A Maskin's IO paper

Original article (link) posted: 30/10/2005

Maskin (1999) “Uncertainty and entry deterrence” Economic Theory, 14

A model where capacity installation by an incumbent firm serves to deter others from entering the industry is considered. The paper shows that uncertainty about demand or costs forces the incumbent to choose a higher capacity level than it would under certainty. The intuitive reason is explained in Introduction, which is stated as follows;

To deter entry, the incumbent must install enough capacity so that, if entry occurred, the entrant’s profit would be zero (or negative). Under certainty, the incumbent will install no more capacity than it would use were entry to occur. With uncertainty, when demand is high, an incumbent that has installed the certainty level of capacity still continues to produce at capacity; price simply rises to reflect the higher demand. But, when demand is low, the incumbent will wish to produce at less than full capacity. This means that the fall in price when demand is low is not so large as the rise in price when demand is high, and so if the entrant’s is zero under certainty, it is positive with certainty. To deter entry, therefore, the incumbent must increase capacity above the certainty level to ensure that when demand is high it produces enough to drive the entrant’s expected profit back down to zero.

Matching and Market

I found insightful comments on the relationship between matching theory and market economy (more specifically, general equilibrium) in the following paper:
Vincent Crawford (1991), "Comparative Statics in Matching Markets" Journal of Economic Theory, 54: 389-400.

Perhaps the most important advantage of the matching approach is its robustness to heterogeneity. A traditional competitive equilibrium cannot exist in general unless the goods traded in each market are homogeneous, because all goods in the same market must sell at the same price. A traditional model of a labor market with the degree of heterogeneity normally encountered therefore has the structure of a multi-market general equilibrium model. But because the markets in such a model are very thin, the usual arguments in support of price-taking are strained. The theory of matching markets replaces this collection of thin markets with a single market game, in which the terms of partnerships are determined endogenously, along with the matching, via negotiations between prospective partners. Gale and Shapley's notion of stability(*), suitable generalized, formalizes the idea of competition, and thereby makes it possible to evaluate the robustness of traditional competitive analysis to heterogeneity. (Stable outcomes in matching markets can in fact be viewed as traditional competitive equilibria when prices are allowed to reflect the differences between matches; see, for example, Shapley and Shubik, 1972(**))

The author, Vince Crawford, who is known as a leading researcher in game theory has written a few influential papers on matching theory. Especially, the following two are of great importance since they initiated the area of (many-to-one) matching with monetary transfers.

"Job Matching with Heterogeneous Firms and Workers"

with Elsie Marie Knoer, Econometrica, Vol. 49(2): 437-450, 1981.

"Job Matching, Coalition Formation, and Gross Substitutes"

with Alexander S. Kelso, Jr., Econometrica, Vol. 50(6): 1483-1504, 1982.

* Gale and Shapley (1962) "College Admissions and the Stability of Marriage" American Mathematics Monthly, 69: 9-15.

** Shapley and Shubik (1972) "The Assignment Game. 1. The Core" International Journal of Game Theory, 1: 111-130.

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

Gilboa's View on Theory

What is theory, or what is the role of theory especially in social sciences? In his book, "Theory of Decision under Uncertainty," Professor Gilboa shows thought-provoking argument.




The following quotes are all from Chapter 7: "The Role of Theories."

Theories are never correct, and in the case of the social sciences they tend to be almost always wrong. The question is, therefore, not whether they are right or wrong, but whether they are wrong in a way that invalidates the conclusions drawn from them. In other ways, theories are tools for reasoning and rhetorical devices.

The last standpoint I think is more or less common among great Israeli theorists such as Bob Aumann and Ariel Rubinstein. In a later part, Gilboa also says as follows:

Recall that we are not hoping to obtain theories that are very accurate. We use the theories more often as reasoning aids.

Then, the author further offers philosophical argument on science, referring the key thinkers such as Friedman, Popper, and Kuhn.

It follows that the degree to which we are willing to accept an assumption does not need to be a monotone function of its degree of accuracy. The assumption is tested based not only on its direct implications, but also on its indirect implications, which may involve nontrivial theorems.

The preceding discussion brings to mind Friedman's celebrated argument that theories should not be judged based on the validity of their assumptions, but on that of their conclusions. This argument is a bit extreme, and I would be careful to accept it (because of the following two reasons).
1) It is generally hard to draw a sharp distinction between assumptions and conclusions, completely ignoring the veracity of the former and testing only the latter.
2) Justifiably or not, it (= Friedman's argument) has become a bit of an excuse not to question the theory.

The logical positivist heritage (coupled with Popper's contribution) suggests that our theories should be falsifiable. The axiomatization we saw earlier is formulated in terms of conditions that can be violated. However, a theory such as utility maximization is not always easy to falsify. [...] Only in carefully designed controlled experiments can one hope to unambiguously refute a theory, but then one faces questions of external validity: the fact that a theory fails in artificial experimental environment may not be an indication that it will also fail in natural environment, to which it was presumably intended in the first place.

It started with Kuhn (1962), who asked questions about scientific paradigms and the way they changed. Kuhn described scientific evolution as a social phenomenon that need not converge to any objective truth. Rather, it was a process involving many factors, including accumulating evidence on the one hand, but also personal interests and tastes on the other.

The postmodern critique sometimes appears to confound descriptive and normative claims. It may well be true that science will never be able to be completely objective. But this does not mean that is shouldn't try. [...] There are instances of postmodern critique that sound to me similar to the argument, "We know that wars are inevitable. Hence, let's start shooting people."

R&D investments and the persistence of monopoly

Original article (link) posted: 26/10/2005

R&D-intensive industries are natural context in which to address the following questions; “Do dominant firms tend to maintain, or even increase, their market dominance?” and “Is market power temporary or is it permanent?”
Gilbert and Newbery (1982) develop a strong argument in the view of persistence of incumbency. They claim that a monopolist has more to lose from letting competition in than a potential entrant has from challenging the monopolist. As a result, the tendency should be towards persistence, not alternation, of market dominance. Interestingly enough, they relate their model to a model of an auction market and state that preemption is a Nash equilibrium of the corresponding auction game. (A monopolist has higher willingness to pay than that of an entrant and hence bids higher amount. I think this result can be quoted in my license auctions paper.)
Reinganum (1982) makes the point that Gilbert and Newbery’s result depends on their assumptions on the deterministic process of R&D. She shows that with uncertainty, there are cases when the probability the monopolist is replaced by an entrant is greater than the probability of persistence, hence R&D would decrease the market dominance. Her logic is as follows. Under uncertainty, with positive probability, the potential entrant does not succeed in inventing a new product, even though it invests a positive amount. When this happens, a successful incumbent would only be replacing its monopoly product with another monopoly product. Because of this “replacement” effect, a monopolist has less incentive to engage in R&D that a competitive firm has.

References
Gilbert and Newbery (1982) “Preemptive Patenting and the Persistence of Monopoly” AER, 72
Reinganum (1982) “Uncertain Innovation and the Persistence of Monopoly” AER, 73

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).

References
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