Epsilon-Efficiency in a Dynamic Partnership with Adverse Selection and Moral Hazard

For a dynamic partnership with adverse selection and moral hazard, we design a direct profit division mechanism that satisfies ϵ-efficiency, periodic Bayesian incentive compatibility, interim individual rationality, and ex-post budget balance. In addition, we design a voting mechanism that implements the profit division rule associated with this direct mechanism in perfect Bayesian equilibrium. For establishing these possibility results, we assume that the partnership exhibits intertemporal complementarities instead of contemporaneous complementarities; equivalently, an agent’s current effort affects other agents’ future optimal efforts instead of current optimal efforts. This modelling assumption fits a wide range of economic settings.

Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy

The solution concept of a Bayesian equilibrium of a Bayesian game is inherently an interim concept. The corresponding ex ante solution concept has been termed a Harsányi equilibrium; examples have appeared in the literature showing that there are Bayesian games with uncountable state spaces that have no Bayesian approximate equilibria but do admit a Harsányi approximate equilibrium, thus exhibiting divergent behaviour in the ex ante and interim stages. Smoothness, a concept from descriptive set theory, has been shown in previous works to guarantee the existence of Bayesian equilibria. We show here that higher rungs in the countable Borel equivalence relation hierarchy can also shed light on equilibrium existence. In particular, hyperfiniteness, the next step above smoothness, is a sufficient condition for the existence of Harsányi approximate equilibria in purely atomic Bayesian games.

Temporal Induced Self-Play for Stochastic Bayesian Games

One practical requirement in solving dynamic games is to ensure that the players play well from any decision point onward. To satisfy this requirement, existing efforts focus on equilibrium refinement, but the scalability and applicability of existing techniques are limited. In this paper, we propose Temporal-Induced Self-Play (TISP), a novel reinforcement learning-based framework to find strategies with decent performances from any decision point onward. TISP uses belief-space representation, backward induction, policy learning, and non-parametric approximation. Building upon TISP, we design a policy-gradient-based algorithm TISP-PG. We prove that TISP-based algorithms can find approximate Perfect Bayesian Equilibrium in zero-sum one-sided stochastic Bayesian games with finite horizon. We test TISP-based algorithms in various games, including finitely repeated security games and a grid-world game. The results show that TISP-PG is more scalable than existing mathematical programming-based methods and significantly outperforms other learning-based methods.

Information Redundancy Neglect versus Overconfidence: A Social Learning Experiment

We study social learning in a continuous action space experiment. Subjects, acting in sequence, state their beliefs about the value of a good after observing their predecessors’ statements and a private signal. We compare the behavior in the laboratory with the Perfect Bayesian Equilibrium prediction and the predictions of bounded rationality models of decision-making: the redundancy of information neglect model and the overconfidence model. The results of our experiment are in line with the predictions of the overconfidence model and at odds with the others’. (JEL C91, D12, D82, D83)

Tripartite Coordinated Regulation of New Energy Vehicles Based on Dynamic Bayesian Game

Manufacturers are disseminating false or ambiguous information regarding new energy vehicles (NEVs), which has led to skepticism from consumers about the quality of NEVs. In this research, we simultaneously considered the relationship among manufacturers, consumers, and governments from the perspective of stakeholders, and then we analyzed the tripartite coordinated regulation. In view of the serious information asymmetry of NEVs, we innovatively developed the Bayesian dynamic game model. By solving refined Bayesian equilibrium strategies, this study explores the effects of key influencing factors on strategic choices. On the basis of the conclusion, relevant countermeasures and suggestions are put forward to engender effective regulation by governments.

Network Formation with Asymmetric Players and Chance Moves

We propose a model of network formation as a two-stage game with chance moves and players of various types. First, the leader suggests a connected communication network for the players to join. Second, nature selects a type vector for players based on the given probability distribution, and each player decides whether or not to join the network keeping in mind only his own type and the leader’s type. The game is of incomplete information since each player has only a belief over the payoff functions of others. As a result, the network is formed, and each player gets a payoff related to both the network structure and his type. We prove the existence of the Bayesian equilibrium and propose a new definition of the stable partially Bayesian equilibrium defining the network to be formed and prove its existence. The connection between the stable partially Bayesian equilibrium and the Nash equilibrium in the game is examined. Finally, we investigate the characteristics of the network structures under the stable partially Bayesian equilibrium in a three-player game with the major player as well as in the n-player game with a specific characteristic function.

Knowledge, Awareness and Probabilistic Beliefs

Bayesian game theory investigates strategic interaction of players with full awareness but incomplete information about their environment. We extend the analysis to players with incomplete awareness, who might not be able to reason about all contingencies in the first place. We develop three logical systems for knowledge, probabilistic beliefs and awareness, and characterize their axiom systems. Bayesian equilibrium is extended to games with incomplete awareness and we show that it is consistent with common prior and speculative trade, when common knowledge of rationality is violated.

Linear Bayesian equilibrium in insider trading with a random time under partial observations

<abstract><p>In this paper, the insider trading model of Xiao and Zhou (<italic>Acta Mathematicae Applicatae, 2021</italic>) is further studied, in which market makers receive partial information about a static risky asset and an insider stops trading at a random time. With the help of dynamic programming principle, we obtain a unique linear Bayesian equilibrium consisting of insider's trading intensity and market liquidity parameter, instead of none Bayesian equilibrium as before. It shows that (i) as time goes by, both trading intensity and market depth increase exponentially, while residual information decreases exponentially; (ii) with average trading time increasing, trading intensity decrease, but both residual information and insider's expected profit increase, while market depth is a unimodal function with a unique minimum with respect to average trading time; (iii) the less information observed by market makers, the weaker trading intensity and market depth are, but the more both expect profit and residual information are, which is in accord with our economic intuition.</p></abstract>

A Novel Attack-and-Defense Signaling Game for Optimal Deceptive Defense Strategy Choice

Increasingly, more administrators (defenders) are using defense strategies with deception such as honeypots to improve the IoT network security in response to attacks. Using game theory, the signaling game is leveraged to describe the confrontation between attacks and defenses. However, the traditional approach focuses only on the defender; the analysis from the attacker side is ignored. Moreover, insufficient analysis has been conducted on the optimal defense strategy with deception when the model is established with the signaling game. In our work, the signaling game model is extended to a novel two-way signaling game model to describe the game from the perspectives of both the defender and the attacker. First, the improved model is formally defined, and an algorithm is proposed for identifying the refined Bayesian equilibrium. Then, according to the calculated benefits, optimal strategies choice for both the attacker and the defender in the game are analyzed. Last, a simulation is conducted to evaluate the performance of the proposed model and to demonstrate that the defense strategy with deception is optimal for the defender.

A Discretionary Lane-Changing Decision-Making Mechanism Incorporating Drivers’ Heterogeneity: A Signalling Game-Based Approach

This paper attempts to propose a discretionary lane-changing decision-making model based on signalling game in the context of mixed traffic flow of autonomous and regular vehicles. The effects of the heterogeneity among different drivers and the endogeneity of same drivers in lane-changing behaviours, e.g., aggressive or conservative, are incorporated through the specification of different payoff functions under different scenarios. The model is calibrated and validated using the NGSIM dataset with a bilevel calibration framework, including two kinds of methods, genetic algorithm and perfect Bayesian equilibrium. Comparative results based on simulation show that the signalling game-based model outperforms the traditional space-based lane-changing model in the sense that the proposed model yields relatively stable reciprocal of time to collision and higher success rate of lane-changing under different traffic densities. Finally, a sensitivity analysis is performed to test the robustness of the proposed model, which indicates that the signalling game-based model is stable to the varying ratios of driver type.