Belief‐Free Equilibria in Repeated Games

We introduce a class of strategies that generalizes examples constructed in two‐player games under imperfect private monitoring. A sequential equilibrium is belief‐free if, after every private history, each player's continuation strategy is optimal independently of his belief about his opponents' private histories. We provide a simple and sharp characterization of equilibrium payoffs using those strategies. While such strategies support a large set of payoffs, they are not rich enough to generate a folk theorem in most games besides the prisoner's dilemma, even when noise vanishes.     

Beliefs in Repeated Games

Consider a two‐player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three properties: learnability, a diversity of belief condition called CSP, and consistency. Loosely, if players learn to forecast the path of play whenever each plays a strategy that the other anticipates (in the sense of being in the support of that player's belief) and if the sets of anticipated strategies are sufficiently rich, then neither anticipates any of his opponent's best responses. This generalizes results in Nachbar (1997).     

The Folk Theorem for Games with Private Almost‐Perfect Monitoring

We prove the folk theorem for discounted repeated games under private, almost‐perfect monitoring. Our result covers all finite, n‐player games that satisfy the usual full‐dimensionality condition. Mixed strategies are allowed in determining the individually rational payoffs. We assume no cheap‐talk communication between players and no public randomization device.     

Reputation in Continuous‐Time Games

We study reputation dynamics in continuous‐time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous‐time game is payoff‐equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.     

Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information

This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a player's best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite‐action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite‐action games that converges to a PSNE of the continuum‐action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first‐price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first‐price, multi‐unit, and all‐pay auctions; pricing games with incomplete information about costs; and noisy signaling games.     

Isotone Equilibrium in Games of Incomplete Information

An isotone pure strategy equilibrium exists in any game of incomplete information in which each player's action set is a finite sublattice of multidimensional Euclidean space, types are multidimensional and atomless, and each player's interim expected payoff function satisfies two “nonprimitive conditions” whenever others adopt isotone pure strategies: (i) single‐crossing in own action and type and (ii) quasi‐supermodularity in own action. Conditions (i), (ii) are satisfied in supermodular and log‐supermodular games given affiliated types,and in games with independent types in which each player's ex post payoff satisfies supermodularity in own action and nondecreasing differences in own action and type. This result is applied to provide the first proof of pure strategy equilibrium existence in the uniform price auction when bidders have multi‐unit demand, nonprivate values, and independent types.     

The Economic Value of Market Information for Farmers in Developing Economies

In developing countries, farmers lack information for making informed production, manufacturing/selling decisions to improve their earnings. To alleviate poverty, various non‐governmental organizations (NGOs) and for‐profit companies have developed different ways to distribute information about market price, crop advisory and farming technique to farmers. We investigate a fundamental question: will information create economic value for farmers? We construct a stylized model in which farmers face an uncertain market price (demand) and must make production decisions before the market price is realized. Each farmer has an imprecise private signal and an imprecise public signal to estimate the actual market price. By examining the equilibrium outcomes associated with a Cournot competition game, we show that private signals do create value by improving farmers' welfare. However, this value deteriorates as the public signal becomes available (or more precise). In contrast, in the presence of private signals, the public signal does not always create value for the farmers. Nevertheless, both private and public signals will reduce price variation. We also consider two separate extensions that involve non‐identical private signal precisions and farmers' risk‐aversion, and we find that the same results continue to hold. More importantly, we find that the public signal can reduce welfare inequality when farmers have non‐identical private signal precisions. Also, risk‐aversion can dampen the value created by private or public information.     

Repeated Games with Private Monitoring: Two Players

We investigate two‐player infinitely repeated games where the discount factor is less than but close to unity. Monitoring is private and players cannot communicate. We require no condition concerning the accuracy of players' monitoring technology. We show the folk theorem for the prisoners' dilemma with conditional independence. We also investigate more general games where players' private signals are correlated only through an unobservable macro shock. We show that efficiency is sustainable for generic private signal structures when the size of the set of private signals is sufficiently large. Finally, we show that cartel collusion is sustainable in price‐setting duopoly.     

On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games

A game is better-reply secure if for every nonequilibrium strategy x^* and every payoff vector limit u^* resulting from strategies approaching x^*, some player i has a strategy yielding a payoff strictly above u_i^* even if the others deviate slightly from x^*. If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.     

Bargaining,Reputation, and Equilibrium Selection in Repeated Games with Contracts

Consider a two‐person intertemporal bargaining problem in which players choose actions and offers each period, and collect payoffs (as a function of that period's actions) while bargaining proceeds. This can alternatively be viewed as an infinitely repeated game wherein players can offer one another enforceable contracts that govern play for the rest of the game. Theory is silent with regard to how the surplus is likely to be split, because a folk theorem applies. Perturbing such a game with a rich set of behavioral types for each player yields a specific asymptotic prediction for how the surplus will be divided, as the perturbation probabilities approach zero. Behavioral types may follow nonstationary strategies and respond to the opponent's play. In equilibrium, rational players initially choose a behavioral type to imitate and a war of attrition ensues. How much should a player try to get and how should she behave while waiting for the resolution of bargaining? In both respects she should build her strategy around the advice given by the “Nash bargaining with threats” (NBWT) theory developed for two‐stage games. In any perfect Bayesian equilibrium, she can guarantee herself virtually her NBWT payoff by imitating a behavioral type with the following simple strategy: in every period, ask for (and accept nothing less than) that player's NBWT share and, while waiting for the other side to concede, take the action Nash recommends as a threat in his two‐stage game. The results suggest that there are forces at work in some dynamic games that favor certain payoffs over all others. This is in stark contrast to the classic folk theorems, to the further folk theorems established for repeated games with two‐sided reputational perturbations, and to the permissive results obtained in the literature on bargaining with payoffs as you go.     

Games with Imperfectly Observable Actions in Continuous Time

This paper investigates a new class of two‐player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ℰ(r) of payoff pairs achievable by all public perfect equilibria of the continuous‐time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ℰ(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ℰ(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ℰ(r).     

Strategic Cognition of Operations Executives

The nature of operations executives’ strategic cognition, as the antecedent to their choices about operations strategy, remains underexplored in the literature. This mixed‐methods study examines executives’ thinking about supply chain strategy through the lens of managerial cognition. Our qualitative study at a pharmaceutical distributor, which examined 25 executives’ outlook on the future of the turbulent U.S. healthcare sector and their suggestions for adapting the company's supply chain strategy to that future, suggests that an executive's strategic cognition can be defined by its regulatory focus—whether the executive envisions the future environment in terms of opportunities or threats—and the level of optimism in regards to the envisioned future. We propose a typology that predicts the strategic choices of operations executives based on four types of cognition: pioneering, pushing, protective, and provocative. It describes whether an executive's strategic choices target traditional or novel sources of revenue, and if they seek to influence either the firm's structure and practices or its environment. Our empirical test of the typology using quantitative data collected in a survey of senior operations executives supports the study's propositions associating three of the four types of cognition with their respective preferred strategic choices.     

Institutional Strategies in Emerging Markets

Abstract

We review and integrate a wide range of literature that has examined the strategies by which organizations navigate institutionally diverse settings and capture rents outside of the marketplace. We synthesize this body of research under the umbrella term institutional strategies, which we define as the comprehensive set of plans and actions directed at leveraging and shaping socio-political and cultural institutions to obtain or retain competitive advantage. Our review of institutional strategies is focused on emerging market contexts, settings that are characterized by weak capital market and regulatory infrastructures and fast-paced turbulent change. Under such challenging conditions, strategies aimed at shaping the institutional environment may be especially critical to an organization's performance and long-term survival. Our review reveals that organizations engage in three specific and identifiable sets of institutional strategies, which we term relational, infrastructure-building, and socio-cultural bridging. We conclude by highlighting fruitful avenues for cross-disciplinary dialogue in the hope of promoting future research on emerging markets and defining the next frontier of institutional theory in organizational analysis.     

Level‐k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private‐Value Auctions?

This paper proposes a structural nonequilibrium model of initial responses to incomplete‐information games based on “level‐k” thinking, which describes behavior in many experiments with complete‐information games. We derive the model's implications in first‐ and second‐price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level‐k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common‐value auctions and overbidding in those independent‐private‐value auctions without the uniform value distributions used in most experiments.     

Repeated Games Where the Payoffs and Monitoring Structure Are Unknown

This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define perfect type‐contingently public ex post equilibria (PTXE), which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.     

Private and Public Sector Models for Strategies in Universities*

Increasing formalization of disciplined management of UK universities over the last 30 years has been accompanied by moves to articulate universities' strategies, by attempts to connect organizations' plans and management of activity to those strategies and by a desire to measure how well outcomes are fitted to universities' goals. In this complex change in the orientation of universities' management, lessons have been drawn from the contemporary development of the analysis of strategy and strategic process in commercial and, latterly, in public sector settings. It is argued that there have been very significant errors and weaknesses in the importation of such models of strategy, especially in the stress on strategic planning rather than strategic process and in the insensitivity of universities' planning to the underlying strategy process of the typical university. Most universities, it is argued, mistake planning – and even budgeting – for strategy itself, having failed to make proper sense of their own organizations' processes of generating strategies and putting them into practice. They have typically missed the crucial context of strategy and change. It is argued that there are crucial lessons to be learned from recent advances in theorizing about strategy in the private or commercial sector, particularly in relation to the development of modelling complex and path‐dependent systems; and it is argued strongly that universities' strategic process can fruitfully be analysed through the perspectives of real options analysis. This can also accommodate the richness of universities' traditions of strategy formation and implementation within ‘loose‐coupled’ organizations.     

Who's Who in Networks. Wanted: The Key Player

Finite population noncooperative games with linear‐quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own‐concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich–Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player's centrality and her contribution to the centrality of the others.     

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.     

The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information

The theory of global games has shown that coordination games with multiple equilibria may have a unique equilibrium if certain parameters of the payoff function are private information instead of common knowledge. We report the results of an experiment designed to test the predictions of this theory. Comparing sessions with common and private information, we observe only small differences in behavior. For common information, subjects coordinate on threshold strategies that deviate from the global game solution towards the payoff‐dominant equilibrium. For private information, thresholds are closer to the global game solution than for common information. Variations in the payoff function affect behavior as predicted by comparative statics of the global game solution. Predictability of coordination points is about the same for both information conditions.     

Supply Chain Sourcing Under Asymmetric Information

We study a supply chain with two suppliers competing over a contract to supply components to a manufacturer. One of the suppliers is a big company for whom the manufacturer's business constitutes a small part of his business. The other supplier is a small company for whom the manufacturer's business constitutes a large portion of his business. We analyze the problem from the perspective of the big supplier and address the following questions: What is the optimal contracting strategy that the big supplier should follow? How does the information about the small supplier's production cost affect the profits and contracting decision? How does the existence of the small supplier affect profits? By studying various information scenarios regarding the small supplier's and the manufacturer's production cost, we show, for example, that the big supplier benefits when the small supplier keeps its production cost private. We quantify the value of information for the big supplier and the manufacturer. We also quantify the cost (value) of the alternative‐sourcing option for the big supplier (the manufacturer). We determine when an alternative‐sourcing option has more impact on profits than information. We conclude with extensions and numerical examples to shed light on how system parameters affect this supply chain.