Spisso, Gian Lorenzo (2019) Optimal policy for large herding population. PhD thesis, University of Warwick.

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Abstract

This thesis proposes a reduced-form model of herding for a large population of boundedly rational agents receiving logistic preference shocks. Agents are called at random times to revise a binary choice—smoke or not, vote for or against a party, buy or sell an asset — as they try to align to other agents choices and the policy set by an external planner. I show that the resulting Markov stationary distribution places most probability on configurations of agents choices that maximize the sum of individual utilities, similar to Kandori et al. (2008). Reducing the dimensionality of the economy — by aggregating configurations based on the average value of agents choice — shows that, in fact, since less likely configuration are more frequent, agents spend a long time away from the most likely ones. In particular, when agents are rational and care about coordination, two long-lived equilibria emerge. I study the problem of a planner who has an exogenous preference for one choice and sets a policy to minimize discounted expected costs. An algorithm by Ross (1983) is applied to compute the optimal policy under different assumption to show that the optimal policy is, in general, non-monotonic and at times discontinuous, with a region where the planner “gives up” and sets a policy close to zero. It is shown that the planner maximum policy is always exerted when at least half of the population is opposed to the planner preferred choice. Further, I give bounds on the marginal costs of policy that determines whether long-lived equilibria are still present under the optimal policy.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Distribution (Probability theory), Markov processes, Game theory, Games of chance (Mathematics), Mathematical models
Official Date:	September 2019
Dates:	Date Event September 2019 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Turner, Matthew S.
Format of File:	pdf
Extent:	v, 95 leaves : illustrations
Language:	eng

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