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.
2011-02-28
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:
2011-02-22
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:
The publisher's description says:
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.
2011-02-19
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*.
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*.
2011-02-12
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:
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.
2011-02-05
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
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
2011-01-30
Japan Crowned Kings of Asia
Congratulations!!
Japan became the first team to win the AFC Asian Cup FOUR times as Tadanari Lee's goal in the second period of extra time clinched a 1-0 victory over Australia at Khalifa Stadium. See more in this article.Many many thanks to our national team for having shown us such great games in this Asia Cup tournament :) You guys are really awesome!! (the following movie is also great!)
2011-01-25
Aumann's survey
Original article (link) posted: 20/10/2005
Aumann (1985) “What is Game Theory Trying to Accomplish?” in Frontiers of Economics
This is a survey article by Professor Aumann, a Nobel Laureate of this year. The paper consists of 18 sections. The first 8 sections concerned with generalities of game theory with particular attention of the concept of science, sections 9-17 illustrate four equilibrium concepts (Nash Equilibrium, Core, Von Neumann-Morgenstern Stable Set, and Shapley Value) with applications, and section 18 concludes. In the first half of the paper, he put his point of view about game theory (or economics) as a science, which is very deep and insightful. It is highly recommended to read first 8 chapters for those who are interested in such questions as “What is (social) science?” and “What is the definition of science or truth?”.
His main claim is stated in Introduction as follows;
A solution concept (could be replaced with “a scientific theory”) should be judged more by what it does than by what it is; more by its success in establishing relationships and providing insights into the workings of the social processes to which it is applied than by considerations of a priori plausibility based on its definition alone.
Aumann (1985) “What is Game Theory Trying to Accomplish?” in Frontiers of Economics
This is a survey article by Professor Aumann, a Nobel Laureate of this year. The paper consists of 18 sections. The first 8 sections concerned with generalities of game theory with particular attention of the concept of science, sections 9-17 illustrate four equilibrium concepts (Nash Equilibrium, Core, Von Neumann-Morgenstern Stable Set, and Shapley Value) with applications, and section 18 concludes. In the first half of the paper, he put his point of view about game theory (or economics) as a science, which is very deep and insightful. It is highly recommended to read first 8 chapters for those who are interested in such questions as “What is (social) science?” and “What is the definition of science or truth?”.
His main claim is stated in Introduction as follows;
A solution concept (could be replaced with “a scientific theory”) should be judged more by what it does than by what it is; more by its success in establishing relationships and providing insights into the workings of the social processes to which it is applied than by considerations of a priori plausibility based on its definition alone.
2011-01-20
What is the New Keynesian Approach?
I received a comment on the previous post (link) asking about the new Keynesian approach. So, let me try to provide some information based on the author's explanation of this concept. According to Walsh, the new Keynesian approach employs equilibrium models with some frictions or rigidities. He says, the new Keynesian approach uses
Another essential book on the new Keynesian monetary economics, written by one of the leading researchers in the field, is the following. This might also be useful for students and central bank economists alike.
models based on dynamic optimization and nominal rigidities in consistent general equilibrium framework.The monetary frictions or rigidities that Walsh refers include
money-in-utility function, cash-in-advance, search model of money, informational, portfolio, and nominal rigidities, and credit frictions,which are all discussed in the book.
Another essential book on the new Keynesian monetary economics, written by one of the leading researchers in the field, is the following. This might also be useful for students and central bank economists alike.
2011-01-18
Walsh 3rd
A leading advanced textbook in monetary economics has been revised and released last year.
Monetary Theory and Policy, Third Edition
The author describes the new edition, which seems to be an essential reference in the field, as follows:
Monetary Theory and Policy, Third Edition
The author describes the new edition, which seems to be an essential reference in the field, as follows:
This third edition reflects the latest advances in the field, incorporating new or expanded material on such topics as monetary search equilibria, sticky information, adaptive learning, state-contingent pricing models, and channel systems for implementing monetary policy. Much of the material on policy analysis has been reorganized to reflect the dominance of the new Keynesian approach. Monetary Theory and Policy continues to be the only comprehensive and up-to-date treatment of monetary economics, not only the leading text in the field but also the standard reference for academics and central bank researchers.
2011-01-14
Summary of IO Papers (by O. Williamson)
Original article (link) posted:18/10/2005
Industrial Organization (edited by O. Williamson) contains 23 important IO papers in the literature. The below is the list of short summaries of selected papers written by the editor, O. Williamson which are quoted from the ‘Introduction’. Since most of the papers are still relevant and must-read for IO researchers, the list may be a helpful guide for you. Please enjoy it!
Alchian (1950) “Uncertainty, Evolution, and Economic Theory”
The paper is significant in several directions. For one thing, selection arguments play a large role in virtually all forms of long-run competitive analysis. Second, the use of simplifying assumptions of an ‘as if’ hyperrationality kind can sometimes be justified by invoking selection arguments. And third, Alchian’s treatment of evolutionary issues is insightful and is carefully nuanced.
Holmstrom (1982) “Moral Hazard in Teams”
The author extends earlier work of a principal/single-agent kind to include relations between multiple agents in teams. The paper develops a sufficient statistic condition on relative performance evaluation according to which competition among agents is not valued because it induces added effort but rather than because it is a device to extract information optimality.
Grossman and Hart (1986) “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration”
Although the formal modeling of incomplete contracting is formidably difficult, the paper develops a model in which both ex-ante alignment and ex post adaptation differences between market and hierarchical models of organization are recognized.
Dixit (1980) “The Role of Investment in Entry-Deterrence”
The paper sets out the basic logic and demonstrates the critical importance of investments in durable, nonredeployable assets to effect entry deterrence. Given credible pre-entry commitments, the logic of entry barriers was made secure. But inasmuch as a duopoly setup is highly specialized, the empirical significance and antitrust enforcement ramifications of the argument can be questioned.
Aghion and Bolton (1987) “Contracts as a Barrier to Entry”
What the paper examines is whether an incumbent supplier can fashion a penalty clause, the effects of which penalty make the incumbent better off. It is shown that penalties can be devised such that lower cost entrants can be deterred – although not necessarily precluded – from entering.
Milgrom and Robertes (1982) “Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis”
The use of limit pricing here turns on an information asymmetry between the sitting monopolist (or incumbent) and the potential entrant. Whereas the incumbent knows its costs, the potential entrant can only infer them. The incumbent would like to signal to the potential entrant that it has low costs, thereby to deter entry. Although it can do this by setting a low price, the entrant is alert to the strategic nature of the game and redcognizes that signaling can be used for strategic purpose.
Kreps and Wilson (1982) “Reputation and Imperfect Information”
The paper shows that the introduction of a small amount of imperfect or incomplete information can transform such a game into one whereby monopolists strategically contest entry. The logic of unraveling gives way to a logic of reputation in an intertemporal framework into which imperfect information has been introduced.
Baumol, Pazner and Willig (1986) “On the Theory of Perfectly-Contestable Markets”
The paper summarizes the central arguments of their influential book and advances the argument that the perfectly contestable market – that in which asset-specificity is negligible, whence assets are easily redeployable to alternative uses and by alternative users – is usefully regarded as an analytical and public policy benchmark.
Salop (1979) “Monopolistic Competition with Outside Goods”
The author uses a spatial competition model to investigate monopolistic competition. Salop’s treatment nicely displays the key features of a monopolistically competitive contest in a spatial equilibrium setting.
Industrial Organization (edited by O. Williamson) contains 23 important IO papers in the literature. The below is the list of short summaries of selected papers written by the editor, O. Williamson which are quoted from the ‘Introduction’. Since most of the papers are still relevant and must-read for IO researchers, the list may be a helpful guide for you. Please enjoy it!
Alchian (1950) “Uncertainty, Evolution, and Economic Theory”
The paper is significant in several directions. For one thing, selection arguments play a large role in virtually all forms of long-run competitive analysis. Second, the use of simplifying assumptions of an ‘as if’ hyperrationality kind can sometimes be justified by invoking selection arguments. And third, Alchian’s treatment of evolutionary issues is insightful and is carefully nuanced.
Holmstrom (1982) “Moral Hazard in Teams”
The author extends earlier work of a principal/single-agent kind to include relations between multiple agents in teams. The paper develops a sufficient statistic condition on relative performance evaluation according to which competition among agents is not valued because it induces added effort but rather than because it is a device to extract information optimality.
Grossman and Hart (1986) “The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration”
Although the formal modeling of incomplete contracting is formidably difficult, the paper develops a model in which both ex-ante alignment and ex post adaptation differences between market and hierarchical models of organization are recognized.
Dixit (1980) “The Role of Investment in Entry-Deterrence”
The paper sets out the basic logic and demonstrates the critical importance of investments in durable, nonredeployable assets to effect entry deterrence. Given credible pre-entry commitments, the logic of entry barriers was made secure. But inasmuch as a duopoly setup is highly specialized, the empirical significance and antitrust enforcement ramifications of the argument can be questioned.
Aghion and Bolton (1987) “Contracts as a Barrier to Entry”
What the paper examines is whether an incumbent supplier can fashion a penalty clause, the effects of which penalty make the incumbent better off. It is shown that penalties can be devised such that lower cost entrants can be deterred – although not necessarily precluded – from entering.
Milgrom and Robertes (1982) “Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis”
The use of limit pricing here turns on an information asymmetry between the sitting monopolist (or incumbent) and the potential entrant. Whereas the incumbent knows its costs, the potential entrant can only infer them. The incumbent would like to signal to the potential entrant that it has low costs, thereby to deter entry. Although it can do this by setting a low price, the entrant is alert to the strategic nature of the game and redcognizes that signaling can be used for strategic purpose.
Kreps and Wilson (1982) “Reputation and Imperfect Information”
The paper shows that the introduction of a small amount of imperfect or incomplete information can transform such a game into one whereby monopolists strategically contest entry. The logic of unraveling gives way to a logic of reputation in an intertemporal framework into which imperfect information has been introduced.
Baumol, Pazner and Willig (1986) “On the Theory of Perfectly-Contestable Markets”
The paper summarizes the central arguments of their influential book and advances the argument that the perfectly contestable market – that in which asset-specificity is negligible, whence assets are easily redeployable to alternative uses and by alternative users – is usefully regarded as an analytical and public policy benchmark.
Salop (1979) “Monopolistic Competition with Outside Goods”
The author uses a spatial competition model to investigate monopolistic competition. Salop’s treatment nicely displays the key features of a monopolistically competitive contest in a spatial equilibrium setting.
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