Experimental Game Theory in GEB

I found an interesting website in Games and Economic Behavior (GEB), one of the leading academic journals in game theory. As titled "Two decades of experimental game theory in Games and Economic Behavior," this special online issue shows 17 articles on experimental game theory which have been published in GEB. It says:
Assembling this Virtual Special Issue on Experimental Game Theory has been an eye-opener. The first step was to go back through all the issues to get a bigger picture of the range of papers that we have published in this area. Games and Economic Behavior (GEB) was founded in 1989 at a time when there really wasn’t a subfield of experimental game theory as such. It wasn’t until a year later that this journal published its first article based on laboratory experiments, in the March 1990 issue – exactly twenty years ago.
See here for the detailed information.


Liquidity and Financial Crisis

Here comes a long-awaited economics book on liquidity, which has great importance especially after having financial crisis.

In Inside and Outside Liquidity, leading economists Bengt Holmstrom and Jean Tirole offer an original unified perspective on the following questions that are center of all financial crises:

  • Why do financial institutions, industrial companies, and households hold low-yielding money balances, Treasury bills, and other liquid assets?
  • When and to what extent can the state and international financial markets make up for a shortage of liquid assets, allowing agents to save and share risk more effectively?

The publisher's description says:
In a slight, but important departure from the standard of finance, the authors show how imperfect pledgeability of corporate income leads to a demand for as well as a shortage of liquidity with interesting implications for the pricing of assets, investment decisions, and liquidity management.
The book surely attracts those who are interested in liquidity and financial crisis.


Lecture 7 (Dutta): Repeated Games 2

Original article (link) posted: 25/10/2005

We continued to examine the Abreu-Pearce-Stacchetti (APS) operator, particularly focusing on the following two theorems.

Theorem1 (Necessity)
V* = LV*

Theorem2 (Sufficiency)
If V = LV (and V is bounded), then V is a subset of V*

where L is APS operator and V* is the set of SPE payoffs of the repeated game.

The proof of Theorem 1 is not difficult. We used "unimprovability" to prove Theorem 2. APS operator also establishes following results.

1. V* is compact
2. V* is increasing in the discount factor
3. APS operator is monotone

Using the third result with two theorems mentioned above, we can derive the algorithm to compute SPE payoffs. That is, starting with a large set of candidate equilibrium payoffs (say, a convex hull of the set of feasible payoffs), we just need to apply the APS operator iteratively until the sequence of sets will converge. Then, the limit must coincide with V*.


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.


Lecture 6 (Dutta): Repeated Games 1

Original article (link) posted: 21/10/2005

Repeated Games: Set-Up
We first checked the definitions of the followings; a stage game, a repeated game, a subgame, strategies, histories, a Nash equilibrium, a subgame perfect NE, feasible payoffs, and individually rational payoffs.
Note) Any points in the convex hull of the pure strategy payoffs are feasible when the discount factor is sufficiently large. (The proof is done by using time-averaging strategies. See Sorin(1986))

Abreu-Pearce-Stachetti Characterization
Then, we investigated APS operator, which captures the similar idea of Bellman operator in a single-agent dynamic optimization problem.
Since this blog is not designed for writing messy equations, I will not cover the mathematical argument about APS operator here. You can check the chapter 5 of Fudenberg and Tirole (1991) ("Dynamic Programming and Self-Generation" in 5.5.4) or the original paper by APS (1990).

Abreu, Pearce and Stachetti (1990) "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring" Econometrica, 58
Sorin (1986) "On Repeated Games with Complete Information" Math. of Operations Research, 11-1