Harsanyi [4, 5] develops expected utility theory of von Neumann and Morgenstern [21] to provide two formalizations of utilitarianism. Weymark [22, 23] refers to these results as Harsanyi’s Aggregation and Impartial Observer Theorems. In this paper, we are concerned only with Aggregation Theorem. Sen [6] argues that von Neumann-Morgenstern expected utility theory is an ordinal theory and, theref...

We propose a concept to study the stability of social and economic networks when players are farsighted and allocations are determined endogenously. A set of networks is a von Neumann-Morgenstern farsightedly stable set with bargaining if there exists an allocation rule and a bargaining threat such that (i) there is no farsighted improving path from one network inside the set to another network...

The role of mathematics in economic analysis is not yet a settled question. Smith, Ricardo, Mill and other eminent classical economists did not use mathematics in their economic theorizations. We have defined classical mathematical economics as the whole body of literature in mathematical treatment of economics originating mainly from the contributions of Cournot,  Jevons and Walras. There are ...

A century ago the pioneers in game theory John von Neumann (1903—1957) and Oskar Morgenstern (1902—1978) were born. At the age of 23 (December 7, 1926) John von Neumann presented for the Mathematical Society in Göttingen his paper 'Zur Theorie der Gesellschaftspiele', which appeared in 1928 ([1]; for an English translation, see [2]). This paper, inspired by parlour games (cf. [3]), contained al...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

1. Solutions. When von Neumann and Morgenstern first defined the solution of a cooperative game, they did so in the context of characteristic function games with side payments. They defined a solution to be a set S of imputations such that: (a) " N o / contained in S is dominated by an x contained in S". (b) "Every/ not contained in S is dominated by some x contained in S". Condition (a) is cal...

This paper re-examines two major concerns about the validity of Pascal's Wager: (1) The classical von Neumann-Morgenstern Theorem seems to contradict the rationality of maximising expected utility when the utility function's range contains in nite numbers (McClennen 1994). (2) Apparently, the utility of salvation cannot be re exive under addition by real numbers (which Pascal's Pensée 233 deman...

We briefly survey the rise of game theory as a topic of study in artificial intelligence, and explain the term algorithmic game theory. We then describe three broad areas of current inquiry by AI researchers in algorithmic game theory: game playing, social choice, and mechanism design. Finally, we give short summaries of each of the six articles appearing in this issue. 1 Algorithmic Game Theor...

Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy of Sciences in Paris by Borel, who had posed the problem settled by Von Neumann’s proof) is translat...

Game Theory was founded by von Neumann and Morgenstern and can be defined as the study of mathematical models of interactive decision making. Game Theory provides general mathematical techniques for analyzing situations in which two or more individuals, called players, make decisions that will influence one another’s welfare. The dominant aspect of Game Theory is the belief that each player is ...