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Optimal use of communication resources with Markovian Payoff functions

Wittur, Nicola (2018) Optimal use of communication resources with Markovian Payoff functions. PhD thesis, The London School of Economics and Political Science (LSE).

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Abstract

Our work is based on the model proposed in the paper “Optimal Use of Communication Resources” by Olivier Gossner, Penelope Hernandez and Abraham Neyman, [6]. We propose two models that consider an alteration of the payoff function in [6]. The general setup is as follows. A repeated game is played between a team of two players, consisting of a forecaster and an agent, and nature. We assume that the forecaster and the agent share the same payoff function. The forecaster, contrary to the agent, is able to observe future states of nature that have an impact on the team’s payoff. A given pair of strategies for the players induces a sequence of actions and thus implements an average distribution on the actions of interest, i.e., on those actions that determine the payoff. We let the team’s stage payoff not only depend on actions played in one stage, but on actions played in two consecutive stages. We introduce two models that vary w.r.t. the specification of the payoff function and the actions played by nature, with the aim of characterizing the implementable average distributions. This characterization is achieved through an information inequality based on the entropy function, called the information constraint. It expresses a key feature of the strategies of the players, namely the fact that the information used by the agent cannot exceed the amount of information sent by the forecaster. In each model we develop an information constraint that characterizes the implementable distributions as follows. On the one hand, we show that every implementable distribution fulfills the information constraint. And on the other hand, we prove that a certain set of distributions that fulfill the designated information constraint is implementable.

Item Type: Thesis (PhD)
Additional Information: © 2018 Nicola Wittur
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Supervisor: Gossner, Olivier
URI: http://etheses.lse.ac.uk/id/eprint/3871

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