TY - JOUR

T1 - Coalitional Expected Multi-Utility Theory

AU - Hara, Kazuhiro

AU - Ok, Efe A.

AU - Riella, Gil

N1 - Funding Information:
Kazuhiro Hara: kazuhiro.hara@fgv.br Efe A. Ok: efe.ok@nyu.edu Gil Riella: gil.riella@fgv.br We thank Miguel Ballester, Jean Pierre Benoit, Eddie Dekel, Ozgur Evren, Faruk Gul, Paulo Klinger Mon-teiro, Hiroki Nishimura, and the participants of seminars at Cal Tech, EESP/FGV, LSB, LSE, MIT, Tel Aviv University, University of Brasilia, University of Paris I, Waseda University, XVII Latin American Workshop in Economic Theory, and the 39th Meeting of the Brazilian Econometric Society. We are also grateful for the various comments and critiques of four referees of this journal. Riella would like to acknowledge the financial support of CNPq of Brazil, Grant 304560/2015-4. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES), Finance Code 001.

PY - 2019/5

Y1 - 2019/5

N2 - This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision-maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

AB - This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision-maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

KW - Affine binary relations

KW - existence of mixed strategy Nash equilibrium

KW - justifiable preferences

KW - nontransitive and incomplete expected utility representations

KW - preference for portfolio diversification

KW - preference reversal phenomenon

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U2 - 10.3982/ECTA14156

DO - 10.3982/ECTA14156

M3 - Article

AN - SCOPUS:85065923776

VL - 87

SP - 933

EP - 980

JO - Econometrica

JF - Econometrica

SN - 0012-9682

IS - 3

ER -