Bayesian Equilibrium Research Articles

The epistemic spirit of divinity

We study strategic reasoning in a signaling game where players initially have common belief in an outcome distribution and in the event that the sender's beliefs are independent of her type. We characterize the behavioral implications of these epistemic hypotheses by means of a rationalizability procedure with belief restrictions. Our solution concept is related to, but weaker than Divine Equilibrium (Banks and Sobel, 1987). First, we do not obtain a sequential equilibrium, but just a perfect Bayesian equilibrium with heterogeneous off-path beliefs (Fudenberg and He, 2018). Second, when we model how the receiver may rationalize a particular deviation, we take into account that some types could have preferred a different deviation, and we show this is natural and relevant via an economic example.

On fraud and certification of green production

AbstractWe present a novel model of fraud and certification in green production. We focus on settings where firms decide between a green or a standard version of a product together with an advertising strategy that can include fraud. In addition, green firms can choose to certify their production to guarantee the truthfulness of their claims. This results in four production‐advertising possibilities (standard, genuine green, fraudulent green, and certified green), by which we provide new insights about the prevalence of fraud and certification. We characterize the perfect Bayesian equilibrium of the resulting game for given green production costs, certification costs, and consumers' willingness to pay for standard production, and we perform comparative statics for the main parameters of the resulting game. We find that changes in certification and green production costs affect consumers' beliefs differently, whereby increases in certification and decreases in green production costs can broaden the likelihood of fraud. These novel results are robust to different market structures and question the general desirability of public subsidies for promoting green production without accompanying certification.

Interacting mechanisms: A perspective on generalized principal–agent problems

Myerson (1982) formalizes general principal–agent problems, in which agents have private information and choose actions. His contribution is best known for a version of the revelation principle in the case of a single principal but he also introduces a model of interacting principals. We push the latter forward by studying the perfect Bayesian equilibrium outcomes of the corporations’ game in which every principal proposes a mechanism to his agents. We show that several versions of the revelation principle hold in our framework and that, under certain conditions, every principals’ equilibrium, as defined in Myerson (1982), is a perfect Bayesian equilibrium outcome of the corporations’ game.

Method for countering strategic attacks in zero-boundary trusted networks

This paper proposes a detection method for countering strategic attacks in zero-boundary trusted networks. In a normal network, malicious nodes are only a minority; therefore, this paper employs a simple game-theoretic approach to suppress the occurrence of malicious events. Firstly, the paper introduces a behavior-based event inference method to detect malicious events, wherein nodes reference the inference results of other nodes to form composite reports. Subsequently, the paper introduces a simple game, allowing malicious nodes to choose not to falsify reports under disadvantaged scenarios, reaching a Bayesian equilibrium with normal nodes, thereby reducing the incidence of malicious events. This method demonstrates significant effectiveness in conventional networks where malicious nodes constitute a minority.

An extensive study of security games with strategic informants

Over the past years, game-theoretic modeling for security and public safety issues (also known as security games) have attracted intensive research attention and have been successfully deployed in many real-world applications for fighting, e.g., illegal poaching, fishing and urban crimes. However, few existing works consider how information from local communities would affect the structure of these games. In this paper, we systematically investigate how a new type of players – strategic informants who are from local communities and may observe and report upcoming attacks – affects the classic defender-attacker security interactions. Characterized by a private type, each informant has a utility structure that drives their strategic behaviors.For situations with a single informant, we capture the problem as a 3-player extensive-form game and develop a novel solution concept, Strong Stackelberg-perfect Bayesian equilibrium, for the game. To find an optimal defender strategy, we establish that though the informant can have infinitely many types in general, there always exists an optimal defense plan using only a linear number of patrol strategies; this succinct characterization then enables us to efficiently solve the game via linear programming. For situations with multiple informants, we show that there is also an optimal defense plan with only a linear number of patrol strategies that admits a simple structure based on plurality voting among multiple informants.Finally, we conduct extensive experiments to study the effect of the strategic informants and demonstrate the efficiency of our algorithm. Our experiments show that the existence of such informants significantly increases the defender's utility. Even though the informants exhibit strategic behaviors, the information they supply holds great value as defensive resources. Compared to existing works, our study leads to a deeper understanding on the role of informants in such defender-attacker interactions.

Returns from herding as a function of the social network of agents: a simulation study

PurposeThis study combines different perspectives on herding, viewing it as a social network heuristic in comparison to other heuristics. The purpose is to use the heuristic view of herding as found in early literature and test it on grounds of efficiency and payoff, in essence, combining the heuristic and rational agent view of herding. The simulated double auction setting includes agents embedded in a social network, allowing for an examination of herding alongside rational behaviour and imperfect signals.Design/methodology/approachIn each round of the simulation, levels of homophily, density and fractions of types of agents is set and agents are allowed to follow their respective heuristics under those conditions. Characteristics of the social network, such as the size, levels of different homophilies, density and fractions of different types of agents are varied randomly to gauge their effect on the performance of herders vis-à-vis others and the overall market efficiency through simulation based approach. The data used for the study has been developed in Python and linear models are estimated using R.FindingsHerding decreases total surplus in private value double auctions, but herders are not worse off than other agents and perform equally in common value auctions. Further, herders and random offerers reduce payoffs of other agents as well, and herding effects the surplus per transaction and not the quantum.Research limitations/implicationsThis study explores herding as a strategic behaviour coexisting with rationality and other strategies in specific circumstances. It presents intriguing findings on the impact of herding on individual outcomes and market efficiency, raising new avenues for future research. Implication to research includes a dent on the “sieve” argument of markets rooting out irrationality and from it, a policy implication that follows is the need for corrective measures as markets cannot self-correct this, given herders do not perform worse than others.Originality/valueThe study links the phenomenon of herding to the dynamics of social networks and heuristic-based learning mechanisms that sets apart this research from the majority of existing literature, which predominantly conceptualizes herding as an outcome derived from a perfect Bayesian Equilibrium and a rational learning process.

Voluntary Disclosure in Asymmetric Contests

Abstract This article studies the incentives for interim voluntary disclosure of verifiable information in probabilistic all-pay contests with two-sided incomplete information. Private information may concern marginal cost, valuations, and ability. Our main result says that, if the contest is uniformly asymmetric, then full revelation is the unique perfect Bayesian equilibrium outcome. This is so because the weakest type of the underdog reveals her type in an attempt to moderate the favourite, while the strongest type of the favourite tries to discourage the underdog—so that the contest unravels. This strong-form disclosure principle is robust with respect to correlation, partitional evidence, randomized disclosures, sequential moves, and continuous type spaces. Moreover, the assumption of uniform asymmetry is not needed when incomplete information is one-sided. However, the principle may break down when type distributions are too similar, contestants possess commitment power, or information is unverifiable. In fact, cheap talk will always be ignored, even if mediated by a trustworthy third party.

Compromise, Don’t Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity

Compromise, Don’t Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity

Contests with sequential entry and incomplete information

This paper provides a general study of a contest modeled as a multiplayer incomplete‐information, all‐pay auction with sequential entry. The contest consists of multiple periods. Players arrive and exert efforts sequentially to compete for a prize. They observe the efforts made by their earlier opponents, but not those of their contemporaneous or future rivals. We establish the existence and uniqueness of a symmetric perfect Bayesian equilibrium (PBE) and fully characterize the equilibrium. Based on the equilibrium result, we show that a later mover always secures a larger ex ante expected payoff. Further, we endogenize the timing of moves and show that all players choose to move in the last period in the unique equilibrium that survives iterated elimination of strictly dominated strategies (IESDS).

Sophisticated banking contracts and fragility when withdrawal information is public

I study whether self‐fulfilling bank runs can occur when banks use sophisticated contracts and withdrawal decisions are public information. In a finite‐agent version of Diamond and Dybvig (1983) with correlated types, I first present an example in which a bank run perfect Bayesian equilibrium exists. However, its existence relies on off‐path beliefs that are unreasonable in terms of forward induction. To discipline beliefs, I use forward induction equilibrium (Cho (1987)) as the solution concept. I show that, whenever the allocation rule is strictly incentive compatible, the truth‐telling strategy is the unique forward induction equilibrium in the withdrawal game, and no bank run occurs. Therefore, with forward induction, sophisticated contracts can prevent bank runs when there is public information about withdrawal decisions.

Game Analysis and Optimization for Evolutionary Dynamic Heterogeneous Redundancy

Dynamic Heterogeneous Redundancy (DHR) has been considered as a proactive defense architecture against unknown vulnerabilities and backdoors. It is a heterogeneous, fault-tolerant, and redundant system, which ensures the security by constantly switching heterogeneous executors. However, a limited number of heterogeneous executors can be merely switched and combined statically. It is difficult to cope with persistent threats. In this paper, we propose an evolutionary DHR system, add evolutionary sub-strategies of executors to solve this problem, optimizing defense mechanisms of DHR. To demonstrate theoretical validity, a game-theoretic analysis of the DHR security mechanism is performed under dynamic incomplete information, and the dilemma of defense is discussed. We construct a DHR game model based on evolutionary, and the results are extended to the general case to analyze the Bayesian equilibrium when each service strategy has a different number of evolved sub-strategies. In addition, the correlation factor is added to the game to investigate the impact of the correlation between different heterogeneous executors on defense results. Finally, Gambit and NS2 simulation experiments for the proposed method are shown. To verify the applicability of the physical system, a prototype DHR system based on dynamic evolution was constructed. We collect key configuration information and modified them randomly. It ensures that the information scanned by the attacker is different each time. Finally, the effectiveness of the physical system is verified by nmap and metasploit tools.

Sequential Bayesian persuasion

I study a Bayesian persuasion model in which multiple senders sequentially persuade one receiver, after observing signal structures of prior senders and their realizations. I develop a geometric method, recursive concavification, to characterize the Perfect Bayesian Equilibrium paths. I prove the existence of the silent equilibrium, where at most one sender provides nontrivial information. I also show that when there are only two senders and the receiver has a finite action space, it is generically without loss to focus on silent equilibrium. Finally, I show that if there are two senders who have zero-sum payoffs, the truth-telling signal structure is always supported in equilibrium.

Blessing or curse? Impact of incomplete information in a networked cournot competition

Networked markets are prevalently seen in different industries. Current research mainly focuses on settings with a transparent network. However, in many applications, firms choose their actions without fully knowing their competitors’ information. This study examines oligopolies in networked markets when firms’ production costs are incomplete information. We characterize the unique Bayesian equilibrium supply quantities for any given network under incomplete information. Our results connect the equilibrium outcome with the underlying competition and information structures. We find that when the production cost of a firm is high, incomplete information helps increase its total production quantity. In contrast, the impact is the opposite in the presence of low production costs. However, the impact of incomplete information on a firm’s supply allocation on each edge depends not only on its production cost but also on the network position of the edge. We also find that, unlike the case in single-market, the low-cost firm always suffers from incomplete information, while the high-cost firm benefits from incomplete information only under certain conditions. Moreover, we show that changes in global network structure that do not directly relate to a firm may alter its information preference. We study several extensions and find that not only do firms with cost advantage prefer complete information, but those high-cost firms with smaller cost disadvantages are also more likely to prefer a transparent competition environment. The case of heterogeneous logistic costs is also considered, and we show that for firms of high-cost type, the logistic cost advantage may hedge its benefit from incomplete information. Our findings imply that a firm has to consider not only its own cost type and local competition but also the global network structure to determine its preference for information structure. Moreover, our results may be helpful to the market regulator that, when promoting information transparency, firms with better production technology are more likely to support the movement.

Testing rational hypotheses in signaling games

We introduce a solution concept for signaling games, called Rational Hypothesis Testing Equilibrium (RHTE). Beliefs are updated via Ortoleva’s (2012) Hypothesis Testing model, allowing for conditioning on information sets off the path. Hypotheses are conjectures by the uninformed player about opponent’s strategies that rationalize sending an unexpected message. Each RHTE is a Perfect Bayesian Equilibrium, but not vice versa. RHTE features a number of desirable properties: First, beliefs are structurally consistent in the spirit of Kreps and Wilson (1982). Second, beliefs are consistent with mutual knowledge of rationality. Third, RHTE can be related to the prominent refinement concepts, including the Intuitive Criterion, strategic stability, and undefeated equilibrium. In the Spence game, RHTE restricts the admissible wages, significantly reducing the number of equilibria. Finally, we show that our equilibrium notion offers an alternative explanation for the experimental results in Brandts and Holt (1992, 1993).

Calculation of Perfect Bayesian Equilibrium in a Signaling Game

Calculation of Perfect Bayesian Equilibrium in a Signaling Game

A Bayesian formulation for perturbed current tomography in tokamaks

An initial investigation into the application of Bayesian inference to the reconstruction of the spatial distribution of current perturbations in tokamaks from diagnostic signals is presented. Previous work in Bayesian equilibrium current tomography is extended to the case of a complex phasor representation of harmonically time varying current distributions. A forward function to predict the response of magnetic diagnostics is constructed using only electrodynamics and not reduced models of ideal MHD. The extension of this forward function to incorporate a fully kinetic model of the plasma state is suggested. The response of soft x-ray diagnostics, and the motional Stark effect diagnostic to the current perturbations are also predicted and the integration of all diagnostics into a single estimate of the current perturbation is proposed. Simulations with synthetic diagnostics in simple geometry demonstrate that the perturbed current distribution can be reconstructed subject to prior assumptions regarding solution smoothness.

Accomplice plea bargains in the presence of costly juror effort

This is the first paper to study accomplice plea bargains when motivated jurors incur an effort cost. I find that a prosecutor who wishes to ensure punishment for the guilty, and acquittal for the innocent, induces a unique perfect Bayesian equilibrium which is fully separating, simultaneously minimizing court costs as well as jurors' cognitive efforts. In this equilibrium, a very harsh plea bargain (with negligible plea discounting) is offered, and is accepted by all guilty defendants, and rejected by all innocent ones. Though the prosecutor has the ability to induce semi-separating equilibria, he will prefer the fully separating one. We can use the Cho-Kreps intuitive criterion to show that a pooling equilibrium does not exist. My results contrast sharply with the plea bargaining literature which finds a tradeoff between sorting efficiency and the harshness of punishments meted out to the guilty and which does not support a fully separating equilibrium.

Incentive compatibility in sender-receiver stopping games

We introduce a model of sender-receiver stopping games, in which the sender observes the current state, and sends a message to the receiver to either stop the game, or to continue. The receiver, only seeing the message, then decides to stop the game, or to continue. The payoff to each player is a function of the state when the receiver quits, with higher states leading to better payoffs.We prove existence and uniqueness of responsive Perfect Bayesian Equilibrium (PBE) when players are sufficiently patient. The responsive PBE has a simple structure, with a threshold strategy for the sender, and the receiver obediently following the recommendations of the sender. Hence, the sender alone plays the decisive role, and therefore always obtains the best possible payoff for himself.

Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

We study a generalization of the static model of [11] with two risk neutral insiders to the case where each insider is partially informed about the value of the stock. First, we provide a necessary and sufficient condition for the uniqueness of the linear Bayesian equilibrium. Specifically, we show that, when the covariance matrix of the errors terms of the insiders' signals, is not singular, the linear Bayesian equilibrium is not unique. Then, we carry out a comparative statics analysis.

A participant selection based vehicle platoon asynchronous federated learning framework

AbstractIn the vehicular network, federated learning is an emerging paradigm to train deep learning models safely. However, the non‐identically independent distributed data collected by intelligent connected vehicles, expensive training overhead, and the existence of malicious participants significantly affect the efficiency of training and constrain the development of federated learning in the vehicular network. To address the above issues, this paper proposes a participant selection‐based asynchronous federated learning framework for an intelligent connected vehicle platoon. We proposed a platoon‐based asynchronous federated learning framework that effectively improves training efficiency through data share and asynchronous optimization. Also, We designed a signaling game‐based participant selection strategy that accurately identifies the potentially malicious participants by analyzing the Perfect Bayesian Equilibrium. The comparison experiment result shows the training model using our proposed scheme converges faster than the baseline scheme and gains approximately 10% higher accuracy.