This paper presents a complete survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection theories. We present all...

Subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept used in applications of stochastic games, which makes it imperative to develop efficient numerical methods to compute an SSPE. For this purpose, this paper develops an interior-point path-following...

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions...

A set of coalition structures <em>P</em> is farsightedly stable (i) if all possible deviations from any coalition structure p belonging to <em>P</em> to a coalition structure outside <em>P</em> are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improvingpath from any...

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions...

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show: 1. non-existence of stationary subgame-perfect equilibrium (SSPE). 2. the recursive equations and optimality conditions...

We show that in the canonical non-cooperative multilateral bargaining game, a subgame perfect equilibrium exists in pure stationary strategies, even when the space of feasible payoffs is not convex. At such an equilibrium there is no delay. We also have the converse result that randomization...

In a local interaction model agents situated on a circle play bilateral prisoners' dilemmas with their immediate neighbors and have three possible strategies: cooperate in all interactions (altruistic), defect in all interactions (egoistic), or cooperate with one immediate neighbor with...

We study bankruptcy games where the estate and the claims have stochastic values. We use the Weak Sequential Core as the solution concept for such games. We test the stability of a number of well known division rules in this stochastic setting and find that most of them are unstable, except for...