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We investigate, both theoretically and experimentally, an institutional mechanism designed to enhance cooperation. In this mechanism, contributors have the option to voluntarily contribute to the public good and decide whether to join a (sub)group where partners equally share the contribution cost. Theoretically, stable cost-sharing partnerships enhance efficiency since their partners fully contribute, while outsiders would free-ride. Our data reveal that individual joining and contribution behaviors do not always align with benchmark predictions: partnerships are not always formed, and when they are, they are not always of the optimal size; partners often contribute less than maximally, and outsiders more than minimally. Nonetheless, we document systematic evidence of partnership formation and significantly improved provision of public goods across rounds.

We say a model is continuous in utilities (resp., preferences) if small perturbations of utility functions (resp., preferences) generate small changes in the model’s outcomes. While similar, these two questions are different. They are only equivalent when the following two sets are isomorphic: the set of continuous mappings from preferences to the model’s outcomes, and the set of continuous mappings from utilities to the model’s outcomes. In this paper, we study the topology for preference spaces defined by such an isomorphism. This study is practically significant, as continuity analysis is predominantly conducted through utility functions, rather than the underlying preference space. Our findings enable researchers to extrapolate continuity in utility as indicative of continuity in underlying preferences.

The core as a solution concept captures the set of allocations against which no objection exists by any coalition of agents. However, Aumann and Maschler (1961. The Bargaining Set for Cooperative Games . Princeton Univ NJ) emphasized that the objection mechanism does not talk about repercussions from agents and thus introduced the bargaining set. Vind (1992. “Two Characterizations of Bargaining Sets.” Journal of Mathematical Economics 21: 89–97) later introduced the notion of a global bargaining set. In this paper, we consider a club economy proposed by Ellickson et al. (1999. “Clubs and the Market.” Econometrica 67: 1185–217) where club goods are consumed parallel to private goods to capture the social aspects of consumption. We introduce the global bargaining set for our club economy and provide characterizations of it in terms of the size of the (counter-) objecting coalitions thereby extending the works of Schjødt and Sloth (1994. “Bargaining Sets with Small Coalitions.” International Journal of Game Theory 23: 49–55) and Hervés-Estévez and Moreno-García (2015. “On Restricted Bargaining Sets.” International Journal of Game Theory 44: 631–45). In the process, we obtain Schmeidler’s (1972. “A Remark on the Core of an Atomless Economy.” Econometrica 40: 579) and Vind’s (1972. “A Third Remark on the Core of an Atomless Economy.” Econometrica 40: 585) theorem for atomless club economies as simple corollaries. We provide further interpretations of the global bargaining set in terms of approximately robustly efficient states, a notion familiarised by Bhowmik and Kaur (2023. “Competitive Equilibria and Robust Efficiency with Club Goods.” Journal of Mathematical Economics 108: 102876) for club economies.

We examine a two-bidder auction setting in which the distributions for the bidders’ valuations are asymmetric over a support consisting of three elements. For the first price auction, for each parameter values we derive the unique Bayes Nash Equilibrium in closed form. We rely on this result to compare the revenue in the first price auction with the revenue in the second price auction. The latter is often revenue superior to the former, and we determine precisely, given a distribution for the value of a bidder, when a distribution for the value of the other bidder exists such that the first price auction is superior to the second price auction.

We study income and price effects for intertemporal consumer problems with monetary and non-monetary dynamic constraints. We focus on short and long-run responses to a permanent change in income or price, and we characterize how such responses depend on the law of motion of non-monetary dynamic constraints and on time discounting. We provide a dynamic analog to the Slutsky equation, and we show the conditions under which the elasticity of demand to income or price is smaller in the long than in the short run, or even has opposite sign.

Consider a war of attrition game in continuous time with complete information, in which N  ≥ 2 players compete for N − K prizes. I focus on the equilibria in which the strategies follow exponential distributions, which are memoryless. When K  = 1, such an equilibrium can be explicitly characterized. The equilibrium certainly exists if N  = 2. If N  ≥ 3, it exists as long as the weakest player is not too weak compared to the average. If it exists, the equilibrium is unique under some conditions. When K  ≥ 2, the game typically has nondegenerate equilibria in which K − 1 relatively weak players concede at the beginning. The model can be extended to the case in which the players have loser-dependent valuations. The model helps to solve a generalized exit game in a “nature oligopoly” and an all-pay auction with ascending bids.

This research studies the endogenous choice of simultaneous (Cournot) or sequential (Stackelberg) moves in a quantity-setting duopoly in which firms have social concerns and convex technologies. A parsimonious non-cooperative endogenous timing game (ETG) is developed to determine the sub-game perfect Nash equilibrium (SPNE). The article shows that the market structure strictly depends on the (endogenous) adoption of the available technology. In detail, when costs are convex, the sequential move equilibrium can emerge as the SPNE of the ETG. Results contrast the SPNE emerging in a duopoly – with or without CSR – in which firms produce with constant returns to scale technologies (linear costs), where only simultaneous competition occurs. The article also discusses the welfare outcomes corresponding to the SPNE. The main findings also offer empirical and policy implications. The paper finally considers a mixed duopoly and shows that the results of Amir and De Feo (2014. “Endogenous Timing in a Mixed Duopoly.” International Journal of Game Theory 43: 629–58) – sequential move equilibrium – are confirmed. Still, it pinpoints new results about the private firm’s degree of social concern in determining the market leadership when goods are strategic substitutes .

This paper provides a detailed guide to solving a model characterized by risk-aversion heterogeneity, utilizing the dynamic programming approach in conjunction with the finite difference method. Although this model is characterized by a system of three partial differential equations (PDEs) – two related to the agents’ value functions and one to the risky asset price – it is surprisingly unnecessary to solve the full 3-PDEs system. Solving the 2-PDEs system for the agents’ value functions is sufficient, as, in equilibrium, the risky asset price is a function of these values. This problem is further simplified since each agent’s PDE can be solved independently due to the properties of the value function under constant relative risk aversion (CRRA) preferences. Finally, we demonstrate that applying the finite difference method with the implicit approach and an upwind scheme is straightforward for this type of asset pricing model.

This paper introduces ex ante information heterogeneity between players into an otherwise standard global game so that both a type with superior private information and that with inferior private information coexist. We first derive the condition under which a unique threshold equilibrium exists. We then show that less-informed (resp. more-informed) players are more likely to attack the regime than more-informed (resp. less-informed) players when (i) the fundamental is perceived to be weak (resp. strong) according to the public signal and (ii) the cost of attack is low (resp. high). We finally derive the implication of our finding on optimal information allocation problem in the context of team production.