Volume 2, Issue 1-2

The note consists of showing the marginal rates of substitution (MRS) explicitly in Nash's product formula and contract curve given by the Jacobian determinant, which otherwise are contained therein only implicitly. Two simple examples from duopoly and bilateral monopoly are used to show the MRS's explicitly in the mathematical structure of the bargaining game. We learn from the note that, while the MRS's are implicit in the mathematical structure of the game, the MRS's after suitable transformation can be shown explicitly in the product formula and contract curve. This MRS showing puts the structure of the game in a context familiar to economists.

We address the converse of a Wald–Vorob'ev theorem. In a non cooperative game, if the strategy set of any individual player is precompact, we show that the strategy sets of all the other players is precompact.

We generalize the Shapley-Shubik market model for indivisible goods by considering the case where agents need middlemen to exchange their indivisible goods. In this model, there always exist competitive equilibria in which transaction takes place directly between sellers and buyers or indirectly through the middlemen. Furthermore, the incentives of middlemen to enter the market exist. We derive these results from the existence of an integral solution for a partitioning linear program.

Playing a bargaining game, the players with non-conforming expectations were trying to enlarge their share of a sugar-pie. The first player, who was not very keen on sweets, placed an emphasis on quality. In contrast, for the second player, all sweet options, whatever they might be, were open. Thus, this paper aims to determine the negotiating power of the first player, if equal division of the pie was desirable, i. e., both players aimed to get 1/2 of the available sweets.