We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to specific classes of games for which we provide new equivalence results. These include non-continuous conve...

The world oil market is modelled as a two-person non-zero-sum game in normal form with each player having a continuum of strategies. The two players are the oil importing nations (OPIC) and the oil exporting nations (OPEC). The game is solved in the noncooperative sense using the equilibrium point solution concept due to Nash. The Nash equilibrium point solution yields an analytic expression fo...

This article reconsiders the Harsanyi–Sen debate concerning whether Harsanyi is justified in interpreting his Aggregation and Impartial Observer Theorems as providing axiomatizations of utilitarianism. Sen’s criticism and its formalization by Weymark are based on the claim that von Neumann–Morgenstern utility theory is ordinal, whereas Harsanyi’s utilitarian conclusions require cardinal utility...

This sequel to previous chapters on objective and subjective expected utility reviews conditions for players in a non-cooperative game to be Bayesian rational — i.e., to choose a strategy maximizing the expectation of each von Neumann–Morgenstern utility function in a unique cardinal equivalence class. In classical Nash equilibrium theory, players’ mixed strategies involve objective probabiliti...

We consider the infinite-horizon optimal portfolio liquidation problem for a von Neumann-Morgenstern investor in the liquidity model of Almgren (2003). Using a stochastic control approach, we characterize the value function and the optimal strategy as classical solutions of nonlinear parabolic partial differential equations. We furthermore analyze the sensitivities of the value function and the...

Given a set of possible vector outcomes and the set of lotteries over it, we define sets of (a) von Neumann-Morgenstern representations of preferences over the lotteries, (b) mappings that yield the certainty equivalent outcomes corresponding to a lottery, (c) mappings that yield the risk premia corresponding to a lottery, (d) mappings that yield the acceptance set of lotteries corresponding to...

Harsanyi’s original position treats personal identity, upon which each individual’s utility depends, as risky. Pattanaik’s critique is related to the problem of scaling “state-dependent” von Neumann–Morgenstern utility when determining subjective probabilities. But a unique social welfare functional, incorporating both level and unit interpersonal comparisons, emerges from contemplating an “ext...

We consider Arrovian aggregation of preferences over lotteries that are represented by skew-symmetric bilinear (SSB) utility functions, a significant generalization of von Neumann-Morgenstern utility functions due to Fishburn, in which utility is assigned to pairs of alternatives. We show that the largest domain of preferences that simultaneously allows for independence of irrelevant alternativ...

I propose a generalization of the probabilistic voting model in two-candidate elections. Unlike in all previous works, I assume that the candidates have general von Neumann-Morgenstern utility functions defined over the voting outcomes. For a finite number of voters, I derive necessary and sufficient conditions for the existence of a local Nash equilibrium in which the policy platforms of the c...

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler (An Expected utility theory for state-dependent preferences. Working paper no. 48-80 of the Foerder Institute for Economic Research, Faculty of Social Sciences, Tel AvivUniversity, 1980). A decision-maker is supposed to possess a preference relation on acts and another preference relation on sta...