Jörg Oechssler

On the Dynamic Foundation of Evolutionary Stability in Continuous Models

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games.

Brown–von Neumann–Nash dynamics: The continuous strategy case

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous- time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown-von Neumann-Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.

Cooperation as a result of learning with aspiration levels

It is shown that a win-stay, lose-hift behavior rule with endogenous aspiration levels yields cooperation in a certain class of games. The aspiration level in each round equals the current population average. The class of games includes the prisoners dilemma and Cournot oligopoly and thus yields an explanation for cooperation and collusion.

Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust☆

A well-known result by Vega-Redondo (1997) implies that in symmetric Cournot oligopoly, imitation leads to the Walrasian outcome where price equals marginal cost. In this paper, we show that this result is not robust to the slightest asymmetry in fixed costs. Instead of obtaining the Walrasian outcome as unique prediction, every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is still a good predictor of behavior.

Explaining cross-supplies

Cross-supplies describe the phenomenon that two or more firms in the same industry supply each other with their final products. A prominent example is the cooperation in the European flat-glass industry, which was recently criticized by the European Commission. In a simple model we attempt to explain what incentives firms may have to use cross-supplies (instead of producing the goods themselves) and what welfare effects cross-supplies have if they are used. Contrary to the ruling of the European Commission we find that cross-supplies improve welfare whenever they are employed. Furthermore, for a large range of parameters, they even benefit consumers.

Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies.

Uniform vs. discriminatory auctions with variable supply - experimental evidence

In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the sellers cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more efficient auction format.

Competition Among Conventions

A convention can be seen as a way of resolving a coordination problem. If different conventions exist in various geographical, social or other entities (called &201C;groups&201D;) and if there is some mobility between these groups, which conventions, if any, will emerge as the successful ones? A simple evolutionary process is suggested and it is shown that the process converges to a Nash equilibrium for all games satisfying weak acyclity. Further, if the process converges, it converges to an efficient convention for all games in which the Pareto optimal symmetric equilibria are strict. Hence, the paper presents an explanation for the endogenous evolution of efficiency. In contrast to most recent studies in evolutionary game theory, the conclusions do not rely on random &201C;mutations&201D;. Instead, the driving force is the tendency of players to have increased interaction with member of their own group (viscosity).

Does Noise Undermine The First-Mover Advantage? An Evolutionary Analysis Of Bagwell'S Example

Bagwell (1995) considered a simple Stackelberg-type game in which one player benefits from the others 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.

Informational cascades with continuous action spaces

The recent literature on informational cascades has nurtured the impression that cascades can occur only if the action space is coarser than the signal space. In particular, it is sometimes claimed that with continuous action spaces cascades are impossible. In this note we present a simple counter-example showing that this conclusion is not necessarily warranted.