Payoff-relevant State Research Articles

Signaling through Bayesian persuasion

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems.

Maximizing Social Welfare and Agreement via Information Design in Linear-Quadratic-Gaussian Games

Information design in an incomplete information game involves a designer that aims to influence players' actions through signals generated from a designed probability distribution to optimize its objective function. For quadratic design objective functions, if the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, the information design problem is a semidefinite program (SDP) [1]. In this note, we seek to characterize the optimal information design analytically by leveraging the SDP formulation, when the design objective is to maximize social welfare or the agreement among players' action. We show that full information disclosure maximizes social welfare when there is a common payoff state, the payoff dependencies among players' actions are homogeneous, or when the signals are public. When the objective is to maximize the agreement among players' actions, not revealing any information is optimal. When the objective is a weighted combination of social welfare and agreement terms, we establish a threshold weight below which full information disclosure is optimal under public signals for games with homogeneous payoffs. Numerical results corroborate the analytical results, and identify partial information disclosure structures that are optimal.

Private disclosure with multiple agents

This study examines a mechanism design problem where the principal can affect the agents' knowledge of a payoff-relevant state, namely, the principal designs and commits to an information disclosure policy that generates agent-specific private signals, while the principal directly observes neither the state nor the signal profile. We solve this problem by constructing a novel class of disclosure policies that exhibit individually uninformative, aggregately revealing, and immune to unilateral misreporting properties and show that the principal achieves the same payoff as if she could directly observe the state and implement state-contingent allocation rules. Moreover, we prove that our disclosure policy is robust to information-sharing among a certain number of agents and remains optimal in various settings.

A protocol for repeated bargaining

We propose a protocol for repeated bargaining where occasional periods of good outside opportunities yield improved outcomes but also higher breakout probabilities, yet there is a lot of risk sharing. Crucially, we only consider Markov perfect equilibria that have neither non payoff-relevant state variables that are costly to compute nor a contrived process of equilibrium selection.

Discontinuous and continuous stochastic choice and coordination in the lab

We experimentally test theoretical predictions on equilibrium selection in a two-player coordination (investment) game. Through a minimal visual variation, our design prompts participants to play strategies whereby investing probability is either continuous or discontinuous in the payoff-relevant state. When participants use continuous strategies, average behavior is consistent with play in the risk-dominant equilibrium, the unique theoretical prediction. When they use discontinuous strategies, average behavior is closer to the payoff-dominant equilibrium strategy. In this case, the theory predicts multiple equilibria, for which we find no support. Additionally, we extend the theory to heterogeneous populations: the set of equilibria monotonically decreases in the proportion of players who use continuous strategies.

Complexity in insurance selection: Cross-classified multilevel analysis of experimental data

This paper uses laboratory experiments to test the predictions of expected utility theory applied to the context of coverage selection and the effects of complexity on the quality of decision making. Participants choose from menus of stylized insurance plans that vary across three measures of complexity. In each menu one insurance plan stochastically dominates the other options. Out of the three complexity measures, Coverage Similarity and State Complexity, have a statistically significant negative effect on participants’ ability to choose efficiently. Individuals’ decisions can be predicted by the expected utility paradigm only to a certain extent. When the number of payoff relevant states associated with an insurance plan increases, participants violate rationality axioms by selecting first order dominated plans. Similarly, the rate of dominated choices increases when the difference in the level of coverage between plans in the same choice menu is low.

Information Preferences of Individual Agents in Linear-Quadratic-Gaussian Network Games

We consider linear-quadratic-Gaussian (LQG) network games in which agents have quadratic payoffs that depend on their individual and neighbors’ actions, and an unknown payoff-relevant state. An information designer determines the fidelity of information revealed to the agents about the payoff state to maximize the social welfare. Prior results show that full information disclosure is optimal under certain assumptions on the payoffs, i.e., it is beneficial for the average individual. In this paper, we provide conditions for general network structures based on the strength of the dependence of payoffs on neighbors’ actions, i.e., competition, under which a rational agent is expected to benefit, i.e., receive higher payoffs, from full information disclosure. We find that all agents benefit from information disclosure for the star network structure when the game is homogeneous. We also identify that the central agent benefits more than a peripheral agent from full information disclosure unless the competition is strong and the number of peripheral agents is small enough. Despite the fact that all agents expect to benefit from information disclosure ex-ante, a central agent can be worse-off from information disclosure in many realizations of the payoff state under strong competition, indicating that a risk-averse central agent can prefer uninformative signals ex-ante.

Counterfactuals with Latent Information

We describe a methodology for making counterfactual predictions in settings where the information held by strategic agents and the distribution of payoff-relevant states of the world are unknown. The analyst observes behavior assumed to be rationalized by a Bayesian model, in which agents maximize expected utility, given partial and differential information about the state. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of the state and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, the counterfactual prediction is described by finitely many linear inequalities, even though the latent parameter, the information structure, is infinite dimensional. (JEL D44, D82, D83)

High dimensional decision making, upper and lower bounds

A decision maker’s utility depends on her action a∈A⊂Rd and the payoff relevant state of the world θ∈Θ. One can define the value of acquiring new information as the difference between the maximum expected utility pre- and post information acquisition. In this paper, I find asymptotic results on the expected value of information as d→∞, by using tools from the theory of (sub)-Gaussian processes and generic chaining.

Costly information and random choice

Consider an agent who decides whether to employ an information structure to learn about a payoff-relevant state of the world before making a decision. Information is costly either because (1) the agent has to wait some time until the information structure becomes available and is impatient, or because (2) she has to pay a fixed and menu-independent cost to use the information structure. For each menu of options the analyst observes random choice from the menu and whether the agent acquires the information. We give an axiomatic characterization of when this random choice is consistent with either of the cases (1) or (2). We identify the information structure the agent can employ, as well as its costs. We also discuss implications of our approach for sequential sampling.

Endogeneity in Discrete Bayesian Games: U.S. Cellphone Service Deployment

In some Bayesian games, payoff-relevant states are influenced by unobserved player- or game-level heterogeneity that also also effects strategic decisions directly. Ignoring such endogeneity in empirical analysis leads to erroneous inference of structural parameters and policy implications. We introduce a control-function approach for estimating discrete Bayesian games with such endogeneity. We apply the method to analyze an entry game of deploying 4G-LTE technology by major U.S. cellphone service providers, taking existing network deployment in the focal market and current deployment in neighboring markets as endogenous. Using lagged demographics of neighboring markets as instruments, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across local markets. Moreover, the entry of a fourth national provider, enabled by a partial divestiture of the merger’s assets, would not completely offset its negative impact on market entries and the population served. We also find that ignoring endogeneity in network deployment skews the policy implications by underpredicting the merger’s negative impacts on market entry.

Altruistic observational learning

We report a laboratory experiment that tests the causal impact of altruism on observational learning behavior. Once endowed with a private signal, subjects submit their guess about the payoff-relevant state in two parallel sequences. In the observed sequence, guesses are revealed publicly so that subjects in both sequences can benefit from guesses that are informative. Unobserved guesses, on the other hand, never reveal any information to others as they remain private. We find that observed guesses are significantly more informative than unobserved guesses. The strong responses to private information benefit information aggregation as observational learning behavior is informationally more efficient in the observed sequence than in standard equilibrium outcomes. Once the incentives to make the empirically optimal guess are large enough, observed and unobserved behave quite similarly, and observed guesses are significantly less informative if fewer successors can benefit from the revelation of private signals. These findings are well in line with the qualitative predictions of an observational learning model where players have altruistic preferences.

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.

Social Learning in General Information Environments

I study a social learning model in which agents make decisions sequentially and learn about an unknown payoff-relevant state through two sources – a signal about the state itself (a state-signal) and a signal about the actions taken by previous agents (an action-signal). Our objective is to provide general conditions on the action-signals that lead the agents to eventually behave as if they know the state, i.e., that lead to information aggregation. When the agents’ action-signals are what I call weakly separating, it is shown that information aggregation occurs when the agents’ state-signals are unboundedly informative in the sense of Smith and Sorensen (2000). This result provides a unifying criterion to evaluate when information aggregation occurs, and shows that it can occur even in very opaque environments. The theory is illustrated with applications to privacy protection on digital platforms and the regulation of third-party information provision in social learning environments.

Communication and Information Aggregation for the Tricky Question

We consider common-value voting in which a variable that is independent of the payoff-relevant state determines the meaning and precision of voters' private signals about the payoff-relevant state. Multiple senders sharing the same objective with the voters receive noisy signals that are contingent on the realized variable, and they send messages to the voters simultaneously. We show that by focusing on ``natural equilibria'', when the population of voters is sufficiently large, no information is transmitted by senders, and then information aggregation fails. We also propose a solution: if senders' messages are aggregated into binary levels, information transmission succeeds, and information is fully aggregated asymptotically.

Subjective Information Choice Processes

We propose a class of dynamic models that capture subjective (and hence unobservable) constraints on the amount of information a decision maker can acquire, pay attention to, or absorb, via an Information Choice Process (icp). An icp specifies the information that can be acquired about the payoff-relevant state in the current period, and how this choice affects what can be learned in the future. In spite of their generality, wherein icps can accommodate any dependence of the information constraint on the history of information choices and state realizations, we show that the constraints imposed by them are identified up to a dynamic extension of Blackwell dominance. All the other parameters of the model are also uniquely identified. Behaviorally, the model is characterized by a novel recursive application of static properties.

Information Design

A designer commits to a signal distribution that is informative about a payoff-relevant state. Conditional upon the privately observed signals, agents take actions that affect their payoffs as well as those of the designer. We show how to derive the (designer) optimal information structure in static finite environments. We fully characterize it in a symmetric binary setting for a parameterized game. In this environment, conditionally independent private signals are never strictly optimal. (JEL C72, D78, D82, D83)

Costly Information and Random Choice

We consider an agent who decides whether to employ an information structure to learn about a payoff-relevant state of the world before making a decision. Information is costly either because (1) the agent has to wait for the availability of the information structure and is impatient or because (2) she has to pay a fixed and menu-independent cost to use the information structure. For each menu of options we assume the analyst observes random choice from the menu and whether the agent acquires the information. We give a full characterization of when this random choice is consistent with either of the cases (1) or (2) and show how the analyst can distinguish between the two cases using random choice data. We show in either case how random choice data allows identification of the information structure the agent can employ and respectively discount factor or additive costs.

Counterfactuals with Latent Information

We describe a methodology for making counterfactual predictions when the information held by strategic agents is a latent parameter. The analyst observes behavior which is rationalized by a Bayesian model in which agents maximize expected utility, given partial and differential information about payoff-relevant states of the world. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, there is a finite dimensional description of the sharp counterfactual prediction, even though the latent parameter, the type space, is infinite dimensional.

Persuasion in Networks: Public Signals and k-Cores

We consider a setting where agents in a social network take binary actions, which exhibit local strategic complementarities. The agents are a priori uninformed about an underlying payoff-relevant state. An information designer wants to maximize the expected number of agents who take action 1, and she can commit to a signaling mechanism which upon the realization of the state sends an informative signal to all the agents. We study the structure and design of the optimal public signaling mechanisms. We establish that given a signal realization, the set of agents who take action 1 correspond to a k-core of the underlying network, for some k. Using this we show that the designer’s payoff is an increasing step function of the posterior mean her signals induce. We provide a convex optimization formulation and an algorithm that obtain the optimal information structure whenever the designer’s payoff exhibits this structure. The latter structural property is prevalent, thereby making our approach useful well beyond network persuasion. The optimal mechanism is based on a double-interval partition of the set of states. In particular, it associates up to two subintervals of the set of possible state realizations with each k-core. When the state is in these intervals the mechanism publicly reveals this, which induces the agents in k-core to take action 1. We also study a class of random networks with known limiting degree distributions, and provide a framework for obtaining asymptotically optimal public signaling mechanisms for these networks. Our approach relies on characterizing the sizes of the cores of such networks (asymptotically) and uses only the degree distribution of the random networks, thereby making it useful even when the network structure is not fully known. Finally, we explore which networks are more amenable to persuasion, and show that more assortative connection structures lead to larger payoffs for the designer. On the other hand, the dependence of the designer’s payoff to the agents’ degrees can be quite counterintuitive. In particular, we focus on networks sampled uniformly at random from the set of all networks consistent with a degree sequence. We show that when the degrees of some nodes increase, this can reduce the designer’s payoff, despite the increase in the extent of the network externalities.