This chapter surveys a sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents (“coalitions”) deliberately get together to jointly determine within-group actions, while interacting noncooperatively across groups. The chapter describes a variety of solution concepts, using an umbrella model that adopts an explicit real-time approach. Players band together, perhaps disband later and re-form in shifting alliances, all the while receiving payoffs at each date according to the coalition structure prevailing at the time. We use this model to nest two broad approaches to coalition formation, one based on cooperative game theory, the other based on noncooperative bargaining. Three themes that receive explicit emphasis are agent farsightedness, the description of equilibrium coalition structures, and the efficiency implications of the various theories.
Aim: To present a systematic development of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to Chess and Go in small strides at a gradient that is not too steep. Presentation: Mostly informal; examples of combinatorial games sampled from various strategic viewing points along scenic mountain trails illustrate the theory. Add-on:Atasteof constraint logic, a new tool to prove intractabilities of games.
This chapter reviews the origin and development of game-theoretic ideas in biology. It covers more than half a century of research and focuses on those models and conceptual advancements that are rooted in fundamental biological theory and have been exposed to substantial empirical scrutiny. The different areas of research—ranging from molecules and microbes to animals and plants—are described using informative examples rather than attempting an all-encompassing survey.
Many auctions involve the sale of a variety of distinct assets. Examples are airport time slots, delivery routes, network routing, and furniture. Because of complementarities or substitution effects between the different assets, bidders have preferences not just for particular items but for sets of items. For this reason, economic efficiency is enhanced if bidders are allowed to bid on bundles or combinations of different assets. This paper surveys the state of knowledge about the design of combinatorial auctions and presents some new insights. Periodic updates of portions of this survey will be posted to this journal's Online Supplements web page at http://joc.pubs.informs.org/OnlineSupplements.html
We provide an overview and synthesis of the literatures analyzing games where players are connected via a network structure. We study, in particular, the impact of the structure of the network on individuals’ behaviors. We focus on the game theoretic modeling, but also include some discussion of analyses of peer effects, as well as applications to diffusion, employment, crime, industrial organization, and education.
This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in repeated games of incomplete information.
We consider algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents' interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. Our main technical contribution concerns the study of a representative task scheduling problem for which the standard mechanism design tools do not suffice. Journal of Economic Literature Classification Numbers: C60, C72, D61, D70, D80.
Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems from the parallels between the underlying decision-making architectures in both societal systems and distributed engineered systems. In particular, both settings involve an interconnection of decision-making elements whose collective behavior depends on a compilation of local decisions that are based on partial information about each other and the state of the world. Accordingly, there is extensive work in game theory that is relevant to the engineering agenda. Similarities notwithstanding, there remain important differences between the constraints and objectives in societal and engineered systems that require looking at game-theoretic methods from a new perspective. This chapter provides an overview of selected recent developments of game-theoretic methods in this role as a framework for distributed control in engineered systems.
I survey and discuss the recent literature on testing experts or probabilistic forecasts, which I would describe as a literature on “strategic hypothesis testing” The starting point of this literature is some surprising results of the following type: suppose that a criterion forjudging probabilistic forecasts (which I will call a test) has the property that if data are generated by a probabilistic model, then forecasts generated by that model pass the test. It, then, turns out an agent who knows only the test by which she is going to be judged, but knows nothing about the data-generating process, is able to pass the test by generating forecasts strategically.The literature identifies a large number of tests that are vulnerable to strategic manipulation of uninformed forecasters, but also delivers some tests that cannot be passed without knowledge of the data-generating process. It also provides some results on philosophy of science and financial markets that are related to, and inspired by the results on testing experts.
Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about…what others believe about the rationality of players imply regarding play in a game? Being explicit about these assumptions can be important, because solution concepts are often motivated intuitively in terms of players’ beliefs and their rationality; however, the epistemic analysis may show limitations in these intuitions, reveal what additional assumptions are hidden in the informal arguments, clarify the concepts or show how the intuitions can be generalized. A further premise of this chapter is that the primitives of the model— namely, the hierarchies of beliefs—should be elicitable, at least in principle. Building upon explicit assumptions about elicitable primitives, we present classical and recent developments in epistemic game theory and provide characterizations of a nonexhaustive, but wide, range of solution concepts.
Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols. Over finite time spans the evolution of aggregate behavior is well approximated by the solution of a differential equation. From a different point of view, every revision protocol defines a map—a deterministic evolutionary dynamic—that assigns each population game a differential equation describing the evolution of aggregate behavior in that game. In this chapter, we provide an overview of the theory of population games and deterministic evolutionary dynamics. We introduce population games through a series of examples and illustrate their basic geometric properties. We formally derive deterministic evolutionary dynamics from revision protocols, introduce the main families of dynamics—imitative/biological, best response, comparison to average payoffs, and pairwise comparison—and discuss their basic properties. Combining these streams, we consider classes of population games in which members of these families of dynamics converge to equilibrium; these classes include potential games, contractive games, games solvable by iterative solution concepts, and supermodular games. We relate these classes to the classical notion of an evolutionarily stable state and to recent work on deterministic equilibrium selection. We present a variety of examples of cycling and chaos under evolutionary dynamics, as well as a general result on survival of strictly dominated strategies. Finally, we provide connections to other approaches to game dynamics, and indicate applications of evolutionary game dynamics to economics and social science.
The survey presents recent results in the theory of two-person zero-sum repeated games and their connections with differential and continuous-time games. The emphasis is made on the following A general model allows to deal simultaneously with stochastic and informational aspects. All evaluations of the stage payoffs can be covered in the same framework (and not only the usual Cesàro and Abel means). The model in discrete time can be seen and analyzed as a discretization of a continuous time game. Moreover, tools and ideas from repeated games are very fruitful for continuous time games and vice versa. Numerous important conjectures have been answered (some in the negative). New tools and original models have been proposed. As a consequence, the field (discrete versus continuous time, stochastic versus incomplete information models) has a much more unified structure, and research is extremely active.
In one of the most influential existence theorems in mathematics, John F. Nash proved in 1950 that any normal form game has an equilibrium. More than five decades later, it was shown that the computational task of finding such an equilibrium is intractable, that is, unlikely to be carried out within any feasible time limits for large enough games. This chapter develops the necessary background and formalism from the theory of algorithms and complexity developed in computer science, in order to understand this result, its context, its proof, and its implications.
This chapter reviews developments in the theory of decision making under risk and uncertainty, focusing on models that, over the last 40 years, dominated the theoretical discussions. It also surveys some implications of the departures from the “linearity in the probabilities” aspect of expected utility theory to game theory. The chapter consists of two main parts: The first part reviews models of decision making under risk that depart from the independence axiom, focusing on the rank-dependent utility models and cumulative prospect theory. The second part reviews theories of decision making under uncertainty that depart from the sure thing principle and model the phenomenon of ambiguity and ambiguity aversion.
As a selling mechanism, auctions have acquired a central position in the free market economy all over the globe. This development has deepened, broadened, and expanded the theory of auctions in new directions. This chapter is intended as a selective update of some of the developments and applications of auction theory in the two decades since Wilson (1992) wrote the previous Handbook chapter on this topic.
Utility and subjective probability involve the systematic study of people's preferences and beliefs, including quantitative representations of preference and belief that facilitate analyses of problems in decision making and choice behavior. Its history spans more than 250 years and is mainly because of people in economics, mathematics, statistics, and psychology. Utility theory is primarily concerned with properties of a binary relation on a set X, where X could be a set of commodity bundles, decision alternatives, monetary gambles, n-tuples of pure strategies, and so forth, and x > y is interpreted as x is preferred to y. The formal development of utility and subjective probability is based on the notion of a binary relation. Special types of binary relations are identified by conjunctions of properties that are equivalence, linear order, weak order, and partial order.
This chapter discusses moral hazard. The principal–agent relationship embodies a special form of moral hazard, which can be called “one-sided,” but moral hazard can also be “many-sided.” The paradigmatic model of many-sided moral hazard is the partnership in which there are many agents but no principal. The output of the partnership depends jointly on the actions of the partners and on the stochastic environment; each partner observes only the output (and his or her own action) but not the actions of the other partners or the environment. This engenders a free-rider problem. As in the case of principal–agent relationships, a partnership, too, may last many periods. The chapter presents the principal–agent model formally and describes some salient features of optimal principal–agent contracts when the relationship lasts a single period. In a large class of cases, equilibrium in the one-period game is Pareto-inefficient. This is a well-known problem in providing risk-averse agent insurance while simultaneously giving the agent the incentives to take, from the principal's perspective, appropriate actions. The chapter also discusses other properties of static contracts such as monotonicity of the agent's compensation in observed profits.
