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Correlated Equilibrium Strategies with Multiple Independent Randomization Devices

Yohan Pelosse Orcid Logo

"Correlated Equilibrium Strategies with Multiple Independent Randomization Devices,", Volume: Working Papers 2024-05, Swansea University, School of Management.

Swansea University Author: Yohan Pelosse Orcid Logo

Abstract

A primitive assumption underlying Aumann (1974,1987) is that all players of a game may correlate their strategies by agreeing on a common single ’public roulette’. A natural extension of this idea is the study of strategies when the assumption of a single random device common to all the players (pub...

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Published: Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management.
URI: https://cronfa.swan.ac.uk/Record/cronfa66300
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spelling v2 66300 2024-05-04 Correlated Equilibrium Strategies with Multiple Independent Randomization Devices 455a04210e95a07e6fbea54f2cc4d6be 0000-0001-8546-918X Yohan Pelosse Yohan Pelosse true false 2024-05-04 SOSS A primitive assumption underlying Aumann (1974,1987) is that all players of a game may correlate their strategies by agreeing on a common single ’public roulette’. A natural extension of this idea is the study of strategies when the assumption of a single random device common to all the players (public roulette) is dropped and (arbitrary) disjoint subsets of players forming a coalition structure are allowed to use independent random devices (private roulette) a la Aumann. Under multiple independent random devices, the coalition's mixed strategies form an equilibrium of the induced non-cooperative game played across the coalitions–the ’partitioned game’–when the profile of such coalitions’ strategies is a profile of correlated equilibria. These correlated equilibria which are the mutual joint best responses of the coalitions are called the Nash coalitional correlated equilibria (NCCEs) of the game. The paper identifies various classes of finite and infinite games where there exists a non-empty set of NCCEs lying outside the regular correlated equilibrium distributions of the game. We notably relate the class of NCCEs to the ’coalitional equilibria’ introduced in Ray and Vohra (1997) to construct their ’Equilibrium Binding Agreements’. In a ’coalitional equilibrium’, coalitions’ best responses are defined by Pareto dominance and their existence are not guaranteed in arbitrary games without the use of correlated mixed strategies. We characterize a family of games where the existence of a non-empty set of non-trivial NCCEs is guaranteed to coincide with a subset of coalitional equilibria. Most of our results are based on the characterization of the induced non-cooperative ’partitioned game’ played across the coalitions. Working paper "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management. Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management. 0 0 0 0001-01-01 COLLEGE NANME Social Sciences School COLLEGE CODE SOSS Swansea University 2024-06-24T14:28:17.1144787 2024-05-04T07:43:59.3949970 Faculty of Humanities and Social Sciences School of Social Sciences - Economics Yohan Pelosse 0000-0001-8546-918X 1 66300__30274__cae61952556349488c3118caf29880d6.pdf Wp-Swansea-NCCE-Mar24.pdf 2024-05-04T09:01:02.0595622 Output 454372 application/pdf Author's Original true false
title Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
spellingShingle Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
Yohan Pelosse
title_short Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
title_full Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
title_fullStr Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
title_full_unstemmed Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
title_sort Correlated Equilibrium Strategies with Multiple Independent Randomization Devices
author_id_str_mv 455a04210e95a07e6fbea54f2cc4d6be
author_id_fullname_str_mv 455a04210e95a07e6fbea54f2cc4d6be_***_Yohan Pelosse
author Yohan Pelosse
author2 Yohan Pelosse
format Working paper
container_title "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices,"
container_volume Working Papers 2024-05, Swansea University, School of Management.
institution Swansea University
college_str Faculty of Humanities and Social Sciences
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hierarchy_top_id facultyofhumanitiesandsocialsciences
hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Social Sciences - Economics{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Social Sciences - Economics
document_store_str 1
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description A primitive assumption underlying Aumann (1974,1987) is that all players of a game may correlate their strategies by agreeing on a common single ’public roulette’. A natural extension of this idea is the study of strategies when the assumption of a single random device common to all the players (public roulette) is dropped and (arbitrary) disjoint subsets of players forming a coalition structure are allowed to use independent random devices (private roulette) a la Aumann. Under multiple independent random devices, the coalition's mixed strategies form an equilibrium of the induced non-cooperative game played across the coalitions–the ’partitioned game’–when the profile of such coalitions’ strategies is a profile of correlated equilibria. These correlated equilibria which are the mutual joint best responses of the coalitions are called the Nash coalitional correlated equilibria (NCCEs) of the game. The paper identifies various classes of finite and infinite games where there exists a non-empty set of NCCEs lying outside the regular correlated equilibrium distributions of the game. We notably relate the class of NCCEs to the ’coalitional equilibria’ introduced in Ray and Vohra (1997) to construct their ’Equilibrium Binding Agreements’. In a ’coalitional equilibrium’, coalitions’ best responses are defined by Pareto dominance and their existence are not guaranteed in arbitrary games without the use of correlated mixed strategies. We characterize a family of games where the existence of a non-empty set of non-trivial NCCEs is guaranteed to coincide with a subset of coalitional equilibria. Most of our results are based on the characterization of the induced non-cooperative ’partitioned game’ played across the coalitions.
published_date 0001-01-01T14:28:15Z
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