Positional Non-Cooperative Equilibrium

Alberti, Riccardo and Secco, Emanuele Lindo and Nagar, Atulya K. (2018) Positional Non-Cooperative Equilibrium. The Journal of Game Theory, 7 (2). ISSN 2325-0046 (Accepted for Publication)

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Abstract

This paper presents and analyses a game theoretic model for resource allocation, where agents are status-seeking and consuming positional goods. We propose a unified framework to study the competition for resources where agents’ preferences are not necessarily ordered according to the absolute amount of goods they consume, but may depend on the consumption of others as well as on individual valuation of the goods at stake. Our model explicits the relation between absolute good distribution, individual evaluation and the level of consumption adopted by the opponents; such relation has the form of a status function.We show that given a certain set of properties, there exists only one possible status function. The competition mechanism implemented to maximise one own’s status is central in this work. As a result of the mathematical formulation, we show that the standard utility-maximisation paradigm emerges as a special case (non-positional competition). We then define a new class of games where the individual evaluations are negotiable and serve only the purpose of maximising one own’s status.

Item Type: Article
Additional Information and Comments: This is the author's version of an article that has been accepted for publication in The Journal of Game Theory. The final version will be available at http://journal.sapub.org/jgt
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Emanuele Secco
Date Deposited: 16 Jul 2018 14:54
Last Modified: 16 Jul 2018 14:55
URI: http://hira.hope.ac.uk/id/eprint/2573

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