A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

The Intrinsic Value of Decision Rights

Philosophers, psychologists, and economists have long argued that certain decision rights carry not only instrumental value but may also be valuable for their own sake. The ideas of autonomy, freedom, and liberty derive their intuitive appeal—at least partly—from an assumed positive intrinsic value of decision rights. Providing clean evidence for the existence of this intrinsic value and measuring its size, however, is intricate. Here, we develop a method capable of achieving these goals. The data reveal that the large majority of our subjects intrinsically value decision rights beyond their instrumental benefit. The intrinsic valuation of decision rights has potentially important consequences for corporate governance, human resource management, and optimal job design: it may explain why managers value power, why employees appreciate jobs with task discretion, why individuals sort into self‐employment, and why the reallocation of decision rights is often very difficult and cumbersome. Our method and results may also prove useful in developing an empirical revealed preference foundation for concepts such as “freedom of choice” and “individual autonomy.”     

Supply Networks as a Complex Adaptive System: Toward Simulation‐Based Theory Building on Evolutionary Decision Making

In this article, we examine how the firms embedded in supply networks engage in decision making over time. The supply networks as a complex adaptive system are simulated using cellular automata (CA) through a dynamic evolution of cooperation (i.e., “voice” decision) and defection (i.e., “exit” decision) among supply network agents (i.e., firms). Simple local rules of interaction among firms generate complex patterns of cooperation and defection decisions in the supply network. The incentive schemes underlying decision making are derived through different configurations of the payoff‐matrix based on the game theory argument. The prisoner's dilemma game allows capturing the localized decision‐making process by rational agents, and the CA model allows the self‐organizing outcome to emerge. By observing the evolution of decision making by cooperating and defecting agents, we offer testable propositions regarding relationship development and distributed nature of governance mechanisms for managing supply networks.     

Consistency of Higher Order Risk Preferences

Risk aversion (a second‐order risk preference) is a time‐proven concept in economic models of choice under risk. More recently, the higher order risk preferences of prudence (third‐order) and temperance (fourth‐order) also have been shown to be quite important. While a majority of the population seems to exhibit both risk aversion and these higher order risk preferences, a significant minority does not. We show how both risk‐averse and risk‐loving behaviors might be generated by a simple type of basic lottery preference for either (1) combining “good” outcomes with “bad” ones, or (2) combining “good with good” and “bad with bad,” respectively. We further show that this dichotomy is fairly robust at explaining higher order risk attitudes in the laboratory. In addition to our own experimental evidence, we take a second look at the extant laboratory experiments that measure higher order risk preferences and we find a fair amount of support for this dichotomy. Our own experiment also is the first to look beyond fourth‐order risk preferences, and we examine risk attitudes at even higher orders.     

Strategic Learning and the Topology of Social Networks

We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals and by observing the actions of their neighbors in a social network. We show that the question of whether or not the agents learn efficiently depends on the topology of the social network. In particular, we identify a geometric “egalitarianism” condition on the social network that guarantees learning in infinite networks, or learning with high probability in large finite networks, in any equilibrium. We also give examples of nonegalitarian networks with equilibria in which learning fails.     

Rushes in Large Timing Games

We develop a continuum player timing game that subsumes standard wars of attrition and pre‐emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single‐peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump‐shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fear relaxes the first mover advantage in pre‐emption games, asking that the least quantile beat the average; greed relaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre‐emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.     

Bounded Memory and Biases in Information Processing

Before choosing among two actions with state‐dependent payoffs, a Bayesian decision‐maker with a finite memory sees a sequence of informative signals, ending each period with fixed chance. He summarizes information observed with a finite‐state automaton. I characterize the optimal protocol as an equilibrium of a dynamic game of imperfect recall; a new player runs each memory state each period. Players act as if maximizing expected payoffs in a common finite action decision problem. I characterize equilibrium play with many multinomial signals. The optimal protocol rationalizes many behavioral phenomena, like “stickiness,” salience, confirmation bias, and belief polarization.     

Altruism in Networks

We provide the first analysis of altruism in networks. Agents are embedded in a fixed network and care about the well‐being of their network neighbors. Depending on incomes, they may provide financial support to their poorer friends. We study the Nash equilibria of the resulting game of transfers. We show that equilibria maximize a concave potential function. We establish existence, uniqueness of equilibrium consumption, and generic uniqueness of equilibrium transfers. We characterize the geometry of the network of transfers and highlight the key role played by transfer intermediaries. We then study comparative statics. A positive income shock to an individual benefits all. For small changes in incomes, agents in a component of the network of transfers act as if they were organized in an income‐pooling community. A decrease in income inequality or expansion of the altruism network may increase consumption inequality.     

Power Enhancement in High‐Dimensional Cross‐Sectional Tests

We propose a novel technique to boost the power of testing a high‐dimensional vector H : θ = 0 against sparse alternatives where the null hypothesis is violated by only a few components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high‐dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a “power enhancement component,” which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and strengthens the power under sparse alternatives. The null distribution does not require stringent regularity conditions, and is completely determined by that of the pivotal statistic. The proposed methods are then applied to testing the factor pricing models and validating the cross‐sectional independence in panel data models.     

Market‐Triggered Changes in Capital Structure: Equilibrium Price Dynamics

We analyze the internal consistency of using the market price of a firm's equity to trigger a contractual change in the firm's capital structure, given that the value of the equity itself depends on the firm's capital structure. Of particular interest is the case of contingent capital for banks, in the form of debt that converts to equity, when conversion is triggered by a decline in the bank's stock price. We analyze the problem of existence and uniqueness of equilibrium values for a firm's liabilities in this context, meaning values consistent with a market‐price trigger. Discrete‐time dynamics allow multiple equilibria. In contrast, we show that the possibility of multiple equilibria can largely be ruled out in continuous time, where the price of the triggering security adjusts in anticipation of breaching the trigger. Our main condition for existence of an equilibrium requires that the consequences of triggering a conversion be consistent with the direction in which the trigger is crossed. For the design of contingent capital with a stock price trigger, this condition may be interpreted to mean that conversion should be disadvantageous to shareholders, and it is satisfied by setting the trigger sufficiently high. Uniqueness follows provided the trigger is sufficiently accessible by all candidate equilibria. We illustrate precise formulations of these conditions with a variety of applications.     

The Dynamics of Inequality

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long‐run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high‐growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.     

Bargaining and Cooperation in Strategic Form Games

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the “proposer commitment” procedure, is presented. It is inspired by Nash's two‐player variable‐threat model; a key feature is the commitment to “threats.” We establish links to classical cooperative game theory solutions, such as the Shapley value in the transferable utility case. However, we show that even in standard pure exchange economies, the traditional coalitional function may not be adequate when utilities are not transferable. (JEL: C70, C71, C78, D70)     

The Farsighted Stable Set

Harsanyi (1974) criticized the von Neumann–Morgenstern (vNM) stable set for its presumption that coalitions are myopic about their prospects. He proposed a new dominance relation incorporating farsightedness, but retained another feature of the stable set: that a coalition S can impose any imputation as long as its restriction to S is feasible for it. This implicitly gives an objecting coalition complete power to arrange the payoffs of players elsewhere, which is clearly unsatisfactory. While this assumption is largely innocuous for myopic dominance, it is of crucial significance for its farsighted counterpart. Our modification of the Harsanyi set respects “coalitional sovereignty.” The resulting farsighted stable set is very different from both the Harsanyi and the vNM sets. We provide a necessary and sufficient condition for the existence of a farsighted stable set containing just a single‐payoff allocation. This condition roughly establishes an equivalence between core allocations and the union of allocations over all single‐payoff farsighted stable sets. We then conduct a comprehensive analysis of the existence and structure of farsighted stable sets in simple games. This last exercise throws light on both single‐payoff and multi‐payoff stable sets, and suggests that they do not coexist.     

Investment and Competitive Matching

We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk‐investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations.     

Tenable Strategy Blocks and Settled Equilibria

When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set‐valued concepts, coarsely and finely tenable blocks, that formalize this notion for finite normal‐form games. We then identify settled equilibria, which are Nash equilibria with support in minimal tenable blocks. For a generic class of normal‐form games, our coarse and fine concepts are equivalent, and yet they differ from standard solution concepts on open sets of games. We demonstrate the nature and power of the solutions by way of examples. Settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games. With fine tenability, we obtain invariance under the insertion of a subgame with a unique totally mixed payoff‐equivalent equilibrium, a property that other related concepts have not satisfied.     

Inference on Causal Effects in a Generalized Regression Kink Design

We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed assignment variable. We characterize a broad class of models in which a sharp “Regression Kink Design” (RKD or RK Design) identifies a readily interpretable treatment‐on‐the‐treated parameter (Florens, Heckman, Meghir, and Vytlacil (2008)). We also introduce a “fuzzy regression kink design” generalization that allows for omitted variables in the assignment rule, noncompliance, and certain types of measurement errors in the observed values of the assignment variable and the policy variable. Our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. Using a kink in the unemployment benefit formula, we apply a fuzzy RKD to empirically estimate the effect of benefit rates on unemployment durations in Austria.     

Quality Management and Cooperative Values: Investigation of Multilevel Influences on Workgroup Performance

Unsuccessful quality initiatives often are attributed to an organizational culture that does not recognize the importance of the cooperative values that underlie “soft” quality management practices, like customer focus and empowerment. Yet, the literature remains unclear as to how quality management and cooperative values interrelate by failing to incorporate the multilevel influences on this relationship in organizations. This research analyzes a multilevel model based on sociotechnical systems and quality management theories. Secondary data are used to test an explanation of how organizational‐level and workgroup‐level quality management practices relate to cooperative cultural values and workgroup performance. A single‐level model is also tested to demonstrate its inadequacies. Based upon the support for a multilevel model, managerial insights are provided that aid in deciding where resources should be allocated during a quality initiative.     

First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue

We explore the impact of private information in sealed‐bid first‐price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning‐bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.     

An Alternative Theoretical Explanation and Empirical Insights into Overordering Behavior in Supply Chains*

The beer game and the supply line underweighting theory are central to our knowledge of decision making in dynamic environments such as supply chains. The core of these theories is that people are incapable of recognizing the pipeline inventory and this is the main cause of overordering and dysfunctional behavior. This article identifies lacunae in the theoretical and empirical foundations of extant literature and proposes an alternate explanation, a “correction model,” explaining why overreactions occur. We adopt a multi‐method research design, comprising a field case study and laboratory experiments, to ground our findings. [Submitted: July 19, 2010. Revisions received: December 8, 2010; March 14, 2011. Accepted: March 28, 2011.]