理论论文

People participate in protests even though it is costly, benefits are not exclusive to participants, and each individual is unlikely to be pivotal. Building on these characteristics, I propose a sequential model of protest formation where opportunities to participate arrive stochastically, and the protest succeeds if participation surpasses a threshold. I show a unique equilibrium exists and characterize its dynamics. If the unique equilibrium involves participation, the time between participation decisions shortens as the protest progresses—a pattern observed empirically. A player with an opportunity becomes sequentially pivotal if, after abstaining, the protest will likely end before another opportunity arrives. (JEL D72, D84, D91)

We study misperceptions of private-signal correlation in an incomplete-information Cournot duopoly game. Exaggerating the correlation between players' demand signals is beneficial when agents hold flexible beliefs about price elasticity but is harmful when their beliefs are dogmatically correct. For agents with flexible beliefs who learn elasticity by observing prices, correlation misperceptions indirectly distort behavior through elasticity misinference. If agents know the true elasticity, this learning channel is eliminated. Correlation misperceptions have opposite direct and indirect effects on behavior, so the presence of elasticity inference can reverse an error's viability. (JEL C72, D21, D43, D81, D82, D83)

This paper investigates how to persuade multiple interacting receivers under arbitrary equilibrium selection and when receivers’ preferences may exhibit psychological traits. Our main result characterizes the conditions under which the sender can categorize information using partitions and then disclose partition-related information without altering the equilibrium outcome. This finding broadens the traditional direct approach based on the revelation principle, which categorizes messages solely by equilibrium actions. Consequently, our results support a generalized direct approach, which we apply to study information disclosure in fostering fairness within groups where members may demonstrate altruistic behaviors.

We extend global games á la Carlsson and van Damme (1993) to environments where the risk-dominant equilibrium is selected even if there is no dominance solvable game in the underlying class of games. Strict dominance can emerge in the global game from strategic uncertainty due to discrete payoff changes in underlying games, and we provide sufficient conditions on payoff changes that warrant iterated dominance of the risk-dominant equilibrium. Thus, strategic uncertainty creates strictly dominant actions as well as fostering iterated dominance, in contrast to global games hitherto where strategic uncertainty does only the latter. Discrete payoff changes tend to arise, in particular, in situations where a public good can be provided with varying degrees of coordination depending on the state, so that coordinating actions can be strategic substitutes and free-riding incentives are present. We illustrate our findings in a stylized public good provision model.

In a recent paper, Lin & Palfrey (2024) developed a theory of cognitive hierarchies (CH) in sequential games and observed that this solution concept is not reduced-normal-form invariant. In this paper I qualify and explain this observation. I show that the CH model is normal-form invariant, and that the differences arising from the application of the CH model to the reduced normal form depend only on how randomization by level-0 types is modeled. Indeed, while the uniform behavior strategy in the extensive form yields the uniform mixed strategy in the normal form, the latter does not correspond to the uniform randomization in the reduced normal form, because different reduced strategies may correspond to sets of equivalent strategies with different cardinalities. I also comment on (i) the invariance of the CH model to some transformations of the sequential game, and (ii) the independence of conditional beliefs about co-players' level-types.

Quantal response equilibrium (QRE), a statistical generalization of Nash equilibrium, is a standard benchmark in the analysis of experimental data. Despite its influence, nonparametric characterizations and tests of QRE are unavailable beyond the case of finite games. We address this gap by completely characterizing the set of QRE in a class of binary-action games with a continuum of types. Our characterization provides sharp predictions in settings such as global games, volunteer's dilemma, and the compromise game. Further, we leverage our results to develop nonparametric tests of QRE. As an empirical application, we revisit the experimental data from Carrillo and Palfrey (2009) on the compromise game.

The effect of group size and effort cost on rent dissipation in the standard Tullock rent seeking model is examined using a laboratory experiment. Data support qualitative comparative static Nash equilibrium predictions as reductions in both group size and effort cost increase effort levels. However, effort and dissipation rates are above Nash predictions for all treatments. In addition, while cutting per-unit effort costs in half increases individual effort levels, they do not fully double as predicted and therefore lower rent dissipation, creating a policy-relevant “streamlining effect”. A quantal response equilibrium, which adds stochastic elements into the game structure, predicts the observed higher effort levels and dissipation but is proven to be unable to explain the streamlining effect. A modification of quantal response that incorporates implementation error noise and loss aversion outperforms other estimated models and tracks the observed all data patterns more closely, including the streamlining effect.

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.

We consider contests with a large set (continuum) of participants and axiomatize contest success functions that arise when performance is composed of both effort and a random element, and when winners are those whose performance exceeds a cutoff determined by the designer’s budget constraint. Any such Random Performance Function (RPF) satisfies a Co-monotonicity property, which implies that opponents’ effort distributions can be unambiguously ranked based on how competitive they are. We prove that Co-monotonicity, along with standard continuity and monotonicity properties, in fact characterize the class of RPFs. We also describe necessary and sufficient conditions for the noise term to have an additive structure. “The idea of a continuum of traders may seem outlandish to the reader. Actually, it is no stranger than a continuum of prices or of strategies or a continuum of ‘particles’ in fluid mechanics... It should be emphasized that our consideration of a continuum of traders is not merely a mathematical exercise; it is the expression of an economic idea.” In: Markets with a continuum of traders, Robert J. Aumann, Econometrica 1964

We report on the topological structure of logit quantal response equilibria for asymmetric, two-player, two-choice games in normal form, via catastrophe theory. We present three main outcomes: first, a novel, smooth potential function for the underlying dynamics, relative to which logit equilibria arise as stationary points comprising a parameterised hyper-surface; secondly, a proof that all catastrophes within this manifold are of order at most three, i.e. “folds and cusps”; thirdly, discovery of a new topological phenomenon, the “pleated loop”, corresponding to a pair of opposed pitchfork bifurcations. This we exhibit for games, such as Prisoner's Dilemma, that have a unique Nash equilibrium, with multiple logit equilibria for finite precision parameters. These results extend work at the intersection of stochastic decision theory and catastrophe theory with economic games. Their application to the problem of bifurcations in the tracing procedure for logit solutions, proposed by McKelvey and Palfrey, is discussed throughout.

This paper introduces a refinement of Nash equilibrium (NE) to determine the relevance of weakly dominated NE in games. We adapt Harsanyi (1973)'s concept of “approachability,” originally based on games with randomly disturbed payoffs, and extend it to a broader family that encompasses the most widely used equilibrium models of imperfectly rational behavior. We identify a singular NE refinement, approximate payoff monotone equilibrium (APME), that coincides with the set of NE that are approachable by regular quantal response equilibria as well as control cost models. We advocate for APME based on its 1) foundation in models that rationalize empirically observed behavior; 2) ability to discriminate between equilibria without automatically discarding weakly dominated behavior; and 3) computational simplicity in applications where the structure of NE is known. We illustrate the value of APME in three applications in which empirical studies suggest that weakly dominated NE are relevant.

We propose an extensive-form solution concept, with players who neglect information from hypothetical events but make inferences from observed events. Our concept modifies cursed equilibrium (Eyster and Rabin 2005) and allows that players can be cursed about endogenous information.

We consider a setting where each player of a normal-form game privately designs an information structure before playing the game. One of these designs is chosen at random to determine the distribution of the private messages that players receive. These messages allow players to correlate their actions; however, private information design implies a push from correlated to Nash equilibria. Indeed, the sequential equilibrium payoffs of the private information design extensive-form game are correlated equilibrium payoffs of the underlying normal-form game, but not all correlated equilibrium payoffs are sequential equilibrium payoffs. In generic 2-player games, the latter are specific convex combinations of two Nash equilibrium payoffs. In any 2-player game, imposing optimal beliefs from private information design allows us to obtain sufficient epistemic conditions for Nash equilibrium that require only knowledge of players' rationality.

In a game in extensive form, we say that a sequence of trembles destabilizes an outcome if there is no corresponding sequence of payoff perturbations and Nash outcomes converging to the outcome. We use equilibrium destabilization to characterize sequential equilibria and sequentially stable outcomes, and to reinterpret standard selection criteria in signaling games as a means of ruling out implausible equilibria by identifying destabilizing tremble sequences. We show that the existence of a maximally destabilizing sequence of trembles (destabilizing all outcomes but one) significantly simplifies studying strategically stable behavior in complex games such as finitely repeated games.

By showing that a one-shot deviation property holds for almost all large games with i.i.d. randomly drawn payoffs in which a convention (in the sense of Young, 1993a) exists, long-run outcomes under behavioral rules are characterized by social choice rules.

This paper analyzes the extent to which well-known results on the relationship between the bargaining set, the core, and the kernel in one-to-one assignment games generalize to many-to-one assignment markets, and by extension, many-to-many markets. Using a minimal counterexample, we show that the bargaining set does not necessarily coincide with the core and that the kernel may not be contained within the core. We would like to highlight that the failure of the coincidence between the core and the bargaining set, as observed in the many-to-one assignment game, is quite notable. This is especially true when compared to various other highly structured games, many of which emerge from combinatorial optimization problems, such as the one underlying many-to-one assignment games.

We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent’s marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.

We introduce the family of games with intertemporal externalities, where two disjoint sets of players play sequentially. Coalitions formed by the present cohort generate worth today. Moreover, today’s partition of players exerts an externality on the future; the worth of a coalition formed by future players is influenced by this externality. We adapt the classic Shapley axioms and study their implications in our class of games. They do not suffice to single out a unique solution. We introduce two values using the interpretation of the Shapley value as the players’ expected contributions to coalitions: the one-coalition externality value and the naive value. We state a relationship between these values and the Shapley value of an associated game in characteristic function form. Our main results characterize the two values by adding one additional property to the classic Shapley axioms. A property of equal treatment of contributions leads to characterizing the one-coalition externality value. A property of equal treatment of externalities characterizes the naive value.

When organizations adopt artificial intelligence (AI) to recognize individuals’ negative emotions and accordingly allocate limited resources, strategic users are incentivized to game the system by misrepresenting their emotions. The value of AI in automating such emotion-driven allocation may be undermined by gaming behavior, algorithmic noise in emotion detection, and the spillover effect of negative emotions. We develop a game-theoretical model to understand emotion AI adoption, particularly in customer care, and analyze the design of the associated allocation policies. We find that adopting emotion AI is valuable if the spillover effect of negative emotions is negligible compared with resource misallocation loss, regardless of algorithmic noise and gaming behavior. We also quantify the welfare impacts of emotion AI on the users, organization, and society. Notably, a stronger AI is not always socially desirable and regulation on emotion-driven allocation is needed. Finally, we characterize conditions under which leveraging the AI system is preferred to hiring human employees in emotion-driven allocation. We also explore the alternative application of using emotion AI to monitor strategic employees and compare it with hiring a human manager for monitoring. Intriguingly, algorithmic noise may increase the profit of AI monitoring. Our work provides implications for designing, adopting, and regulating emotion AI.

Growing political polarization has reshaped the business landscape, shifting the mix of private and public politics companies face and requiring managers to develop more sophisticated nonmarket strategies. Yet the literature has largely continued to study strategies aimed at public and private politics in isolation. We analyze repertoires of nonmarket strategies and how they evolve over time in a formal game theoretic model of the policy life cycle, providing an integrated framework for studying public and private politics. Industry may resist activist campaigns or concede to them and may also lobby to block legislation when public politics is viable. The evolution of public opinion in a polarized world divides the game into two distinct phases, an initial phase of pure private politics and a subsequent phase with both public and private politics. Polarization delays social consensus and intensifies activism while increasing industry resistance to it. As public concern about an issue rises over time, industry resistance to activist campaigns weakens, and lobbying becomes costlier and less likely. We reveal important complementarities between strategies: The ability to lobby in the latter phase makes industry more resistant to activist campaigns during both phases of the life cycle. Our analysis demonstrates clearly and precisely how suboptimal strategic decisions may result from a failure to fully coordinate nonmarket strategy instruments.