Monotonicity and competitive equilibrium in cake-cutting

Léon Walras (1874) had already realised that his neo-classical general equilibrium model could not accommodate autonomous investments. In the early 1960s, Amartya Sen analysed the same issue in a simple, one-sector macroeconomic model of a closed economy. He showed that fixing investment in the model, built strictly on neo-classical assumptions, would make the system overdetermined, and thus one should loosen some neo-classical conditions of competitive equilibrium. He analysed three not neo-classical “closure options”, which could make the model well-determined in the case of fixed investment. His list was later extended by others and it was shown that the closure dilemma arises in the more complex computable general equilibrium (CGE) models as well, as does the choice of adjustment mechanism assumed to bring about equilibrium at the macro level. It was also illustrated through several numerical models that the adopted closure rule can significantly affect the results of policy simulations based on a CGE model. Despite these warnings, the issue of macro closure is often neglected in policy simulations. It is, therefore, worth revisiting the issue and demonstrating by further examples its importance, as well as pointing out that the closure problem in the CGE models extends well beyond the problem of how to incorporate autonomous investments into a CGE model. Several closure rules are discussed in this paper and their diverse outcomes are illustrated by numerical models calibrated on statistical data. First, the analyses are done in a one-sector model, similar to Sen’s, but extended into a model of an open economy. Next, the same analyses are repeated using a fully-fledged multi-sectoral CGE model, calibrated on the same statistical data. Comparing the results obtained by the two models it is shown that although they generate quite similar results in terms of the direction and — to a somewhat lesser extent — of the magnitude of change in the main macro variables using the same closure option, the predictions of the multi-sectoral CGE model are clearly more realistic and balanced.

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Holding a group together: non-game-theory vs. game-theory

The Economic Journal ◽

10.1093/ej/ueab026 ◽

2021 ◽

Author(s):

Michael Richter ◽

Ariel Rubinstein

Keyword(s):

Game Theory ◽

Nash Equilibrium ◽

Competitive Equilibrium ◽

Solution Concept ◽

Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

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Competitive equilibrium fraud in markets for credence-goods

Journal of Mathematical Economics ◽

10.1016/j.jmateco.2021.102519 ◽

2021 ◽

pp. 102519

Author(s):

Yen-Lin Chiu ◽

Edi Karni

Keyword(s):

Competitive Equilibrium ◽

Credence Goods

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Truthful fair division without free disposal

Social Choice and Welfare ◽

10.1007/s00355-020-01256-0 ◽

2020 ◽

Vol 55 (3) ◽

pp. 523-545 ◽

Cited By ~ 1

Author(s):

Xiaohui Bei ◽

Guangda Huzhang ◽

Warut Suksompong

Keyword(s):

Fair Division ◽

Multiple Agents ◽

Two Agents ◽

Free Disposal ◽

Cake Cutting ◽

Strategic Agents ◽

Additional Constraints

Abstract We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

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