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Bayesian Persuasion: Reduced Form Approach, 2022 (with Juuso Toikka and Akhil Vohra)
We introduce reduced form representations of Bayesian persuasion problems where the variables are the probabilities that the receiver takes each of her actions. These are simpler objects than, say, the joint distribution over states and actions in the obedience formulation of the persuasion problem. This can make a difference in computational and analytical tractability which we illustrate with two applications. The first shows that with quadratic receiver payoffs, the worst-case complexity scales with the number of actions and not the number of states. If |A | and |S | denote the number of actions and states respectively, the worst case complexity of the obedience formulation is O(|A |^{2.5} max{|A | ^{2.5} ,|S | ^{2.5}). The worst case complexity of the reduced form representation is O(|A |^{3} ). In the second application, the reduced form leads to a simple greedy algorithm to determine the maximum value a sender can achieve in any cheap talk equilibrium
Contagion and Equilibria in Diversified Financial Networks, 2021 (with Victor Amelkin and Santosh Venkatesh)
Diversified cross-shareholding networks are thought to be more resilient to shocks, but diversification also increases the channels by which a shock can spread. To resolve these competing intuitions we introduce a stochastic model of a diversified cross-shareholding network in which a firm’s valuation depends on its cash endowment and the shares it owns in other firms. We show that a concentration of measure phenomenon emerges: almost all realized network instances drawn from any probability distribution in a wide class are resilient to contagion if endowments are sufficiently large. Furthermore, the size of a shock needed to trigger widespread default increases with the exposure of firms to each other. Distributions in this class are characterized by the property that a firm’s equity shares owned by others are weakly dependent yet lack “dominant” shareholders.
We introduce reduced form representations of Bayesian persuasion problems where the variables are the probabilities that the receiver takes each of her actions. These are simpler objects than, say, the joint distribution over states and actions in the obedience formulation of the persuasion problem. This can make a difference in computational and analytical tractability which we illustrate with two applications. The first shows that with quadratic receiver payoffs, the worst-case complexity scales with the number of actions and not the number of states. If |A | and |S | denote the number of actions and states respectively, the worst case complexity of the obedience formulation is O(|A |^{2.5} max{|A | ^{2.5} ,|S | ^{2.5}). The worst case complexity of the reduced form representation is O(|A |^{3} ). In the second application, the reduced form leads to a simple greedy algorithm to determine the maximum value a sender can achieve in any cheap talk equilibrium
Contagion and Equilibria in Diversified Financial Networks, 2021 (with Victor Amelkin and Santosh Venkatesh)
Diversified cross-shareholding networks are thought to be more resilient to shocks, but diversification also increases the channels by which a shock can spread. To resolve these competing intuitions we introduce a stochastic model of a diversified cross-shareholding network in which a firm’s valuation depends on its cash endowment and the shares it owns in other firms. We show that a concentration of measure phenomenon emerges: almost all realized network instances drawn from any probability distribution in a wide class are resilient to contagion if endowments are sufficiently large. Furthermore, the size of a shock needed to trigger widespread default increases with the exposure of firms to each other. Distributions in this class are characterized by the property that a firm’s equity shares owned by others are weakly dependent yet lack “dominant” shareholders.
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NETWORKSno. 1 (2024): 131-152
Journal of Economic Theorypp.105819, (2024)
JOURNAL OF MATHEMATICAL ECONOMICS (2023): 102863-102863
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ACM Conference on Fairness, Accountability and Transparency (FAccT) (2022): 574-586
semanticscholar(2022)
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ECONOMETRICAno. 1 (2021): 163-179
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