Mathematical Institutional Economics

An overview is given of the utilization of strategic market games in the development of a game theory based theory of money and financial institutions

Cooperative and Noncooperative Solutions, and the \u27Game within a Game\u27

In a previous essay, we developed a simple (in)efficiency measure for matrix games. We now address the difficulties encountered in assessing the usefulness and accuracy of such a measure

Money as Minimal Complexity

We consider mechanisms that provide traders the opportunity to exchange commodity i for commodity j , for certain ordered pairs ij . Given any connected graph G of opportunities, we show that there is a unique mechanism M G that satisfies some natural conditions of “fairness” and “convenience.” Let M ( m ) denote the class of mechanisms M G obtained by varying G on the commodity set {1, …, m }. We define the complexity of a mechanism M in M (m) to be a pair of integers τ( M ), π( M ) which represent the “time” required to exchange i for j and the “information” needed to determine the exchange ratio (each in the worst case scenario, across all i not equal to i ≠ j ). This induces a quasiorder \preceq on M ( m ) by the rule M \preceq M ’ if τ( M ) ≤ τ( M ’) and π( M ) ≤ π( M ’). We show that, for m \u3e 3, there are precisely three \preceq-minimal mechanisms M G in M ( m ), where G corresponds to the star, cycle and complete graphs. The star mechanism has a distinguished commodity — the money — that serves as the sole medium of exchange and mediates trade between decentralized markets for the other commodities. Our main result is that, for any weights λ, μ \u3e 0; the star mechanism is the unique minimizer of λτ( M ) + μπ ( M ) on M ( m ) for large enough m

Unifying EU Representation at the IMF Executive Board

The consequences of consolidating EU representation at the IMF Executive Board by regrouping the 27 Member States into two EU constituencies, euro area and non-euro area, are discussed. In particular we contrast voting power as proposed by Penrose-Banzhaf (PBI) and Shapley-Shubik (SSI), and other respectively related measures of blocking (or veto) power and decision efficiency as proposed by Coleman and Paterson. Hitherto, IMF-specific literature is PBI-based. However, theoretical reasons and empirical plausibility arguments for the SSI are compelling. The (SSI) voting power of the two large constituencies – U.S.A. and euro area – reflects their corresponding voting shares over a range of majority thresholds, whereas PBI voting power reduces to only half of vote share at the majority threshold of 85% needed for some Executive Board decisions. SSI-related estimates of veto power are generally lower than the Coleman indices. Correspondingly, the efficiency of collective decision-making is considerably underestimated by the Coleman measure;International Monetary Fund, European Union, Voting power analysis, Veto power

Minimally Complex Exchange Mechanisms: Emergence of Prices, Markets, and Money

We consider abstract exchange mechanisms wherein individuals submit “diversified” offers in m commodities, which are then redistributed to them. Our first result is that if the mechanism satisfies certain natural conditions embodying “fairness” and “convenience” then it admits unique prices, in the sense of consistent exchange-rates across commodity pairs ij that equalize the valuation of offers and returns for each individual. We next define certain integers τ ij , π ij , and k i which represent the “time” required to exchange i for j , the “difficulty” in determining the exchange ratio, and the “dimension” of the offer space in i ; we refer to these as time- , price- and message- complexity of the mechanism. Our second result is that there are only a finite number of minimally complex mechanisms, which moreover correspond to certain directed graphs G in a precise sense. The edges of G can be regarded as markets for commodity pairs, and prices play a stronger role in that the return to a trader depends only on his own offer and the prices. Finally we consider “strongly” minimal mechanisms, with smallest “worst case” complexities τ = max τ ij and pi = max π ij . Our third main result is that for m \u3e 3 commodities that there are precisely three such mechanisms, which correspond to the star, cycle, and complete graphs, and have complexities ( π,τ ) = (4,2), (2, m − 1), ( m 2 − m , 1) respectively. Unlike the other two mechanisms, the star mechanism has a distinguished commodity — the money — that serves as the sole medium of exchange. As m approaches infinity it is the only mechanism with bounded ( π,τ )

On Marilda Sotomayor's extraordinary contribution to matching theory

Financial support the research grants ECO2012-31962, 2014SGR-142, and ICREA AcademiaWe report on Marilda Sotomayor's extraordinay contribution to Matching Theory on the occasion of her 70th anniversar

Cost Innovation: Schumpeter and Equilibrium. Part 1. Robinson Crusoe

Modifying a parallel dynamic programming approach to a simple deterministic economy, we consider the effect of an innovation in the means of production. The success of the innovation is assumed to depend on the availability of financing, locus of financial control, the amount of resources invested, and on a random event. The relationship between money and physical assets is critical. In this first part stress is laid on the innovation behavior of Robinson Crusoe in a premonetary economy, then on his actions in a monetary economy in partial equilibrium. Part 2 considers the closed monetary economy with several differentiated agents.Cost innovation, Schumpeter, Circular flow, Strategic market games

The Inter-Institutional Distribution of Power in EU Codecision

This paper analyzes the a priori influence of the European Parliament (EP) and the Council of Ministers (CM) on legislation of the European Union adopted under its codecision procedure. In contrast to studies which use conventional power indices, both institutions are assumed to act strategically. Predicted bargaining outcomes of the crucial Conciliation stage of codecision are shown to be strongly biased towards the legislative status quo. Making symmetric preference assumptions for members of CM and EP, CM is on average much more conservative because of its internal qualified majority rule. This makes CM by an order of magnitude more influential than EP, in contrast to a seeming formal parity between the two ‘co-legislators’.power measurement, European Union codecision procedure, bargaining, spatial voting, decision procedures