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Regular version of the site
Of all publications in the section: 9
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Article
Le Breton M., Shapoval Alexander, Weber S. Journal of Mathematical Economics. 2021. Vol. 92. P. 41-46.

In this paper we examine a game-theoretical generalization of the landscape theory introduced by Axelrod and Bennett (1993). In their two-bloc setting each player ranks the blocs on the basis of the sum of her individual evaluations of members of the group. We extend the Axelrod–Bennett setting by allowing an arbitrary number of blocs and expanding the set of possible deviations to include multi-country gradual deviations. We show that a Pareto optimal landscape equilibrium which is immune to profitable gradual deviations always exists. We also indicate that while a landscape equilibrium is a stronger concept than Nash equilibrium in pure strategies, it is weaker than strong Nash equilibrium.

Added: Dec 23, 2020
Article
Dietzenbacher B., Zarzuelo J. M., Albizuri M. J. Journal of Mathematical Economics. 2020. Vol. 91. P. 11-17.

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai–Smorodinsky solution, and a constrained Kalai solution.

Added: Oct 26, 2020
Article
Kivinen S., Tumennasan N. Journal of Mathematical Economics. 2019. Vol. 83. P. 11-18.

We analyze the convergence of opinions or beliefs in a general social network with non-Bayesian agents. We provide a new sufficient condition under which opinions converge to consensus and the condition is significantly more permissive than that of Lorenz (2005). This condition, which depends on properties of the network, requires agents to incorporate others’ opinions into their own posterior sufficiently often.

Added: Jan 20, 2020
Article
Eichberger J. T., Pirner H. J. Journal of Mathematical Economics. 2018. Vol. 78. No. C. P. 131-141.

In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested by Savage (1954). We will use the Ellsberg (1961) paradox to illustrate the potential of our approach to deal with well-known paradoxes of decision theory.

Added: May 19, 2020
Article
Kabanov Yu., Lèpinette E. Journal of Mathematical Economics. 2013. Vol. 49. No. 6. P. 488-495.
Added: Feb 26, 2015
Article
Kabanov Yu.M., Lèpinette E. Journal of Mathematical Economics. 2013. Vol. 49. No. 6. P. 478-487.
Added: Feb 26, 2015
Article
Peiris U., Tsomocos D. Journal of Mathematical Economics. 2015. Vol. 56. P. 47-57.

We present an integrated framework for the study of the international financial economy with trade, fiat money, monetary and fiscal policy, endogenous default and regulation. Money is introduced via a cash-in-advance requirement and real trade is endogenous. The standard international finance pricing results obtain. Market incompleteness and positive default in equilibrium allow for the study of the transmission of default through the international financial markets and imply a positive role for policy. Finally, we present an example where, due to the trade-off between the non-pecuniary cost of default and the resulting allocation, a Pareto improvement occurs following an increase in interest rates.

Added: Feb 6, 2015
Article
Kudryavtseva O., Nagapetyan T., Kolesnikov A. Journal of Mathematical Economics. 2013. Vol. 49. P. 501-505.

The famous Afriat’s theorem from the theory of revealed preferences establishes necessary and sufficient conditions for the existence of utility function for a given set of choices and prices. The result on the existence of a homogeneous utility function can be considered as a particular fact of the Monge–Kantorovich mass transportation theory. In this paper we explain this viewpoint and discuss some related questions.

Added: Sep 27, 2013
Article
Zuazo-Garin P. Journal of Mathematical Economics. 2017. Vol. 71. P. 135-151.

In everyday economic interactions, it is not clear whether each agent’s sequential choices are visible to other participants or not: agents might be deluded about others’ ability to acquire, interpret or keep track of data. Following this idea, this paper introduces uncertainty about players’ ability to observe each others’ past choices in extensive-form games. In this context, we show that monitoring opponents’ choices does not affect the outcome of the interaction when every player expects their opponents indeed to be monitoring. Specifically, we prove that if players are rational and there is common strong belief in opponents being rational, having perfect information and believing in their own perfect information, then, the backward induction outcome is obtained regardless of which of her opponents’ choices each player observes. The paper examines the constraints on the rationalization process under which reasoning according to Battigalli’s (1996) best rationalization principle yields the same outcome irrespective of whether players observe their opponents’ choices or not. To this respect we find that the obtention of the backward induction outcome crucially depends on tight higher-order restrictions on beliefs about opponents’ perfect information. The analysis provides a new framework for the study of uncertainty about information structures and generalizes the work by Battigalli and Siniscalchi (2002) in this direction.

Added: Sep 14, 2020