We develop a two-country trade model with sequential production in which a technologically backward economy exports intermediates in exchange for final goods from a technologically advanced economy. The advanced country can raise welfare by imposing import tariffs on intermediates, whereas export tariffs on intermediates or import tariffs on final goods are ineffective for the backward economy. Instead, the backward economy resorts to a quantitative export constraint, diverting part of its labor force into a less efficient autarkic production process. We show that non-cooperative policy choices reduce trade and lower welfare in both countries, underscoring the need for a trade agreement. To sustain mutually beneficial liberalization after prior tariff reductions, however, an agreement may have to link tariff cuts to the removal of export constraints, particularly when lifting these constraints is costly for the backward economy.
The rational behavior of a coalition requires the informational precondition that its members take into account the behavior and beliefs of others. In noncooperative games, we define Bayesian coalitional rationality as a mode of collective behavior that no coalition of players wishes to change, in the sense that there is no coalition-wise common belief that mutual gains can be achieved through a tacit coalitional agreement. We establish a fundamental possibility result: the assumption of Bayesian coalitional rationality and common belief of Bayesian coalitional rationality is attainable in a finite model. Under a belief-richness condition, this assumption characterizes the solution concept of Bayesian coalitional rationalizability. Our approach also provides a novel notion of individual rationality in game situations where players may be uncertain about their own types and strategy choices.
Using constructive order-theoretic techniques, we characterize the set of minimal state-space recursive competitive equilibria (RCE) in the canonical small open economy model of sudden stops with price-dependent collateral constraints. In addition, we develop a computable theory of the existence of RCE, as well as a complete constructive theory of equilibrium comparative statics of the entire set of RCE relative to ordered changes in important deep parameters of the economy. Using recent results on iterative monotone comparative statics, we also provide a new iterative approach to checking whether particular RCE are "order stable" relative to ordered changes in the deep parameters (and satisfying the correspondence principle). Finally, we give sufficient conditions for the uniqueness of RCE, and these sufficient conditions are extremely strong relative to applications of these models in the quantitative applied literature.
We derive conditions for individual choices and ϵ -equilibrium prices to be inferred from a finite set of market data in the following sense: Although potential observations are infinite, inference can be attained and known to have been attained after a finite number of observations. While we first examine the case of observations on an individual’s demand at different prices and incomes, our primary focus is on equilibrium, where only profiles of individual endowments and associated equilibrium prices are observable. Our main result is that finite inference is possible in the equilibrium setting if one wants to infer either individual choices or the ϵ -equilibrium correspondence.
This paper develops a tractable model of wishful thinking that captures both the benefits and costs of optimistic biased beliefs and the behaviors they induce. Building on Bratcha and Brown (2012) and Caplin and Leahy (2019), we propose a two-stage framework in which a decision maker selects actions and belief structures under uncertainty, balancing subjective utility against the cost of departing from prior beliefs. The cost is formalized using a ϕ -divergence–based belief distortion function, encompassing measures such as Kullback–Leibler, reverse Kullback-Leibler, and Pearson χ ^2 distances. Our contributions are threefold: (i) we characterize optimal beliefs, showing they twist prior probabilities toward high-utility states across a broad class of divergences; (ii) we link WT behavior to risk-seeking actions via convex risk measures; and (iii) we introduce cognitive censoring and cognitive emergence, capturing extreme beliefs. Methodologically, the model provides new insights into how optimistic beliefs reshape decision-making, extending the theoretical foundations of WT and opening avenues for future research.
In many expert–decision maker settings, information is richer than the language used to convey it. Motivated by this communication friction, we study Bayesian persuasion when the sender is constrained to use k messages. We show that the sender’s value is given by a k-point analogue of concavification, which we call k-concavification. An optimal information structure can be chosen with affinely independent posterior support, allowing the problem to be reduced to a lower-dimensional persuasion problem and then solved by standard concavification. We derive a tight bound on the value of communication capacity that applies to general persuasion games: the gain from a (k+1) st message is at most 2/(k-1) times the value attainable with k messages. Finally, we solve a class of belief-threshold games in which the receiver chooses between a safe default and several risky actions, the sender gets zero from the default and the same positive payoff from any risky action, and a risky action is taken only when the corresponding posterior probability exceeds a threshold. We characterize the optimal coarse information structure, derive comparative statics in the prior and the threshold, and extend the analysis to heterogeneous thresholds and heterogeneous sender values across risky actions.
This paper studies the impact of the order of senders in a sequential Bayesian persuasion game on the receiver’s equilibrium utility. We find that it is always optimal for the receiver to put the more aligned sender before the less aligned sender. Comparative statics analysis shows that when we restrict to senders who are comparable (i.e., a sender is more aligned than the other sender), as the degree of misalignment between senders increases or as the number of senders increases, the receiver’s equilibrium utility may (weakly) decrease. In addition, we find that when senders are comparable, the sequential game performs no worse than the simultaneous game in terms of information disclosure.
Wealthier, risk-averse buyers pay more to speed up transactions in competitive search markets. This, coupled with forward-looking intermediaries who hold vacant homes overnight, implies that a credit expansion produces a boom in prices that slowly recedes over time. This boom is due to a combination of two effects. First, search and matching frictions imply that buyers are willing to pay a higher price to trade faster, not only to consume housing services. Second, the fact that intermediaries are forward-looking implies that trading probabilities today depend on the future evolution of prices. Since agents forecast that prices are higher than in the initial steady state, they turn to trading today. Our theory produces a boom in prices that slowly recedes and a gradual rise of homeownership rate.
We analyze competition in service markets with unit demand prone to adverse selection, such as secured lending and car insurance markets. Incumbent firms learn their customers’ types over time and can price discriminate accordingly. We prove existence of a unique set of mixed strategy equilibria where firms randomize prices over a bounded continuous support. Incumbents earn positive rents. Increased competition through firm entry does not benefit customers if firms know portfolio compositions of competitors. If firms only possess information regarding the aggregate industry client composition, horizontal mergers may reduce industry rents, a finding with implications for competition policy in information-intensive industries.
Berge equilibrium offers an alternative to Nash equilibrium in game theory, emphasizing cooperative stability rather than individual optimization. Despite recent interest, a systematic study of Berge equilibria in finite normal form games is still lacking, with fundamental questions like existence remaining open. This paper characterizes Berge equilibria through a polynomial system of equations, enabling computational algebra and algebraic geometry methods to analyze them. Algorithms based on Gröbner bases determine the existence and computation of Berge equilibria. Furthermore, we show that the set of games admitting completely mixed Berge equilibria is contained within a determinantal variety, whose dimension we explicitly bound from above.
We study the effect of prudence on optimal prevention in two periods with Kreps and Porteus (1978) and Selden (1978) (KPS) preferences. We use consumption smoothing as the benchmark and consider risk-averse decision-makers. In this framework, prudence has a positive effect on prevention, generalizing findings of Menegatti (2009). We extend this result to risk lovers and comparative risk aversion. When saving is endogenized, the preference over the timing of uncertainty resolution becomes irrelevant for prevention, and only the curvature of marginal utility matters. This result allows us to identify a class of decision-makers who are prudent in the KPS model but whose prevention effort coincides with that of a risk-neutral agent. Our findings highlight that the structure of intertemporal preferences critically shapes the link between prudence and prevention.
We build a model of policymaking under the threat of unrest. A policymaker chooses how much effort to spend on a public good; effort is unobservable and the outcome conditional on effort is uncertain. A group of citizens protest if the outcome falls short of a reference point; the reference point is determined endogenously by expectations about the outcome and by the intensity of emotions. We show that the effects of stronger emotional reactions on policymaker’s effort and the probability of protest are nonmonotonic and depend on the group’s ability to inflict damage. Equilibrium may require the policymaker to randomize between providing some effort or no effort at all, in order to temper citizens’ expectations, in which case strong emotional reactions are counterproductive. Optimal emotional reactions are fine-tuned to minimize the probability of protest.
We formulate three sets of axioms to measure inequality of opportunity. First, the basic axioms that any relative measure should satisfy. Second, axioms that capture the ex ante perspective, focusing on inequality between individuals with different circumstances. Third, axioms that capture the ex post perspective, focusing on inequality among individuals with the same responsibility characteristics. Based on these axioms, we characterize the ex ante and ex post classes of inequality of opportunity measures. We also discuss how well existing measures in the literature adhere to the axioms.
This paper studies the equilibrium properties of the direct strategy profile in large finite-player games. Each player in such a strategy profile simply adopts a strategy as she would have used in a symmetric equilibrium of an idealized large game. We show that, under a mild continuity condition, (i) direct strategy profiles constitute a convergent sequence of approximate equilibria as the number of players tends to infinity, and (ii) realizations of such strategy profiles also form a convergent sequence of (pure strategy) approximate equilibria with probability approaching one. Our findings provide a simple and decentralized approach for implementing equilibrium in large games, yielding outcomes that are asymptotically optimal both ex ante and ex post.
This paper examines the effects of differences in sectoral compositions between countries on the liberalization of global tariffs in the coalition-proof Nash equilibrium sense. Using a static tariff-setting game with endogenous trade agreements, I develop a competing exporters model with three countries that differ in their sectoral compositions. I consider two settings that are differentiated by the type of trade agreements that countries can sign: free trade agreements (FTAs) and multilateral trade agreements, i.e., no FTAs. I study both symmetric and asymmetric differences in sectoral compositions across countries and find that, contrary to earlier results based on economic size asymmetries, FTAs act as stumbling blocks to the multilateral trading system when countries sufficiently differ in their sectoral compositions. This result is caused by the existence of a free riding incentive. Lastly, I show that permitting internal tariffs in FTAs typically strengthens the free riding incentive under symmetric sectoral differences, and in the asymmetric case may either mitigate or exacerbate the stumbling-block problem depending on countries’ sectoral compositions.
This paper develops a dynamic game-theoretic framework to analyze security competition between two states that can invest in a technology to eliminate their rival. Extending the canonical one-shot game, our model incorporates a negotiation (settlement) stage and assumes effective diplomacy, which rules out payoff-dominated equilibria. We fully characterize equilibrium behavior across all discount factors and compare outcomes under high and low elimination costs. The dynamic structure reveals why, even with optimal coordination, long-lasting disarmed peace is rare. By combining the dynamics of military escalation with the constraints of effective diplomacy, the model rationalizes historical cycles of peace, arms races, and conflict. Our approach identifies strategic mechanisms that restrict the sustainability of disarmament and clarifies the conditions under which arms races or conflict become inevitable, offering a deeper understanding of the recurrent nature of international conflict under repeated interaction.
In a coordination game with multiple Pareto ordered equilibria and population uncertainty, we show that group size helps select a unique equilibrium, for reasons reminiscent of the global games literature. A critical mass phenomenon emerges at equilibrium. Group size has an emboldening effect on participants.
We develop a two-stage oligopoly model of price competition in markets with both informed and uninformed (captive) consumers. The model introduces a novel mechanism through which interfirm collaborative R D influences market outcomes. In particular, the second stage of the game where firms set prices is a supermodular game allowing us to analyze strategic complementarities in pricing behavior. We show that this type of market friction creates a new channel of influence for collaborative R D. Our analysis reveals how consumer heterogeneity and cost heterogeneity jointly shape the incentives for collaboration among firms, offering new insights into the design of efficient innovation networks in oligopolistic markets.
This paper examines the rationalizability of two-sided aggregate matchings with non-transferable utility under single-peaked preferences. We build upon Echenique et al. (Econometrica 81:153–171, 2013), which considers unrestricted preference domains. In contrast, we restrict preferences to be single-peaked, motivated by the fact that many observable characteristics of agents, such as age and income, are naturally ordered. A matching is rationalizable by single-peaked preferences if there exists a single-peaked preference profile under which the observed matching is stable. We find a characterization for such matchings and extend the result to a multidimensional type setting.
Economists routinely measure individual welfare by (von-Neumann-Morgenstern) utility, for instance when analysing welfare intensity, social welfare, or welfare inequality. Is this welfare measure justified? Natural working hypotheses turn out to imply a different measure. It overcomes familiar problems of utility, by faithfully capturing non-ordinal information, such as welfare intensity – despite still resting on purely ordinal evidence, such as revealed preferences or self-reported welfare comparisons. Social welfare analysis changes when based on this new individual welfare measure rather than utility. For instance, Harsanyi’s ‘utilitarian theorem’ now supports prioritarianism. We compare the standard utility-based versions of utilitarianism and prioritarianism with new versions based on our welfare measure. We show that utility is a hybrid object determined by two rival influences: welfare and the attitude to intrinsic risk, i.e., to risk in welfare. A new version of Harsanyi’s theorem shows that Harsanyi makes the questionable implicit assumption that society is neutral to intrinsic risk, overruling people’s risk attitudes. We thus propose risk-impartial utilitarianism, which adopts people’s (average) risk attitude.
