International Game Theory Review

The paper examines the impact of the firms' choice between export and foreign direct investment on the incentive to innovate, as well as the effects of innovation and technological spillovers on the firms' international strategy and on its changes over time. The innovation process is analysed in the context of a two-country imperfect competition market, modelled as an infinite horizon, non-linear dynamic game, for which Markov perfect equilibria are computed. Where the models are not tractable by analytical techniques, equilibria are calculated by using a computational procedure based on a policy iteration method.

We address the problem of endogenous coalition formation in Cournot oligopoly markets. The formation of coalitions is formalised as an abstract system where the elements of the abstract set are derived from a valuation function and the dominance relation specifies the rules of coalition formation. We focus on a particular instance of this approach: Market structure determination under Cournot competition, and in the resulting Cournot merger system we find von Neumann and Morgenstern stable sets.

We consider dynamic cooperative games in characteristic function form in the sense that the characteristic function evolves over time in accordance with a difference or differential equation that is influenced not only by the current ("instantaneous") characteristic function but also by the solution concept used to allocate the benefits of cooperation among the players. The latter solution concept can be any one of a number of now standard solution concepts of cooperative game theory but, for demonstration purposes, we focus on the core and the Shapley value.

In the process, we introduce some new mechanisms by which players may regard the evolution of cooperative game over time and analyse them with respect to the goal of attaining time consistency either in discrete or in continuous time setting. In discrete time, we illustrate the phenomena that can arise when an allocation according to a given solution concept is used to adapt the values of coalitions at successive time points. In continuous time, we introduce the notion of an "instantaneous" game and its integration over time.

A two-decision competition model is developed where players may choose different strategies at different decisions knowing that their payoff at one decision is not affected by their performance at the other. It is shown that both static solution concepts of Nash and evolutionarily stable equilibria for the two-decision model are directly related to those of the separate decisions. Furthermore, if there are at most two pure strategies at each decision, dynamic stability can also be characterised through a separate analysis of each decision. However, when there are more than two strategies, this last statement is not always true.

Bagwell (1995) considered a simple Stackelberg-type game in which one player benefits from the other's ability to observe his move, assuming they play the unique subgame perfect equilibrium. He showed that introducing noise in the observability of the move eliminates that equilibrium, and thus the advantage. Van Damme and Hurkens (1997) objected that the noisy game also has a mixed strategy equilibrium close to the pure strategy one Bagwell had eliminated. However, we analyse the noisy game with a wide variety of evolutionary and learning dynamics, and find that almost all admit the no-first-mover-advantage equilibrium as a possible outcome, and often they select it uniquely.

Situations involving the linear transformation of products (LTP) with an infinite number of transformation techniques are considered. It is shown that an optimal solution of the dual program of the profit "maximisation" problem exists under certain conditions. Moreover, this solution generates a core-element of the corresponding LTP game.

The aim of this paper is to study the properties of superposition of optimality principles depending on the properties of optimality principles, which it is formed from. Some sufficient conditions for quasiperfectness of superposition of two optimality principles are found. It is shown, in particular, that superposition of any optimality principle like min-max principle with any monotone and continuous optimality principle is a quasiperfect optimality principle.