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We study a model in which before a conflict between two parties escalates into a war (in the form of an all-pay auction), a party can offer a take-it-or-leave-it bribe to the other one for a peaceful settlement. We distinguish between various degrees of peace prospects--implementability, weak security and strong security. We first characterize the necessary and sufficient conditions for peace implementability and weak security. We then show that weak security implies strong security. We also consider a requesting-a-bribe game and characterize the necessary and sufficient conditions for existence of a robust peaceful equilibrium. We find that all such robust peaceful equilibria share the same request.
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We examine the long-term behavior of a Bayesian agent who has a misspecified belief about the time lag between actions and feedback, and learns about the payoff consequences of his actions over time. Misspecified beliefs about time lags result in attribution errors, which have no long-term effect when the agents action converges, but can lead to arbitrarily large long-term inefficiencies when his action cycles. Our proof uses concentration inequalities to bound the frequency of action switches, which are useful to study learning problems with history dependence. We apply our methods to study a policy choice game between a policy-maker who has a correctly specified belief about the time lag and the public who has a misspecified belief.
We study the payoffs that can arise under some information structure from an interim perspective. There is a set of types distributed according to some prior distribution and a payoff function that assigns a value to each pair of a type and a belief over the types. Any information structure induces an interim payoff profile which describes, for each type, the expected payoff under the information structure conditional on the type. We characterize the set of all interim payoff profiles consistent with some information structure. We illustrate our results through applications.
We study how violations of structural assumptions like expected utility and exponential discounting can be connected to reference dependent preferences with set-dependent reference points, even if behavior conforms with these assumptions when the reference is fixed. An axiomatic framework jointly and systematically relaxes general rationality (WARP) and structural assumptions to capture reference dependence across domains. It gives rise to a linear order that determines references points, which in turn determines the preference parameters for a choice problem. This allows us to study risk, time, and social preferences collectively, where seemingly independent anomalies are interconnected through the lens of reference-dependent choice.
We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The governments criterion is to minimize the sum of the total expected costs of holding debt and of debts reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. These are described through a finite-state continuous-time Markov chain. We reduce via filtering techniques the original problem to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialize to a case study in which the economy faces only two regimes, and the macroeconomic indicator has a suitable diffusive dynamics. In this setting we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.
The increasing integration of world economies, which organize in complex multilayer networks of interactions, is one of the critical factors for the global propagation of economic crises. We adopt the network science approach to quantify shock propagation on the global trade-investment multiplex network. To this aim, we propose a model that couples a Susceptible-Infected-Recovered epidemic spreading dynamics, describing how economic distress propagates between connected countries, with an internal contagion mechanism, describing the spreading of such economic distress within a given country. At the local level, we find that the interplay between trade and financial interactions influences the vulnerabilities of countries to shocks. At the large scale, we find a simple linear relation between the relative magnitude of a shock in a country and its global impact on the whole economic system, albeit the strength of internal contagion is country-dependent and the intercountry propagation dynamics is non-linear. Interestingly, this systemic impact can be predicted on the basis of intra-layer and inter-layer scale factors that we name network multipliers, that are independent of the magnitude of the initial shock. Our model sets-up a quantitative framework to stress-test the robustness of individual countries and of the world economy to propagating crashes.
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