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on Game Theory |
| By: | Dirk Bergemann; Stephen Morris; Rafael Veiel |
| Abstract: | Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology" reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. An information structure is said to be simple if each player has a finite set of types and each type has a distinct first-order belief about payoff states. We show that simple information structures are dense in the almost common knowledge topology and thus it is without loss to restrict attention to simple information structures in information design problems. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09149 |
| By: | S. Nageeb Ali; Andreas Kleiner; Kun Zhang |
| Abstract: | This paper studies games of voluntary disclosure in which a sender discloses evidence to a receiver who then offers an allocation and transfers. We characterize the set of equilibrium payoffs in this setting. Our main result establishes that any payoff profile that can be achieved through information design can also be supported by an equilibrium of the disclosure game. Hence, our analysis suggests an equivalence between disclosure and design in these settings. We apply our results to monopoly pricing, bargaining over policies, and insurance markets. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.03608 |
| By: | Gustavo Berganti\~nos; Juan D. Moreno-Ternero |
| Abstract: | We study an index to measure the popularity of artists in music streaming platforms. This index, which can be used to allocate the amount raised via paid subscriptions among participating artists, is based on the Shapley value, a centerpiece in cooperative game theory. We characterize this Shapley index combining several axioms formalizing principles with normative appeal. This permits to place the index in the literature, as an alternative to the well-known (and widely used in the industry) pro-rata and user-centric indices. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.07166 |
| By: | Andrew Koh; Sivakorn Sanguanmoo; Kei Uzui |
| Abstract: | We fully characterize how dynamic information should be provided to uniquely implement the largest equilibrium in dynamic binary-action supermodular games. The designer offers an informational put: she stays silent in good times, but injects asymmetric and inconclusive public information if players lose faith. There is (i) no multiplicity gap: the largest (partially) implementable equilibrium can be implemented uniquely; and (ii) no intertemporal commitment gap: the policy is sequentially optimal. Our results have sharp implications for the design of policy in coordination environments. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09191 |
| By: | Qiang Fu; Zenan Wu; Yuxuan Zhu |
| Abstract: | This paper examines the optimal organizational rules that govern the process of dividing a fixed surplus. The process is modeled as a sequential multilateral bargaining game with costly recognition. The designer sets the voting rule -- i.e., the minimum number of votes required to approve a proposal -- and the mechanism for proposer recognition, which is modeled as a biased generalized lottery contest. We show that for diverse design objectives, the optimum can be achieved by a dictatorial voting rule, which simplifies the game into a standard biased contest model. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.08419 |
| By: | Hanbat Jeong |
| Abstract: | This paper introduces a novel spatial interaction model to explore the decision-making processes of two types of agents-a leader and followers-with central and local governments serving as empirical representations. The model accounts for three key features: (i) resource allocations from the leader to the followers and the resulting strategic interactions, (ii) followers' choices across multiple activities, and (iii) interactions among these activities. We develop a network game to examine the micro-foundations of these processes. In this game, followers engage in multiple activities, while the leader allocates resources by monitoring the externalities arising from followers' interactions. The game's unique NE is the foundation for our econometric framework, providing equilibrium measures to understand the short-term impacts of changes in followers' characteristics and their long-term consequences. To estimate the agent payoff parameters, we employ the QML estimation method and examine the asymptotic properties of the QML estimator to ensure robust statistical inferences. Empirically, we investigate interactions among U.S. states in public welfare expenditures (PWE) and housing and community development expenditures (HCDE), focusing on how federal grants influence these expenditures and the interactions among state governments. Our findings reveal positive spillovers in states' PWEs, complementarity between the two expenditures within states, and negative cross-variable spillovers between them. Additionally, we observe positive effects of federal grants on both expenditures. Counterfactual simulations indicate that federal interventions lead to a 6.46% increase in social welfare by increasing the states' efforts on PWE and HCDE. However, due to the limited flexibility in federal grants, their magnitudes are smaller than the proportion of federal grants within the states' total revenues. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.13810 |
| By: | Chao Huang |
| Abstract: | We study the problem of multilateral collaboration among agents with transferable utilities. Any group of agents can sign a contract consisting of a primitive contract and monetary transfers among the signatories. We propose a dynamic auction that finds a stable outcome when primitive contracts are gross complements for all participants. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.06545 |
| By: | Guillermo Alonso Alvarez; Erhan Bayraktar; Ibrahim Ekren; Liwei Huang |
| Abstract: | In this paper we study a principal-agent problem in continuous time with multiple lump-sum payments (contracts) paid at different deterministic times. We reduce the non-zero sum Stackelberg game between the principal and agent to a standard stochastic optimal control problem. We apply our result to a benchmark model for which we investigate how different inputs (payment frequencies, payments' distribution, discounting factors, agent's reservation utility) affect the principal's value and agent's optimal compensations. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.04262 |
| By: | Antelo, Manel; Bru, Lluís |
| Abstract: | We consider a non-producer patentholder with a cost-reducing innovation that can be used in a homogeneous duopolistic industry. To profit from the innovation, the patentholder can decide to sell it, or license it, and if the latter, the number of licences to grant as well as the corresponding contractual terms. We show that the size (value or quality) of innovation is crucial for that decision. The patentholder prefers to sell a small-sized innovation, in which case the buyer further licenses it to the competitor by means of a pure ad-valorem royalty contract. However, if the innovation is moderate or large, the patentholder retains ownership and licenses it to both firms through 2PT contracts involving per-unit royalties. Sale is shown to be welfare superior to licensing for both consumers and firms. |
| Keywords: | Cost-reducing innovation, sale, licensing, per-unit royalty, ad-valorem royalty, welfare |
| JEL: | L13 L24 |
| Date: | 2024–01 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:122731 |
| By: | Krishna Dasaratha; Benjamin Golub; Anant Shah |
| Abstract: | A principal uses payments conditioned on stochastic outcomes of a team project to elicit costly effort from the team members. We develop a multi-agent generalization of a classic first-order approach to contract optimization by leveraging methods from network games. The main results characterize the optimal allocation of incentive pay across agents and outcomes. Incentive optimality requires equalizing, across agents, a product of (i) individual productivity (ii) organizational centrality and (iii) responsiveness to monetary incentives. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.08026 |
| By: | Aytimur, R. Emre; Suen, Richard M. H. |
| Abstract: | How does the quality of information received by voters affect political polarisation? We address this long-standing question using an election competition model in which voters have to infer an unknown state from some noisy and biased signals. Their policy preferences are shaped by the posterior belief, which is unknown to the parties when they choose their platforms. The greater the uncertainty faced by the parties, the greater the incentive to polarise. We show that better information can either promote or suppress polarisation, depending on the gap between voters' and politicians' beliefs (disagreement). We also examine the welfare implications of polarisation. |
| Keywords: | Polarisation, Voter Information, Bayesian Learning, Election |
| JEL: | D72 D80 |
| Date: | 2024–05–17 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:122695 |