arXiv subjects

Shuige Liu

Publications and source records attributed to Shuige Liu.

11 recordsLinked to original sources

arXiv2025

When Truth Does Not Take on Its Shoes: How Misinformation Spreads in Chatrooms

We examine how misinformation spreads in social networks composed of individuals with long-term offline relationships. Especially, we focus on why misinformation persists and diffuses despite being recognized by most as false. In our psychological game theoretical model, each agent who receives a piece of (mis)information must first decide how to react -- by openly endorsing it, remaining silent, or openly challenging it. After observing the reactions of her neighbors who also received the message, the agent then chooses whether to forward it to others in her own chatroom who have not yet received it. By distinguishing these two roles, our framework addresses puzzling real-world phenomena, such as the gap between what individuals privately believe and what they publicly transmit. A key assumption in our model is that, while perceived veracity influences decisions, the dominant factor is the alignment between an agent's beliefs and those of her social network -- a feature characteristic of communities formed through long-term offline relationships. This dynamic can lead agents to tacitly accept and even propagate information they privately judge to be of low credibility. Our results challenge the view that improving information literacy alone can curb the spread of misinformation. We show that when agents are highly sensitive to peer pressure and the network exhibits structural polarization, even if the majority does not genuinely believe in it, the message still can spread widely without encountering open resistance.

econ.GN↗

arXiv2025

Reasoning about Bounded Reasoning

In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what types their opponents might be, and the depth of higher-order reasoning about rationality. Distinguishing these dimensions matters for interpreting experimental evidence and for understanding when cross-environment variation should be read as changes in beliefs versus changes in cognitive depth, but existing frameworks provide no language to do so. We develop a unified framework by "lifting" static complete-information games into incomplete-information versions in which players are explicitly uncertain about opponents' types. Within this framework, bounded reasoning about opponents' types is represented by transparent first-order belief restrictions, while (higher-order) reasoning depth is captured by bounds on belief in rationality. We analyze three benchmark instances: downward rationalizability, a robust baseline, and two refinements, $\mathsf{L}$-rationalizability and $\mathsf{C}$-rationalizability, which provide epistemic foundations -- with an important nuance -- for classic level-$k$ and Cognitive Hierarchy, respectively, and clarify what "level-$k$" behavior can and cannot reveal about underlying reasoning processes.

econ.TH↗

arXiv2024

Level-$k$ Reasoning, Cognitive Hierarchy, and Rationalizability

We employ a unified framework to provide an epistemic-theoretical foundation for Camerer, Ho, and Chong's (2003) cognitive hierarchy (CH) solution and its dynamic extension, using the directed rationalizability concept introduced in Battigalli and Siniscalchi (2003). We interpret level-$k$ as an information type instead of specification of strategic sophistication, and define restriction $ \Delta^\kappa$ on the beliefs of information types; based on it, we show that in the behavioral consequence of rationality, common belief in rationality and transparency of $\Delta^\kappa$, called $\Delta^\kappa$-rationalizability, the strategic sophistication of each information type is endogenously determined. We show that in static games, the CH solution generically coincides with $\Delta^\kappa$-rationalizability; this result also connects CH with Bayesian equilibrium. By extending $\Delta^\kappa$ to dynamic games, we show that Lin and Palfrey's (2024) dynamic cognitive hierarchy (DCH) solution, an extension of CH in dynamic games, generically coincides with the behavioral consequence of rationality, common strong belief in rationality, and transparency of (dynamic) $\Delta^\kappa$. The same framework can also be used to analyze many variations of CH in the literature.

econ.TH↗

arXiv2024

Quantal Response Equilibrium and Rationalizability: Inside the Black Box

This paper aims to connect epistemic and behavioral game theory by examining the epistemic foundations of quantal response equilibrium (QRE) in static games. We focus on how much information agents possess about the probability distributions of idiosyncratic payoff shocks, in addition to the standard assumptions of rationality and common belief in rationality. When these distributions are transparent, we obtain a solution concept called $Δ^p$-rationalizability, which includes action distributions derived from QRE; we also give a condition under which this relationship holds true in reverse. When agents only have common belief in the monotonicity of these distributions (for example, extreme value distributions), we obtain another solution concept called $Δ^M$-rationalizability, which includes action distributions derived from rank-dependent choice equilibrium, a parameter-free variant of QRE. Our solution concepts also provide insights for interpreting experimental and empirical data.

econ.TH↗

arXiv2022

Pecuniary Externality, Ideology and Sphere of Influence

We build a game-theoretic model to formalize Kindleberger's (1996) idea of the public good of leadership. Two superpowers use ideology to compete for influence by forming clubs whose members benefit more when their orientations are closer to the club's. Pecuniary externalities create complementarity among non-superpowers. Their collective agency forces superpower to compromise by choosing an orientation not aligned with its own. We find that superpowers compromise most when expanding their clubs but less as members become more dependent. Moreover, increased member endowments do not always enlarge the club; disproportionate growth by a few can instead contract it.

econ.GN↗

arXiv2020

Compactification of Extensive Game Structures and Backward Dominance Procedure

We study the relationship between invariant transformations on extensive game structures and backward dominance procedure (BD), a generalization of the classical backward induction introduced in Perea (2014). We show that behavioral equivalence with unambiguous orderings of information sets, a critical property that guarantees BD's applicability, can be characterized by the classical Coalescing and a modified Interchange/Simultanizing in Battigalli et al. (2020). We also give conditions on transformations that improve BD's efficiency. In addition, we discuss the relationship between transformations and Bonanno (2014)'s generalized backward induction.

econ.TH↗

arXiv2018

Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information

We characterize three interrelated concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model for a game with incomplete information. Based on it, we give two groups of characterizations. The first group characterizes permissibility and proper rationalizability. The second group characterizes permissibility in an alternative way and iterated admissibility. In each group, the conditions for the latter are stronger than those for the former, which corresponds to the fact that proper rationalizability and iterated admissibility are two (compatible) refinements of permissibility within the complete information framework. The intrinsic difference between the two groups are the role of rationality: the first group does not need it, while the second group does.

econ.TH↗

arXiv2018

Measuring Information Burden: From Coalition-Based Reasoning to the Price System

The price system is often said to economize on information. This paper asks how much information it saves. I develop a formal framework for measuring the informational burden that agents would have to bear if they had to reason individually over feasible coalitional alternatives. Taking the convergence theorem of Debreu and Scarf (1963) as the benchmark, I ask how much coalition-feasibility information must be held, and how it must be distributed, for individual acceptance decisions to recover the core. Agents' information is represented as finite sets of meaning-bearing sentences in a formal language, and reasoning is modeled as proof in Gentzen's sequent calculus. The main result characterizes the minimal informational structure under which unanimous acceptability coincides with the core for all transferable-utility games on a fixed player set: every coalition must be known to at least one of its members. Removing information about even a single coalition from all of its members suffices to break the equivalence for some game. Applying this result to the $k$-fold replica economy, I identify and count the load-bearing coalitions whose feasibility information must be distributed across the population. The associated average per-agent informational burden grows as $\Theta(4^k/k^{3/2})$ -- exponentially in the size of the economy. This is, precisely and formally, what the price system saves.

econ.TH↗

arXiv2018

Ordered Kripke Model, Permissibility, and Convergence of Probabilistic Kripke Model

We define a modification of the standard Kripke model, called the ordered Kripke model, by introducing a linear order on the set of accessible states of each state. We first show this model can be used to describe the lexicographic belief hierarchy in epistemic game theory, and perfect rationalizability can be characterized within this model. Then we show that each ordered Kripke model is the limit of a sequence of standard probabilistic Kripke models with a modified (common) belief operator, in the senses of structure and the (epsilon-)permissibilities characterized within them.

econ.EM↗

arXiv2018

Characterizing Assumption of Rationality by Incomplete Information

We characterize common assumption of rationality of 2-person games within an incomplete information framework. We use the lexicographic model with incomplete information and show that a belief hierarchy expresses common assumption of rationality within a complete information framework if and only if there is a belief hierarchy within the corresponding incomplete information framework that expresses common full belief in caution, rationality, every good choice is supported, and prior belief in the original utility functions.

econ.EM↗

arXiv2017

A Note on Gale, Kuhn, and Tucker's Reductions of Zero-Sum Games

Gale, Kuhn and Tucker (1950) introduced two ways to reduce a zero-sum game by packaging some strategies with respect to a probability distribution on them. In terms of value, they gave conditions for a desirable reduction. We show that a probability distribution for a desirable reduction relies on optimal strategies in the original game. Also, we correct an improper example given by them to show that the reverse of a theorem does not hold.

econ.EM↗