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.
In this paper we present a series of models, all within the context of a simple two-good economy, which bring out the distinctions between the different types of money and financial institutions. The models emphasize the physical properties of the economic goods, moneys, and trading systems. In Part 1 of the paper, we covered models in which the money is a consumable storable; here in Part 2 we consider economies using 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.
Keywords: Barley, Gold, Fiat and credit, Evolution of money
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.
Keywords: Barley, Gold, Fiat and credit, Evolution of money
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.
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 ri 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) “balanced contributions” property for the Shapley-Shubik power index. In fact, we derive a formula which quantitatively gives the amount of the ‘balanced contributions” 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.
We consider the n-player houseswapping game of Shapley-Scarf (1974), with indifferences in preferences allowed. It is well-known that the strict core of such a game may be empty, single-valued, or multivalued. We define a condition on such games called “segmentability”, which means that the set of players can be partitioned into a “top trading segmentation.” It generalizes Gale’s well-known idea of the partition of players into “top trading cycles” (which is used to find the unique strict core allocation in the model with no indifference). We prove that a game has a nonempty strict core if and only if it is segmentable. We then use this result to devise an O(n3) algorithm which takes as input any houseswapping game, and returns either a strict core allocation or a report that the strict core is empty. Finally, we are also able to construct a linear inequality system whose feasible region’s extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothblum (1991) for the marriage game of Gale and Shapley (1962).
Keywords: Shapley-Scarf economy, Strict core, Linear inequality system, Extreme points
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.
Consider a repeated bimatrix game. We define “bugs” as players whose “strategy” is to react myopically to whatever the opponent did on the previous iteration. We believe that in some contexts this is a more realistic model of behavior than the standard “supremely rational” noncooperative game player.
We consider possible outcome paths that can occur as the result of bugs playing a game. We also compare how bugs fare over a suitable “universe of games,” as compared with standard “Nash” players and “maximin” players.
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.
We show that if y is an odd integer between 1 and 2n - 1, there is an n × n bimatrix game with exactly y Nash equilibria (NE). We conjecture that this 2n - 1 is a tight upper for n < 3, and provide bounds on the number of NEs in m × n nondegenerate games when min(m,n) < 4.