The value is a solution concept for n-person strategic games, developed by Nash, Shapley, and Harsanyi. The value of a game is an a priori evaluation of the economic worth of the position of each player, reflecting the players' strategic possibilities, including their ability to make threats...

We develop a model of assignment games with pairwise-identitydependent externalities. A concept of conjectural equilibrium is proposed, and the universal conjecture is shown to be the necessary and sufficient condition for the general existence of equilibrium. We then apply the solution concept...

Cooperative game theory has proposed different notions of powerful players. For example, big-boss games (Muto et al., 1988) and clan games (Potters et al., 1989) are particular cases of veto games (Bahel, 2016). The present paper extends these veto games by assuming that there is a given subset...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they "fall back" on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...

Each of n ≥ 1 identical buyers (and m ≥ 1 identical sellers) wants to buy (sell) a single unit of an indivisible good. The core predicts a unique and extreme outcome: the entire surplus is split evenly among the buyers when m n and among the sellers when m n; the long side gets nothing. We...

In this paper, we study different notions of stability for three-sided assignment games. Since the core may be empty in this case, we first focus on other notions of stability such as the notions of subsolution and von Neumann-Morgenstern stable sets. The dominant diagonal property is necessary...

In a liability problem, the asset value of an insolvent firm must be distributed among the creditors and the firm itself, when the firm has some freedom in negotiating with the creditors. We model the negotiations using cooperative game theory and analyze the Shapley value to resolve such...

Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their...

We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von...

In many matching problems, it is natural to consider that agents may have preferences not only over the set of potential partners but also over what other matches occur. Once such externalities are considered, the set of stable matchings will depend on what agents believe will happen if they...