Delegated Persuasion and Pareto Efficient Equilibrium Selection in Games
94 Pages Posted: 13 Feb 2024
Date Written: January 10, 2024
Abstract
We investigate two intriguing topics in game theory and decision-making, shedding light on important aspects of strategic interactions.
In the first part, we investigate the concept of delegation within a Bayesian persuasion framework. Bayesian persuasion involves an informed sender strategically transmitting information to a receiver, who then makes deci- sions based on that information. We extend this model by introducing a preplay stage where the receiver can select a representative to act on their behalf. By examining the incentive design of representatives, we reveal that in a binary action model, the receiver has the ability to strategically choose a representative who maximizes their expected payoff subject to the con- straint of what the sender receives, which is an expected payoff of at least the one that is obtained from the worst constant action for him. We provide a constructive approach to achieve this outcome and highlight the limita- tions when generalizing beyond binary actions. This analysis enhances our understanding of how delegation can be employed effectively in decision- making scenarios.
In the second part, we explore the learning dynamics of decision-making in 2 X 2 coordination games within finite populations of rational agents. These agents take an action when they are born in order to maximize their discounted payoffs throughout their life span. We focus specifically on the process of equilibrium selection between the Pareto dominant equilibrium and the risk dominant equilibrium. We introduce agent types to this domain, where agents differentiate themselves based on their death rate, determined according to a stochastic process. We identify a number of novel conditions over the stochastic process for which the Pareto efficient equilibrium is both accessible and absorbing and thus uniquely selected.
Our exploration of delegated persuasion and Pareto efficient equilibrium selection offers insights into strategic decision-making processes. We con- tribute to understanding the incentive design of representatives in Bayesian persuasion and the role of agent heterogeneity in promoting Pareto efficient outcomes in coordination games. These findings have broad applications in various domains, such as politics, business, and finance.
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