Kamien (Handbook of GT 1992)

Original article (link) posted: 12/09/2005

Kamien (1992) "Patent Licensing" Handbook of Game Theory, vol.1, chapter 11

This survey focuses on game-theoretic analysis of patent licensing. In the paper, the interaction between a patentee and licensees is described in terms of a three-stage game. In the first stage, a patentee sells the patent by using some mechanism. Firms in the industry simultaneously decide their buying strategies in the next stage. And finally, patents are distributed according to the rule of a mechanism and market competition (Cournot competition) is realized.
The main focus on the paper is comparison between different mechanisms which are (1) auction (2) fixed fee licensing (3) royalty (4) hybrid of (2)&(3). The interesting result is that licensing auction yields higher revenue than fixed fee or royalty does. In some situations, however, the hybrid mechanism colled "chutzpah" mechanism yields even higher revenue than auction does.
The analyses introduced in this survey has several restrictions such as; no private information, identical firms, only considering profit maximization.
In the end, the paper concludes as follows.

It is often the case that a survey of a line of research is a signal of it having peaked. This is certainly not true for game-theoretic analysis of paten licensing.

I hope this comment is still true although it has been written in 15 year ago...

Interesting Papers on References

Jensen (1989) "Reputational spillovers, innovation, licensing and entry" IJIO, 10-2
Katz and Shapiro (1985) "On the licensing of innovation" Rand, 16
Katz and Shapiro (1986) "How to license intangible property" QJE, 101
Muto (1987) "Possibility of relicensing and patent protection" EER, 31
Reinganum (1989) "The timing of innovation: Research, development and diffusion" in Handbook of IO


Japan eye bigger prize

Congratulations for the great victory!
Blue Samurai, you can go further!!

"I know this is a really big win for Japan," Honda said after helping his side line up a Round of 16 meeting with Paraguay in Pretoria on Tuesday. "I expected to be really jubilant but I'm not as jubilant as I thought I would be because I don't think we are finished here. I believe we can go further in this competition."
(quoted from the article at FIFA's official website: Japan eye bigger prize)

Who is Honda? He has been elected twice as the MOM (man of the match) in this world cup (see the link).
You can also watch this movie:


Fudenberg, Levine and Maskin (Econometrica 1994)

Original article (link) posted: 08/09/2005

In their paper, "The Folk Theorem with Imperfect Public Information", several versions of Folk Theorem are shown. This is a memo for them. Before mentioning actual theorem, let's briefly check their contribution in the literature.

An important hypothesis of the standard Folk Theorem is that the players can observe one another's actions in each repetition, so that deviations from equilibrium strategies are detectable. In contrast, this paper considers games in which players observe only a public outcome that is a stochastic function of the actions played. Thus these are games of moral hazard. The major task of the paper is to provide conditions sufficient for the Folk Theorem to extend to such games. The most important hypotheses concern the way the probability distribution over public outcomes depends on the player's actions.

To see the Folk Theorem with perfect information, you should check Fudenberg and Maskin (Econometrica 1986) "The Folk Theorem for Repeated Games with Discounting and Incomplete Information". (Notice that "Incomplete Information" in the title implies the cases without a public randomization device or some reputation models and do not mean imperfect monitoring cases, which is covered in FLM)

The three versions of Folk Theorem they showed are as follows:

Nash-thread 1
If all pure-action profiles are pairwise identifiable, a "Nash-threat" version of the Folk Theorem obtains: any payoff vector Pareto-dominating a Nash equilibrium of the stage game can be sustained in an equilibrium of the repeated game for discount factors near enough to 1.

Nash-thread 2
If a game has at least one (mixed-action) profile satisfying the conjunction of pairwise identifiability and individual full rank (= "pairwise full rank"), then again the Nash-threat Folk Theorem applies. Generic games possess such a profile provided that the number of possible public outcomes is no less than the total number of elements in the action sets of any two players.

To obtain the conventional "minimax-threat" Folk Theorem requires more stringent conditions. Specifically, besides the hypotheses for the Nash-threat theorem, it suffices to assume that all pure-action profiles satisfy individual full rank.

Finally, I quote their explanation about two examples of inefficient results shown by Radner-Myerson-Maskin and Green-Porter (or Abreu-Pearce-Stacchetti)

Our work makes clear that the R-M-M counterexample relies on there being relatively few possible public outcomes compared to the number of possible actions, so that the genericity result mentioned before does not apply, and that equilibria of the G-P and A-P-S variety are necessarily inefficient only because they are symmetric: if (even slightly) asymmetric equilibria are admitted, the Folk Theorem is restored.


Reserach Advice by Don Davis

Original article (link) posted: 04/09/2005

Professor Davis at Columbia University put the note "Ph.D. Thesis Research: Where do I Start?" on his web site.
There are many interesting advices. Especially the following two are helpful for me.

Don’t Take Courses!
By the third year of a PhD program, your job is research, not more courses! You can take more courses (of course), but you should have a very good reason for doing so. Acceptable reasons include (a) It is a course that takes you to the frontier of research in an area in which you plan to do research or (b) It develops mathematical or econometric techniques that you plan to use in short order. The reason that I advise not taking courses is that it is a convenient, comforting, and seemingly rationalizable way of avoiding the harder, more frustrating, but necessary conversion from being a consumer of research to being a producer of research. Focus on your primary task – developing your own research program.

Don’t teach!
. . . more than you have to. For many, teaching is attached to a stipend or is otherwise economically unavoidable. In this case, do what you must! Moreover, there are some real intellectual and practical advantages from doing a couple of terms of TA work. Explaining the concepts to others is very useful in consolidating them in yourself. But beyond this, the returns become strongly negative. Your job is research – and anything that distracts you from this is a heavy cost. The first cost, which may seem remote at the time that you are deciding on the teaching, is that it could delay completion of the thesis by a year or more. An even larger cost is if it crowds out time to write a really great thesis. As a PhD student, your time is very valuable; treat it that way.

Hum, as Professor Obara recommended to me, I shouldn't teach this year even like a small group seminar... Also, instead of attending classes, it must be better for me to use time for focusing on my own research or going to seminars.


Information in Repeated Games

Original article (link) posted: 31/08/2005

Let's think about Green and Porter model.
What happens if demand becomes less stochastic so that the firms have better obserbability on their output??

Kandori (1992) "The Use of Information in Repeated Games with Imperfect Monitoring"(RES 59) answers this question in a general framework.

In the paper, using the concept called "quasi-garbling" which is Blackwell's definition of informativeness, Kandori elegantly shows that

in the general model of discounted repeated games with imperfect monitoring, the set of payoffs attainable via pure-strategy sequential equilibria becomes larger (in the sense of set inclusion) as the observability of the past actions increases. The intuition behind the assertion is that the more accurately "cheating" is detected, the easier it is to enforce coordination.

Thus, the answer to the first question is

in an oligopoly model of the Green-Porter type, the best symmetric equilibrium becomes better and the most severe symmetric punishment (the worst equilibrium) becomes more severe, as the demand becomes less noisy.

The papers written by Kandori are all clear and elegant! How come he could write so many great papers... Every time I read his paper, I feel losing my confidence and realize how far where he was from where I am standing now :(

Professor Kandori was my senior thesis advisor at University of Tokyo.


A note on Abreu (1986)

Original article (link) posted: 20/08/2005

There has been no systematic attempt to study the maximal degree of collusion sustainable by credible threats for arbitrary values of the discount factor. In view of the motivation for moving from static to repeated models, this has some claims to being the essential question at issue.

As argued by Abreu (1983, Ph.D thesis), the fundamental determinant of the limits of collusion is the severity of punishments with which potential deviants from cooperative behavior can credibly be threatened. Accordingly, this paper concentrates principally on characterizing strategy profiles which yield optimal (in the sense of most severe) punishments.

A particular class of paths called two-phase punishments plays a central role. A two-phase punishment is symmetric; in addition it is stationary after the first period, i.e., in the second phase. I show that the optimal two-phase punishment is:
(1) Globally optimal for a certain range of parameter values.
(2) An optimal symmetric punishment.
(3) More severe than Cournot-Nash reversion.
(4) Easily calculated. (It is completely characterized by a pair of simultaneous equations.)
(5) The second phase of the optimal two-phase punishment is the most collusive symmetric output level which can be sustained by the optimal two-phase punishment itself.
(5) says that the optimal two-phase punishment consists of a stick and carrot; furthermore, the carrot phase is the most attractive collusive regime which can credibly be offered when optimal two-phase punishments are used to deter defections. Thus when we solve for optimal two-phase punishments, we simultaneously determine the maximal degree of collusion sustainable by optimal symmetric punishments. It is worth remarking that the stick-and-carrot property is not a curiosum, but arises naturally from the structure of the problem.

Optimal asymmetric punishments have a rather complicated structure and thus far elude description as complete as that provided for optimal symmetric punishments in the earlier section.

(All quoted from Abreu (1986))

I would like to say something about asymmetric cases below.
For delta large enough, optimal symmetric punishments yield 0 payoff hence they are the most severe punishment (notice that a firm's minmax payoff in the component game is zero). And in this case, all firms simultaneously minmax one another in the first phase of the punishment.
However, if an optimal symmetric punishment yields firms positive payoffs (more than their minmax payoffs), then it is not globally optimal.
Abreu gives characterizations of optimal asymmetric punishments. But they are complicated and much less sharper than those with symmetric cases.


Two essential papers by APS

Original article (link) posted: 20/08/2005

What's the difference between APS (1986) and APS (1990)? The distinction is similar to that of Abreu (1986) and Abreu (1988). The earlier papers (both published in JET), APS (1986) and Abreu (1988), analyze the optimal strategies in actual oligopoly models by using powerful properties in repeated games established by them. The later papers (both in Econometrica) extend the results in generalized situations. Although these two Econometrica papers are more general and sophisticated than those of JET, they may have some drawbacks such as, lack of motivation, too concise explanation (to understand), and more seriously, showing no actual optimal strategies. Two papers in JET are strongly motivated by the actual collusion problems in IO, and hence you can see how useful the properties they found are.

Two APS papers heavily rely on the technique used in dynamic programming. Using those technique, they reduce the repeated game to a static structure from which can be extracted the optimal equilibria in question. That is,they construct a new game by truncating the discounted supergame as follows:
after each first-period history, replace the sequential equilibrium successor by the payoffs associated with that successor.

APS (1990) summarize the distinction of the two papers.

First, it relaxes the restriction of symmetry, showing the theory capable of embracing both asymmetric equilibria of symmetric games and arbitrary asymmetric games. Secondly, the sufficiency of using bang-bang reward functions in efficiently collusive equilibria is strengthened to a necessity theorem. Finally, we provide an algorithm useful in computing the sequential equilibrium value set.
(APS (1990), p.1044)

Finally, I would like to remind you of the difference between Abreu and APS. These papers are essentially different in the sense that the former analyze perfect monitoring cases whereas the latter consider imperfect monitoring cases. Moreover, even though all these papers are inspired by dynamic programming technique, their focus is different more or less. The argument in Abreu is about equilibrium paths, but that in APS is about equilibrium payoff sets.


Abreu (1986) "Extremal Equilibria of Oligopolistic Supergames" JET, 39
Abreu (1988) "On the Theory of Infinitely Repeated Games with Discounting" Econometrica, 56
Abreu, Pearce and Stacchetti (1986) "Optimal Cartel Equilibria with Imperfect Monitoring" JET, 39
Abreu, Pearce and Stacchetti (1990) "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring" Econometrica, 58


Price Rigidities

Original article (link) posted: 16/08/2005

In reality, prices cannot be adjusted continuously.
On the demand side, past prices may affect the firms' current goodwill through consumers' learning about the good or switching costs. On the supply side, past prices affect current inventories.
The presence of price rigidities raises the possibility that price reactions are not bootstrap reactions but are simply attempts to regain or consolidate market share.

(Tirole (1988), p.253-4)

In Maskin and Tirole (1988), they assume two firms choose their prices asynchoronously, at odd (even) periods, firm 1 (2) chooses its price. They consider Markov strategies, the simple pricing strategies that depend only on the "payoff-relevant information", and look for a perfect equilibrium in which the firms use Markov strategies. (They call it "Markov perfect equilibrium")

Despite the restriction to simple (Markov) strategies, multiple equilibria exist (indeed, there also exist several kinked-demand-curve equilibria). However, it can be shown that in any Markov perfect equilibrium, profits are always bounded away from the competitive profit (which is 0).
The intuition here is that if firms were stuck in the competitive price region, with the prospects of small profits in the future, a firm could raise its price dramatically and lure its rival to charge a high price for at least some time (the rival would not hurry back to nearly competitive prices). Thus tacit collusion is not only possible (as in the supergame approach) but necessary. Furthermore, it can be shown that there exists only one pair of equilibrium strategies that sustain industry profits close to the monopoly profit. These strategies from a symmetric kinked-demand-curve equilibrium at the monopoly price, and they are the only symmetric "renegotiation-proof" equilibrium strategies (whatever the current price, the firms cannot find an alternative Markov perfect equilibrium that they both prefer).

(Tirole (1988), p.256)


Remarks on APS by Tirole (1988)

Original article (link) posted: 04/08/2005

Tirole (1988) mentions APS in supplementary section. His description about optimal collusions is very clear, so I will quote it here.

Abreu, Pearce and Stacchetti (1986, 1990) show that one can indeed restrict attention to a collusive phase and a punishment phase, characterized by payoffs V+ and V-, where V+ and V- are now the best and worst elements in the set of symmetric perfect equilibrium payoffs. Furthermore, the collusive phase and the punishment phase take simple forms. In the collusive phase, the firms produce output q+. The punishment phase is triggered by a tail test, i.e., it starts if the market price falls under some threshold level p+. Thus, the collusive phase is qualitatively similar to that presumed in Porter (1983) and Green and Porter (1984). The punishment phase, however, does not have a fixed length; rather, it resembles the collusive phase. The two firms produce (presumably high) output q- each. If the market price exceeds a threshold price p-, the game remains in the punishment phase; if it lies below p-, the game goes back to the collusive phase. Thus, the evolution between the two phases follows a Markovian process. The reader may be surprised by the "inverse tail test" in the punishment phase. The idea is that a harsh punishment requires a high output (higher than is even privately desirable); to ensure that the firms produce a high output, it is specified that in the case of a high price (which signals a low output) the game remains in the punishment phase. (Notice that if one restricted punishments to be of the Cournot type, the optimal length of punishment would be T = "infinity", from the APS result on the harshest possible punishment V-.)
(Tirole (1988), p.265)