Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

Does rational bargaining yield a social contract that is efficient and so inclusive? A core allocation, that is, an allocation that gives each coalition at least as much as it can get on its own, is efficient. However, some coalitional games lack a core allocation, so rationality does not require one in those games. Does rationality therefore permit exclusion from the social contract? I replace realization of a core allocation with another type of equilibrium achievable in every coalitional game. Fully (...) rational agents coordinate the pursuit of incentives so that equilibria of this type are efficient. They adopt a social contract that is efficient and inclusive. (shrink)

Within Luo’s (2001, J. Math. Econ. 36, 95–109) framework of a general system, I establish an equivalence theorem for the conservative stable standard of behavior (CSSB for short) developed by J. Greenberg (“The Theory of Social Situation: An Alternative Game-Theoretic Approach,” Cambridge University Press, 1990). It is shown that a standard of behavior for a situation is a CSSB if, and only if, its graph is a φ-stable set for the associated general system.

Two scenarios illustrate uses of von Neumann–Morgenstern stable sets in the construction of choice functions. A comparison is made to the construction of choice functions by the selection of maximal elements. A characterization is given of choice functions that are von Neumann–Morgenstern stable set rationalizable by acyclic, asymmetric binary relations. Two examples illustrate the use of the characterization.

We study the stable standard of behavior in a perfect foresight situation that was introduced by Xue. We assume that the inducement relations are invertible and coalition free. We show that the conditions are sufficient for the existence of the nonempty-valued optimistic/conservative stable standard of behavior for perfect foresight situation. Moreover, we find that an OSSB-PF supports a Pareto-efficient outcome as a stable outcome; if the preference relations are strict, only the Pareto-efficient outcomes are supported by the OSSB-PF.

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent'' if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty''. In this (...) case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles''. (shrink)

The logical foundations of game-theoretic solution concepts have so far been explored within the con¯nes of epistemic logic. In this paper we turn to a di®erent branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. The branching time framework is extended by adding agents and by de¯ning the notion of prediction. A syntactic characterization of backward induction in terms of the property of internal consistency of prediction (...) is given. (shrink)