International Game Theory Review

This paper studies the commitment value of delegation in a model of dynamic competition. We argue that separating ownership and control delivers an instantaneous first-mover advantage. Thus, delegation would enable an oligopolistic firm to increase its equilibrium profit relative to direct management. We focus on remuneration strategies that provide managers with intertemporal production incentives: future wages depend on current effort. Their composition and functional form are endogenously determined by the requirement for Markov perfection. For the case of linear-quadratic payoffs, we obtain a closed-form solution for the equilibrium wage strategies which is independent of industry structure.

Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy of Sciences in Paris by Borel, who had posed the problem settled by Von Neumann's proof) is translated here for the first time. The proof presented by Von Neumann and Morgenstern (1944) is not Von Neumann's rather involved proof of 1928, but is based on what they called "The Theorem of the Alternative for Matrices" which is in essence a reformulation of an elegant and elementary result by Borel's student Jean Ville in 1938. Ville's argument was the first to bring to light the simplifying role of convexity and to highlight the connection between the existence of minimax and the solvability of systems of linear inequalities. It by-passes nontrivial topological fixed point arguments and allows the treatment of minimax by simpler geometric methods. This approach has inspired a number of seminal contributions in convex analysis including fixed point and coincidence theory for set-valued mappings. Ville's contributions are discussed briefly and von Neuman's original communication, Ville's note, and Borel's commentary on it are translated here for the first time.

This paper investigates the strategic choice between introducing a process or a product innovation in a duopoly model with vertical differentiation, comparing the outcomes in case of Bertrand and Cournot competition. It is shown that under both competitive regimes three equilibria in innovation adoption may arise: two symmetric equilibria, where firms select the same innovation type, and one asymmetric equilibrium. The competitive regime has an impact on the features of the asymmetric equilibrium, since in case of Bertrand competition, the high (low) quality firm chooses a product (process) innovation, while firms make the opposite choices in case of Cournot competition. The presence of a leapfrogging effect (only in the Cournot case) explains these different outcomes. Last, we find that the Cournot competitors tend to favor the introduction of a new product in comparison with the Bertrand competitors.

We reformulate the monetary policy model of Barro and Gordon (1983a) by using an extended game with observable delay where the hierarchy of play between the central bank and the private sector is endogenous. This allows us to endogenise the institutional setup wherein the monetary policy game takes place. We show that positive inflation may be observed due to mixed strategies rather than time inconsistency.

In an article by Hamiache (IJGT, 2001) an axiomatization of the Shapley value has been proposed. Three axioms were called on, inessential game, continuity and associated consistency. This present article proposes a new proof, based on elementary linear algebra. Games are represented by vectors. Associated games are the results of matrix operations. The eigenvalues of the involved matrices are computed and it is shown that they are diagonalizable. The present contribution offers a powerful tool allowing further generalizations of the Shapley value, which were difficult to consider on the basis of the previous proof.

In this note we present an example of a TU game where both the value presented by Aumann and Drèze (1974) and the value introduced by Wiese (2007) do not exhibit a stable coalition structure.

We consider a model of evolution with mutations as in Kandori et al. (1993) [Kandori, M., Mailath, G.J., Rob, R., 1993. Learning, mutation, and long run equilibria in games. Econometrica 61, 29–56], where agents follow best-response decision rules as in Sandholm (1998) [Sandholm, W., 1998. Simple and clever decision rules for a model of evolution. Economics Letters 61, 165–170]. Contrary to those papers, our model gives rise to a birth-death process, which allows explicit computation of the long-run probabilities of equilibria for given values of the mutation rate and the population size. We use this fact to provide a direct proof of the stochastic stability of risk-dominant equilibria as the mutation rate tends to zero, and illustrate the outcomes of the dynamics for positive mutation rates.