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 games with almost perfect information and an infinite time horizon. In such games, at each stage, the players simultaneously choose actions from finite action sets, knowing the actions chosen at all previous stages. The payoff of each player is a function of all actions chosen during...

At each moment in time, some alternative from a finite set is selected by a dynamic process. Players observe the alternative selected and sequentially cast a yes or a no vote. If the set of players casting a yes-vote is decisive for the alternative in question, the alternative is accepted and...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the...

We consider truthful implementation of the socially efficient allocation in a dynamic private value environment in which agents receive private information over time. We propose a suitable generalization of the Vickrey-Clarke-Groves mechanism, based on the marginal contribution of each agent. In...

We study a linear interaction model with asymmetric information. We first characterize the linear Bayes Nash equilibrium for a class of one dimensional signals. It is then shown that this class of one dimensional signals provide a comprehensive description of the first and second moments of the...

We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with...

We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set...