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This chapter describes John Harsanyi's theory of so-called games of incomplete information using Poker as a motivating example. The chapter begins by analyzing a simplified version of Von Neumann's second Poker model. The general theory of incomplete information is then described. Russian Roulette and Cournot Duopoly with incomplete information about costs are used as examples. Harsanyi's purification of mixed strategies is briefly described. The finitely repeated Prisoner's Dilemma, in which the number of repetitions is not common knowledge, is given as an example with incomplete information about the rules of a game.

This chapter shows that in many situations with patient players, the payoffs bounds from Chapter 8 are tight. It then proves various folk theorems for games of public monitoring, including games with a product structure and extensive form games. The chapter discusses the enforceability, identifiability, and rank conditions on the monitoring technology required for the folk theorem, and finally considers games of symmetric incomplete information.

This chapter studies horizontal collusion between interest groups in a Bayesian setting. Various models under complete and incomplete information are introduced and the different results are obtained as a function of the correlation of private information. The role of transaction costs within the coalition is found to be of crucial importance and a number of unresolved issues are outlined for future research.

Repeated games are considered. The discussion explains issues surrounding randomization, observability, feasibility, and convexity. Games with pay-off averaging and discounting are examined, along with finitely repeated games. The ‘no-gain-from-one-shot-deviation’ property of games with continuous pay-offs is discussed and the proof sketched. Finally, games of incomplete information are introduced.

This chapter presents the concept of a Bayesian Nash equilibrium as defined by Harsanyi (1967). His approach was to transform a game of incomplete information into one of imperfect information; any buyer who has incomplete information about other buyers’ values is treated as if he were uncertain about their types. A brief introduction to auctions is provided, and how these can be viewed as games of incomplete information is explained. The notations that will be used throughout the book are defined.

Mechanism Design is introduced, The key classifications of complete and incomplete information are given and the revelation principle is described. Direct mechanisms and dominant strategy implementation are discussed. The Gibbard–Satterthwaite theorem and some positive results are given—for single peaked and quasi-linear preferences.

The goal of decision support is to develop methods that assist decision makers. In this chapter computational methods are brought to bear on a multi-dimensional choice problem with the two-part challenge of efficiently determining the decision-maker’s preferences and then finding the best choice. Computer-aided decision support is growing rapidly. This chapter introduces some technical methods of broad applicability in this area, including specification of utility functions with uncertainty, Markov decision processes, and robust optimization. The author exploits the notion of minimax regret, where the goal is to find an option that minimizes the maximum regret relative to all possible manifestations of an uncertain utility function. This approach is robust to incomplete information and facilitates the important process of preference elicitation from the client. There are opportunities for using such approaches to investigate human decision making based on incomplete information; the impact of cognitive costs, biases, and heuristics; and choices made by groups.

This chapter focuses on the incomplete information that players may have about each other’s preferences, which may induce them to try to seek out additional information, misperceive an opponent’s interests, or try to deceive an adversary. It also considers the circumstances when the possession of information may backfire, creating a “paradox of omniscience.” The discussions cover information revelation in Hamlet; incomplete information in the Magnanimity Game (MG); misperception in the Iran hostage crisis; deception in the Cuban missile crisis; and the paradox of omniscience.

The chapter studies the relationship between bargaining and competition with incomplete information. It considers a model with two uninformed and identical buyers and two sellers. One of the sellers has a privately-known reservation price, which can either be low or high. The other seller’s reservation price is commonly known to be in between the low and high values of the privately-informed seller. Buyers move in sequence, and make offers with the second buyer observing the offer made by the first buyer. The sellers respond simultaneously. The chapter shows that there are two types of (perfect Bayes) equilibria. In one equilibrium, the buyer who moves second does better. In the second equilibrium, buyers expected payoffs are equalized, and the price received by the seller with the known reservation value is determined entirely by the equilibrium of the two-player game between a single buyer and an informed seller. The chapter also discusses extensions of the model to multiple buyers and sellers, and to the case where both sellers are privately informed.

This chapter presents a methodological innovation: the notion of a game of incomplete information. This notion has been extremely useful in the modeling of all sorts of economic phenomena. As an example of this sort of application, the chapter discusses again the problem of entry deterrence in monopoly. It uses games of incomplete information to model situations in which one or more of the players is suspected of being “irrational.” “Rationality” is meant to connote behavior that is in accord with the originally given payoffs, taking into account the predicted behavior of one's opponent(s). “Irrationality” connotes behavior that is taken without much thought of introspection. With this tool, the chapter returns to questions concerning refinements of Nash equilibrium.

This chapter discusses static market structure games. It begins by describing the benchmark case of a monopolist, developing the basic building blocks for subsequent models. It then introduces static models of duopoly, presenting first the case of Bertrand price competition and then discussing the classic Cournot quantity duopoly model. Next, it extends the standard Cournot quantity competition analysis to accommodate a larger number of firms in oligopoly, obtaining the market equilibrium in perfect competition as a polar case. Finally, it explores the impact of incomplete information on market structure in a duopoly.

This chapter shows that limited effects of monetary policy can reflect shortcomings of existing policy frameworks in low-income countries rather than (or in addition to) the structural features often put forward in policy and academic debates. The chapter focuses on two pervasive issues: lack of effective frameworks for implementing policy, so that short-term interest rates display considerable unintended volatility, and poor communication about policy intent. The authors introduce these features into an otherwise standard New Keynesian model with incomplete information. Implementation errors result from insufficient accommodation to money demand shocks, creating a noisy wedge between actual and intended interest rates. The representative private agent must then infer policy intentions from movements in interest rates and money. Under these conditions, even exogenous and persistent changes in the stance of monetary policy can have weak effects, even when the underlying transmission (as might be observed under complete information) is strong.

This chapter explores a number of issues connected with the use of game-theoretic models to organize analytic narratives. First, a causal explanation of the 1936 Rhineland crisis is developed within the confines of a game-theoretic model of asymmetric or unilateral deterrence with incomplete information. In this context, the chapter then introduces the concept of a perfect Bayesian equilibrium. Then, some methodological obstacles that may arise in a more complex case, such as the 1879 Austro-German alliance, are discussed, and suggestions for overcoming them are offered. Finally, the advantages of using game models to more fully understand real world events are highlighted.

This chapter provides the book’s theoretical foundation, establishing that civil war violence results from incomplete information and commitment problems between government and rebel forces. UN peacekeeping reduces violence by making combatants’ use of violence more costly and helping factions commit to peaceful forms of conflict resolution. The two characteristics of peacekeeping missions that best enable them to mitigate violence are capacity and constitution. These characteristics can vary dramatically within and across missions. Capacity is conceptualized as the number of personnel deployed and constitution as the type of personnel deployed. Missions with larger amounts of appropriate personnel better perform violence reduction activities, as do missions constituted with substantial armed troops and police. The capacity and constitution of peacekeeping missions should be considered critical components of peacekeeping’s ability to reduce violence.

This chapter identifies the causes and consequences of bad strategy and poor tactics. It distinguishes three sources of error: incomplete information, wishful thinking, and mixed objectives. The chapter also explains the metaphor of the “game” when referring to the subject matter as the sovereignty game, noting that the sovereignty game is shaped by an evolving set of formal and informal rules and practices. The chapter presents two reasons why wishful thinking is present in secessionist movements: the first follows from the problem of incomplete information and the second is the simple penchant for hope. The chapter also analyses how internal division (factionalism) complicates the strategic and tactical playing field and its effects within self-determination groups. The product of the different causes of bad strategy is a game where play is varied and where actors often make poor choices. The game is coherent enough to shape play but sufficiently vague to produce misaligned tactics. With such awareness, the chapter outlines these causes and their consequences and, in doing so, begin to set the stage for a more prescriptive discussion.

Problems of interaction, which give rise to justice, are structurally problems of game theory, the mathematical theory of interactive decisions. Five problems of interaction are introduced that are all intrinsically important and that help motivate important parts of the discussions in subsequent chapters: the Farmer’s Dilemma, impure coordination, the Stag Hunt, the free-rider problem, and the choice for a powerless party to acquiesce or resist. Elements of noncooperative game theory essential to analyzing problems of justice are reviewed, including especially games in the strategic and extensive forms, the Nash equilibrium, the Prisoner’s Dilemma, and games of incomplete information. Each of the five motivating problems is reformulated game-theoretically. These game-theoretic reformulations reveal precisely why the agents involved would have difficulty arriving at mutually satisfactory resolutions, and why “solutions” for these problems call for principles of justice to guide the agents’ conduct.

This chapter begins with the observation that the INGO world is comprised of both principled and non-principled actors. Unfortunately, actors that work with INGOs do not know what type of organization they are facing and have to rely on signals from INGOs themselves as to their underlying motivations. This chapter takes this basic contention and uses it to develop an alternative theory for when and where we should see advocacy and service INGOs be effective actors for human security outcomes. Understanding (a) uncertainty about the motivational composition of the INGO sector, (b) the peculiarities of the domestic political structures and conditions where the work is taking place, (c) the signals that the organizations send, and (d) the responses of the domestic and international communities are all critical for understanding when and where INGOs will actually matter for human security. The empirical implications of this theory are outlined.