally hard. To overcome this problem, a number of approximation methods were developed for one majority voting games. While it may be possible to extend some of these to k-majority...

The prisoner's dilemma has aroused huge interest in the academic community since its inception. There are two key reasons for this level of interest. First, the game-theoretic analysis of the prisoner's dilemma leads to an outcome (noncooperation) that is worse for all participants than another outcome (cooperation). Second, the prisoner's dilemma...

Over the past decade, concepts and techniques from game theory have been both influential and successful in AI—and indeed, in computer science generally.

Social laws – sets of constraints imposed on the be-haviour of agents within a multi-agent system with the goal of some desirable overall behaviour resulting – are an important mechanism for coordinating multi-agent behaviour. When considering social laws in human environments, the inspiration for social laws in multi-agent systems, we argue that a...

We formalise and investigate the following problem. A principal must delegate a number of decisions to a collection of agents. Once the decisions are delegated, the agents to whom the de-cisions are delegated will act selfishly, rationally, and independently in pursuit of their own preferences. The principal himself is assumed to be self-interested...

Argument aggregation is the problem of combining argumentation frameworks. An argument aggregation procedure takes as input an argument framework for each agent in a system, intuitively representing the beliefs of that agent with respect to a disputed domain of discourse; the output is an argumentation framework that represents the social position...

Research on agent communication languages has typically taken the speech acts paradigm as its starting point. Despite their manifest attractions, speech-act models of communication have several serious disadvantages as a foundation for communication in artificial agent systems. In particular, it has proved to be extremely difficult to give a satisf...

The theory of cooperative games provides a rich mathematical framework with which to understand the interactions between self-interested agents in settings where they can benefit from cooperation, and where binding agreements between agents can be made. Our aim in this talk is to describe the issues that arise when we consider cooperative game theo...

We introduce and study the notion of a Public Environment: a system in which a publicly known program is executed in an environment that is partially observable to agents in the system. Although agents do not directly have access to all variables in the system, they may come to know the values of unobserved variables because they know how the progr...

Weighted voting games (WVGs) are an important mechanism for modeling scenarios where a group of agents must reach agreement on some issue over which they have different preferences. However, for such games to be effective, they must be well designed. Thus, a key concern for a mechanism designer is to structure games so that they have certain desira...

The conventional model of coalition formation considers every possible subset of agents as a potential coalition. However, in many real-world applications, there are inherent constraints on feasible coalitions: for instance, certain agents may be prohibited from being in the same coalition, or the coalition structure may be required to consist of c...

In the last few years, there has been increasing interest from the agent community in the use of techniques from decision theory and game theory. Our aim in this article is to briefly summarise the key concepts of decision theory and game theory and explain why they are useful when building agent-based systems. KeywordsGame theory–decision theory–...

Independent agents that interact within open, distributed, and decentralized environments need to collaboratively regulate their activities in order to facilitate the harmonious and successful achievement of possibly conflicting tasks. Coordination is the process of managing these interactions by identifying and possibly resolving the interdependen...

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete...

We introduce and investigate a natural extension of Dung's well-known model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsistency we are prepared to tolerate: given an incon...

Boolean games are a natural, compact, and expressive class of logic-based games, in which each player exercises unique control over some set of Boolean variables, and has some logical goal formula that it desires to be achieved. A playerʼs strategy set is the set of all possible valuations that may be made to its variables. A playerʼs goal formula...

We address the issue of manipulating games through communication. In the specific setting we consider (a variation of Boolean games), we assume there is some set of environment variables, the value of which is not directly accessible to players; each player has their own beliefs about these variables, and makes decisions about what actions to perfo...

This paper analyzes bilateral multi-issue negotiation where the issues are indivisible, there are time constraints in the form of deadlines and discount factors. The issues are negotiated using the package deal procedure. The set of issues to be negotiated is called the negotiation agenda. The agenda is crucial since the outcome of negotiation depe...

In epistemic logic, Kripke structures are used to model the distribution of information in a multi-agent system. In this paper, we present an approach to quantifying how much information each particular agent in a system has, or how important the agent is, with respect to some fact represented as a goal formula. It is typically the case that the go...

Distributed systems can often be modeled as a collection of distributed (system) variables whose values are constrained by a set of constraints. In distributed multi-agent systems, the set of variables occurring at a site (subsystem) is usually viewed as controllable by a local agent. This agent assigns values to the variables, and the aim is to pr...

We present an abstract framework that allows agents to form coalitions with agents that they believe to be trustworthy. In contrast to many other models, we take the notion of distrust to be our key social concept. We use a graph theoretic model to capture the distrust relations within a society, and use this model to formulate several notions of m...

Boolean games are a natural, compact, and expressive class of logicbased games, in which each player exercises unique control over some set of Boolean variables, and has some logical goal formula that it desires to be achieved. A player’s strategy set is the set of all possible valuations that may be made to its variables. A player’s goal formula m...

Logics of propositional control, such as van der Hoek and Wool- dridge’s CL-PC [14], were introduced in order to represent and rea- son about scenarios in which each agent within a system is able to exercise unique control over some set of system variables. Our aim in the present paper is to extend the study of logics of propo- sitional control to...

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of...

This paper analyzes sequential auctions for budget constrained bidders, for multiple heterogeneous common value objects. In most auctions, bidders not only have valuations for objects but also have budget constraints (i.e., constraints on how much they can actually spend in an auction). Given these constraints, the bidders’ problem is to determine...

This paper proposes and evaluates a model of supply chains as networks of auctions. In this model, companies are represented according to the first level of the Supply Chain Council's SCOR model and the trading strategy of the agents is adapted from a model proposed by Steiglitz and colleagues. Specifically, the highest level of SCOR treats a compa...

We present an introductory survey of temporal and dynamic logics: logics for reasoning about how environments change over time, and how processes change their environments. We begin by introducing the historical development of tem-poral and dynamic logic, starting with the seminal work of Prior. This leads to a discussion of the use of temporal and...

The Shapley value and Banzhaf index are two well known indices for measuring the power a player has in a voting game. However, the problem of computing these indices is computationally hard. To overcome this problem, we analyze approximation methods for computing these indices. Although these methods have polynomial time complexity, finding an appr...

The Game Description Language (GDL) is a special purpose declarative language for defining games. GDL is used in the AAAI General Game Playing Competition, which tests the ability of computer programs to play games in general, rather than just to play a specific game. Software participants in the competition are provided with a game specified in GD...

Although combinatorial auctions have received a great deal of attention from the computer science community over the past decade, research in this domain has focused on settings in which a bidder only has preferences over the bundles of goods they themselves receive, and is indifferent about how other goods are allo-cated to other bidders. In gener...

We introduce Transformation Games (TGs), a form of coalitional game in which players are endowed with sets of initial resources, and have capabilities allowing them to derive certain output resources, given certain input resources. The aim of a TG is to generate a particular target resource; players achieve this by forming a coalition capable of pe...

Theprocessofrationallyrevisingbeliefsinthelightofnewinformationis at opic of great importance and long-standing interest in artif icial intelligence. More- over, significant progress has been made in understanding the philosophical, logical, and computational foundations of belief revision. However, very little research has been reported with respe...

We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other co-existing coalitions. Although externalities play a key role in many real-life situations, very little attention has b...