Payoff Externalities Research Articles

Pioneer, early follower or late entrant: Entry dynamics with learning and market competition

Timing of market entry is one of the most important strategic decisions a firm must make, but its decision process becomes convoluted with information and payoff externalities. The threat of competition pushes firms to enter earlier to preempt their rivals while the possibility of learning makes them cautiously wait for others to take action. This combination amounts to a new class of timing games where a first-mover advantage first emerges as in preemption games but a second-mover advantage later prevails as in wars of attrition. Our model identifies under what conditions a firm becomes a pioneer, early follower or late entrant and provides efficiency implications by highlighting an elusive link between static market competition and dynamic entry competition.

Public communication with externalities

This paper develops a model in which a sender strategically communicates with a group of receivers whose payoffs depend on the sender's information. It is shown that aggregate payoff externalities create an endogenous conflict of interests between the sender and the receivers, rendering full information revelation, in general infeasible. We demonstrate that an exogenous bias in the sender's preferences can improve public information provision and raise welfare. Two applications of the setup are discussed.

Tractable Model of Dynamic Many-to-Many Matching

We develop a tractable, dynamic, and strategic model of many-to-many matching with payoff externalities across links. The joint dynamic surplus or certain second properties of individual utilities, like payoff externalities, can typically be identified. We characterize a class of interior equilibria as solutions to an optimization problem with an objective function that consists of welfare minus an inefficiency loss term. In equilibrium, too few matches are formed. We compare transferable and nontransferable versions of the model; the equilibria of the two versions are equivalent up to a rescaling of parameters. We describe the asymptotic limits of disappearing frictions. (JEL C78, D62, D83, J64)

On the Ratchet Effect with Payoff Externalities

On the Ratchet Effect with Payoff Externalities

Strategic Experimentation with Congestion

This paper considers a two-player game of strategic experimentation with competition. Each agent faces a two-armed bandit problem where she continually chooses between her private, risky arm and a common, safe arm. Each agent has exclusive access to her private arm. However, the common arm can only be activated by one agent at a time. This congestion creates negative payoff externalities. Our main finding is that congestion gives rise to new strategic considerations: players perceive a strategic option value from occupying the common arm, making it more attractive than in the absence of competition or when switching is irreversible. (JEL C72, C73, D62, D83)

Bargaining with informational and payoff externalities

AbstractThis paper studies a dynamic bargaining model with informational externalities between bargaining pairs. Two principals bargain with their respective agents about the price for their work while its cost is agents' private information and is correlated between them. Depending on the equilibrium, information from the other pair helps or hinders principals' ability to offer low prices. A higher correlation can then either increase or decrease principals' payoffs, delay, and welfare.

Repeated coordination with private learning

We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.

Exploration in Teams and the Encouragement Effect: Theory and Experimental Evidence

This paper analyzes a two-person, two-stage model of sequential exploration where both information and payoff externalities exist and tests the derived hypotheses in the laboratory. We theoretically show that, even when agents are self-interested and perfectly rational, the information externality induces an encouragement effect: a positive effect of first player exploration on the optimality of the second player exploring as well. When agents have other-regarding preferences and imperfectly optimize, the encouragement effect is strongest. The explorative nature of the game raises the expected surplus compared with a payoff equivalent public goods game. We empirically confirm our main theoretical predictions using a novel experimental paradigm. Our findings are relevant for motivating and managing groups and teams innovating not only for private but also and especially so, for public goods.This paper was accepted by John List, behavioral economics.

Performance Feedback and Peer Effects: A Review

This paper reviews studies conducted in naturally-occurring work environments or in the laboratory on the impact of performance feedback provision and peer effects on individuals’ performance. First, it discusses to which extent feedback on absolute performance affects individuals’ effort for cognitive or motivational reasons, and how evaluations can be distorted strategically. Second, this paper highlights the positive and negative effects of feedback on relative performance and rank on individuals’ productivity and persistence, but also on the occurrence of anti-social behavior. Relative feedback stimulates effort by informing on the marginal return or the marginal cost of effort, and by activating behavioral forces even in the absence of monetary incentives. These behavioral mechanisms relate to self-esteem, status concerns, competitive preferences and social learning. Relative feedback sometimes discourages or distorts effort, notably if people collude or are disappointment averse. In addition to incentive schemes and social preferences, the management of self-confidence affects the way relative feedback impacts productivity. Third, the paper addresses the question of the identification of peer effects on employees’ performance, their size, their direction and their heterogeneity along the hierarchy. The mechanisms behind peer effects include conformism, social pressure, rivalry, social learning and distributional preferences, depending on the presence of payoff externalities or technological and organizational externalities.

Learning and payoff externalities in an investment game

This paper examines the interplay of informational and payoff externalities in a two-player irreversible investment game. Each player learns about the quality of his project by observing a private signal and the action of his opponent. I characterize the unique symmetric equilibrium in a timing game that features a second-mover advantage, allowing for arbitrary correlation in project qualities. Despite private learning, the game reduces to a stochastic war of attrition. In contrast to the case of purely informational externalities, all investments happen at the same real time instant—irrespective of the sign of the correlation—and beliefs never get trapped in a no-learning region, provided that the second-mover advantage is sufficiently high.

Ethnic conflicts with informed agents: A cheap talk game with multiple audiences

We consider a society on the brink of ethnic conflict due to misinformation. An ‘informed agent’ is a player who has information which may prevent conflict. Can the informed agent achieve peace by communicating privately with the players? The issue is that if the informed agent is known to favour her own ethnicity, she is unable to communicate credibly with the other ethnicity. Despite this, we show that peace can be achieved in equilibrium. Our paper contributes to the literature on cheap talk games with multiple audiences with the novel addition of private signals along with payoff externalities.

Strategic Exit With Information and Payoff Externalities

I consider a stopping game between two players, where observations related to an unknown state of the nature arrive at random. Players not only learn from observing each other, but their payoffs also depend on the presence of the counterpart. I derive a general characterization of an equilibrium in this game. As applications, I consider two stopping time games which can be viewed as models of sponsored research - one is the model where researchers get funded until (if ever) a research project experiences the first failure, the other one is the model where researchers get rewarded if a success is achieved. In either case, the researchers start working on a project of unknown quality. The quality of the project is identified with its ability to generate failures or successes, in the first and second models, respectively. The rate of arrival of success conditioned on the quality of the project is an increasing function of the total time spent on the sponsored research. Observations of failures or successes are public information.I find subgame perfect equilibria in both models and show that in case of two competing researchers, neither equilibrium outcomes, nor cooperative solutions are efficient unless research creates no payoff externalities. In either model, at least one of the researchers experiments inefficiently long, so that a designer of a grant competition would like to stop sponsoring one of the players earlier than in equilibrium. Surprisingly, this result holds in the model where the first success is rewarded no matter whether the laggards are rewarded with a smaller prize or punished.

Private Bayesian persuasion

We consider a multi-receiver Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The utility of the sender is a function of the subset of adopters and the realized state. We first consider a setting with a binary state space and no payoff externalities among receivers. We characterize an optimal signaling policy and the maximal revenue to the sender for two different types of utility functions: supermodular, and anonymous submodular. In particular, for supermodular utilities we show that the optimal policy correlates positive recommendation to adopt the product as much as possible. We generalize these results to the case of a nonbinary state space. The result for supermodular utilities is generalized to the case where receivers have payoff externalities. We also provide a necessary and sufficient condition under which public and conditionally independent signaling policies are optimal.

Observational learning in large anonymous games

I present a model of observational learning with payoff interdependence. Agents, ordered in a sequence, receive private signals about an uncertain state of the world and sample previous actions. Unlike in standard models of observational learning, an agent's payoff depends both on the state and on the actions of others. Agents want both to learn the state and to anticipate others' play. As the sample of previous actions provides information on both dimensions, standard informational externalities are confounded with payoff externalities. I show that in spite of these confounding factors, when signals are of unbounded strength, there is learning in a strong sense: agents' actions are ex post optimal given both the state of the world and others' actions. With bounded signals, actions approach ex post optimality as the signal structure becomes more informative.

Exploration in Teams and the Encouragement Effect: Theory and Experimental Evidence

This paper analyzes a two-person, two-stage model of sequential exploration, where both information and payoff externalities exist, and tests the derived hypotheses in the laboratory. We theoretically show that even when agents are self-interested and perfectly rational, the information externality induces an encouragement effect: a positive effect of first-player exploration on the optimality of the second-player exploring as well. When agents have other-regarding preferences and imperfectly optimize, the encouragement effect is strongest. The explorative nature of the game raises the expected surplus compared to a payoff equivalent public goods game. We empirically confirm our main theoretical predictions using a novel experimental paradigm. Our findings are relevant for motivating and managing groups and teams innovating not only for private but also, and especially so, for public goods.

Sales-Based Rebate Design

We study rebate mechanisms according to which a monopolist selling a product introduces rebates as function of the volume of buyers. This enables the firm to induce payoff externalities that ordinarily do not exist. The monopoly firm sells an indivisible good to a mass of consumers with uncertain valuations corresponding to two sources of uncertainty: a systemic uncertainty corresponding to the realized quality, and an idiosyncratic uncertainty modeling the diversity of consumers’ tastes. Analyzing the equilibria of the induced global game among the consumers, we show that introducing positive externality via an increasing aggregate reward program reduces the profit. Using variational optimization techniques, we identify several key characteristics of the optimal reward program: the optimal solution is a “full-refund or nothing” policy, fully reimbursing the buyers if the realized quality falls in one of the finitely many refund-eligible intervals. The number of intervals, though finite, grow unboundedly as consumers’ tastes become less diverse and valuations concentrate around the true quality. While finding the optimal reward program is in general an intractable problem, we fully characterize the optimal solution in two important instances: one with constraints on the reward size and the other with bounds on the rate of change of the reward with sales volume. Despite their simple and intuitive structures, the corresponding optimal reward programs asymptotically recover the optimal solution. Our analysis sheds light on the potential role of novel technology-enabled features of crowd-based markets in developing new revenue management strategies.

Equilibria in games with weak payoff externalities

Ania (J Econ Behav Organ 65:472–488, 2008) shows that in the class of symmetric games with weak payoff externalities, symmetric Nash equilibria are equivalent to symmetric evolutionary equilibria (Schaffer in J Econ Behav Organ 12:29–45, 1989). We introduce a notion of a game with partial weak payoff externalities. We show that the class of games with partial weak payoff externalities includes most of previously known classes of games in which the equivalence prevails. We also establish a number of pure strategy Nash equilibrium existence results for a game with weak payoff externalities, and for a class of games that includes games with partial weak payoff externalities. The results include, in particular, the existence of pure strategy Nash equilibrium in some finite games.

Strategic Experimentation With Congestion

This paper considers a two-player game of strategic experimentation with competition. Each agent faces a two-armed bandit problem where she continually chooses between her private risky arm and a common, safe arm. Each agent has exclusive access to her private arm. However, the common arm can only be activated by one agent at a time. This congestion creates negative payoff externalities. Our main finding is that congestion gives rise to new strategic considerations: players perceive a strategic option value from occupying the common arm, making it more attractive than in the absence of competition or when switching is irreversible.

Forecast Dispersion in Finite-Player Forecasting Games

AbstractWe study forecast dispersion in a finite-player forecasting game modeled as an aggregate game with payoff externalities and dispersed information. In the game, each agent cares about being accurate as well as about the distance of his forecast from the average forecast; and with a finite number of agents, the agents can strategically influence that average. We show that the finiteness of the number of agents weakens the strategic effect induced by the underlying preference. We find that when each agent prefers to be close to the average forecast, the presence of strategic manipulation of the average forecast contributes to a higher forecast dispersion; when instead each agent wants to be distinctive from the average, the opposite is true.

The social value of information with an endogenous public signal

This paper analyzes the equilibrium and welfare properties of an economy characterized by uncertainty and payoff externalities using a general model that nests several applications. Agents receive a private signal and an endogenous public signal, which is a noisy aggregate of individual actions, and causes an information externality. Agents in equilibrium underweight private information for a larger payoff parameter region in relation to when public information is exogenous. In addition, the socially optimal endogenous degree of coordination is lower than the socially optimal exogenous degree of coordination. The welfare effect of increasing the precision of the noise in the public signal has the same sign with endogenous or exogenous public information, but its magnitude differs. The social value of private information may be overturned in relation to when public information is exogenous: from positive to negative if agents in equilibrium coordinate more than is implied by the socially optimal exogenous degree of coordination, and the opposite if they coordinate less.