Theory Seminar (Tatur)

Original article (link) posted: 29/10/2005

Tatur "On an Evolutionary Model and an Equilibrium Concept"

The paper proposes a new evolutionary equilibrium concept that differs drastically from those of classical equilibrium concepts like ESS, Nash Equilibrium or Correlated Equilibrium. The evolutionary model is characterized the following three crucial features.
1. Imitation (not best response)
There is no sophisticated learning. Instead, players change their strategy by imitating a successful strategy taken by other players ("natural selection")
2. Local Interaction
A single, large, geographically dispersed population plays a finite two player game and only players nearby interact.
3. Correlation
There is a correlation device on which players can condition.

In his model, each player matches a partner only nearby, without knowing if he/she would become a colum player or a row player. An equilibrium set is a set of correlated strategies which survived in the imitation dynamics with random mutations in the geographical setting.
The author applies this equilibrium concept to many games and derives cooperative outcomes most of which cannot be predicted by standard equilibrium concepts such as Nash equilibrium or ESS yet frequently observed in actual economic situations or in experiments. One outstanding result is cooperation in finitely repeated games. His equilibrium concept yields strategies involve cooperation if the repeated game is sufficiently long. Moreover, we show that as the length of the game goes to infinity, the equilibrium payoffs of the repeated game will converge to a point which maximizes the utility of the population.
Just cool!! (Although Princeton faculties didn't seem to like his evolutionary idea...)

Related papers
Ellison (1993) "Learning, Interaction, and Coordination" Econometrica, 61
Morris (2000) "Contagion" RES, 67

Evolutionary Game Theory

The following recent textbook on evolutionary game theory seems to be must-read for those who are interested in this field:




Description on its cover says:

Evolutionary game theory studies the behavior of large populations of strategically interacting agents, and is used by economists to make predictions in settings where traditional assumptions about agents' rationality and knowledge may not be justified. Population Games and Evolutionary Dynamics offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception in biology in the 1970s through recent advances.

As a recommending remark, Daniel Friedman, Professor of Economics at University of California, Santa Cruz, says:

"(this text) is designed to become the standard reference and textbook in its filed for many years."

My amazon booklist on "evolution and learning in game theory" (link in Japanese) might also be helpful.