Cournot versus Walras in Dynamic Oligopolies with Memory

This paper explores the impact of memory in Cournot oligopolies where firms learn through imitation of success (as suggested in Alchian (1950) and modeled in Vega-Redondo (1997)). As long as memory includes at least one period, the long-run outcomes correspond to all the quantities in the interval tension between the evolutionary stability associated to the walrasian outcome, which relies on inter-firm comparisons of simultaneous profits, and the stability of the Cournot-Nash equilibrium, derived from intertemporal comparisons of profits.

Learning, Memory, and Inertia

This paper explores the impact of memory in standard display imitation behavior, focusing on coordination games (as in Kandori et al (1993)) and N-player games where spiteful behavior allows to discard Nash equilibria. It is shown that the way interea is modeled in such examples actually entails a strong "no-memory" assumption. Once inertia is removed (or medeled otherwise), the addition of bounded memory changes the predictions dramatically. The analysis highlights the stability properties of Nash outcomes in purely evolutionary contexts with a finite population of agents.

Finite Population Dynamics and Mixed Equilibria

This paper examines the stability of mixed-strategy Nash equilibria of sym- metric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered and combined with different assumptions about the speed of adjustment. It is found that specific refinements of mixed Nash equi- libria serve to identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2 x 2 case, both im- itation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

Robust stochastic stability

A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.Learning in games, stochastic stability, radius-coradius theorems, logit-response dynamics, mutations, imitation

Trees and Decisions

The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define a tree as a connected directed graph without loops and a distingueshed node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as function from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.

A Comment on "The Selection of Preferences Through Imitation"

We observe that the imitation dynamics of Cubitt and Sugden (CS) is the same as the Replicator Dynamics for a certain class of games. Known results for such games then permit a more complete analysis of the CS imitaion process, containing their results as special cases, and extending them considerably. We also offer a comment on the special role of "pure" prospects, and an as if interpretation of the CS process in terms of payoff-guided imitation.

Does Learning Lead to Coordination on Market Clearing Institutions?

This paper analyzes the question whether traders learn to coordinate on a trading institution that guarantees market clearing, or whether other market institutions can survive in the long run. While we find that the market clearing institution is indeed always stable under a general class of learning dynamics, it turns out that also other, non-market clearing institutions are stable. Hence, in the long run traders may fail to coordinate exclusively on market clearing institutions.industrial organization ;

Trees and Decisions

The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts de?ne a tree as a connected directed graph without loops and a distinguished node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural de?nition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be de?ned as speci?c collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.Decision under uncertainty, Extensive form games, Trees

Hidden Symmetries and Focal Points

This paper provides a general formal framework to define and analyze the concepts of focal points and frames for normal form games. The information provided by a frame is captured by a symmetry structure which is consistent with the payoff structure of the game. The set of alternative symmetry structures has itself a clear structure (a lattice). Focal points are strategy profiles which respect the symmetry structure and are chosen according to some meta-norm, which is not particular to the framed game at hand. We also clarify the difference between different concepts of symmetry used in the literature.symmetry, focal points, Nash equilibria

Does Learning Lead to Coordination in Market Clearing Institutions?

This paper analyzes the question of whether traders learn to coordinate on a trading institution that guarantees market clearing, or whether other market institutions can survive in the long run. While we find that the market clearing institution is indeed always stable under a general class of learning dynamics, it turns out that also other, non-market clearing institutions are stable. Hence, in the long run traders may fail to coordinate exclusively in market clearing institutions.