Absenteeism, Substitutes, and Complements and the Banzhaf Index

We consider the voting-with-absenteeism game of Quint-Shubik (2003). In that paper we defined a power index for such games, called the absentee index. Our analysis was based on the theory of the Shapley-Shubik power index (SSPI) for simple games. In this paper we do an analogous analysis, based on the Banzhaf index instead of the SSPI. The result is a new index, called the absentee Banzhaf index. We provide an axiomatization and multilinear extension formula for this index. Finally, we re-explore Myerson's (1977, 1980) "balanced contributions" property, and the concept of substitutes and complements for simple games (Quint-Shubik 2003), again basing our analysis on the Banzhaf index instead of the SSPI.Simple game, Shapley-Shubik power index, Banzhaf index, Absenteeism, Multilinear extension, Balanced contributions, Substitute, Complement

A Model of Migration

A simple game-theoretic model of migration is proposed, in which the players are animals, the strategies are territories in a landscape to which they may migrate, and the payoffs for each animal are determined by its ultimate location and the number of other animals there. If the payoff to an animal is a decreasing function of the number of other animals sharing its territory, we show the resultant game has a pure strategy Nash equilibrium (PSNE). Furthermore, this PSNE is generated via "natural" myopic behavior on the part of the animals. Finally, we compare this type of game with congestion games and potential games.

Absenteeism, Substitutes, and Complements in Simple Games

A voting with absenteeism game is defined as a pair (G;r) where G is an n-player (monotonic) simple game and r is an n-vector for which r_i is the probability that player i attends a vote. We define a power index for such games, called the absentee index. We axiomatize the absentee index and provide a multilinear extension formula for it. Using this analysis we re-derive Myerson's (1977, 1980) ibalanced contributionsi property for the Shapley-Shubik power index. In fact, we derive a formula which quantitatively gives the amount of the ibalanced contributionsi in terms of the coefficients of the multilinear extension of the game. Finally, we define the notion of substitutes and complements in simple games. We compare these concepts with the familiar concepts of dummy player, veto player, and master player.Simple game, Shapley-Shubik power index, Absenteeism, Multilinear extension, Balanced contributions, Substitute, Complement

A Consumable Money. An Elementary Discussion of Commodity Money, Fiat Money and Credit: Part I

In this paper we present a series of models, all within the context of a simple two-good economy, which bring out the distinctions among the different types of money and financial institutions. The models emphasize the physical properties of the economic goods, moneys, and trading systems. Part 1 covers models in which the money is a consumable storable; the economies in Part 2 use durable money, fiat money, or credit. Under this framework we are able to successfully contrast the role of private money lenders, banks, bilateral credit systems, and credit clearinghouses. We are also able to model the importance of the bankruptcy or default penalty in supporting the use of fiat.Barley, Gold, Fiat and credit, Evolution of money

On Local and Network Games

The knowledge constraints and transactions costs imposed by geographical distance, network connections and time conspire to justify local behavior as a good approximation for global rationality. We consider a class of games to illustrate this relationship and raise some questions as to what constitutes a satisfactory solution concept.Local games, Network games, Advertising

Absenteeism, Substitutes, Complements, and the Banzhaf Index

We consider the voting-with-absenteeism game of Quint-Shubik (2003). In that paper we defined a power index for such games, called the absentee index. Our analysis was based on the theory of the Shapley-Shubik power index (SSPI) for simple games. In this paper we do an analogous analysis, based on the Banzhaf index instead of the SSPI. The result is a new index, called the absentee Banzhaf index. We provide an axiomatization and multilinear extension formula for this index. Finally, we re-explore Myerson’s (1977, 1980) “balanced contributions” property, and the concept of substitutes and complements for simple games (Quint-Shubik 2003), again basing our analysis on the Banzhaf index instead of the SSPI

Sphericity, cubicity, and edge clique covers of graphs

AbstractThe sphericity sph(G) of a graph G is the minimum dimension d for which G is the intersection graph of a family of congruent spheres in Rd. The edge clique cover number θ(G) is the minimum cardinality of a set of cliques (complete subgraphs) that covers all edges of G. We prove that if G has at least one edge, then sph(G)⩽θ(G). Our upper bound remains valid for intersection graphs defined by balls in the Lp-norm for 1⩽p⩽∞

The Demonetization of Gold: Transactions and the Change in Control

Three models of a monetary economy are considered, in order to show the effects of a gold demonetization: the first with a gold money, the second with demonetized gold but no central bank, and the third with demonetized gold, but with a central bank. The distinctions between ownership and control are discussed

On Local and Network Games

The knowledge constraints and transactions costs imposed by geographical distance, network connections and time conspire to justify local behavior as a good approximation for global rationality. We consider a class of games to illustrate this relationship and raise some questions as to what constitutes a satisfactory solution concept

An Elementary Discussion of Commodity Money, Fiat Money and Credit: Part 1

In this paper we present a series of models, all within the context of a simple two-good economy, which bring out the distinctions among the different types of money and financial institutions. The models emphasize the physical properties of the economic goods, moneys, and trading systems. Part 1 covers models in which the money is a consumable storable; the economies in Part 2 use durable money, fiat money, or credit. Under this framework we are able to successfully contrast the role of private money lenders, banks, bilateral credit systems, and credit clearinghouses. We are also able to model the importance of the bankruptcy or default penalty in supporting the use of fiat