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Microeconomics I: Game Theory
Introduction:What is Game Theory?
(see Osborne, 2009, Sect 1.1)
Dr. Michael Trost
Department of Applied Microeconomics
October 25, 2013
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What is game theory?
Game theory is the scientific discipline that studies situationsin which decision-makers interact.
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Situations of interaction
Situations of interaction are situations in which the well-beingof a decision maker depends not only on her own action, butalso on the actions of other decision-makers.
Henceforth, such situations are referred to as games.
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Situations of interaction
EXAMPLES of situations of interaction:
Board and card games (e.g., chess, back gammon, poker,bridge, etc.)
Economic games (e.g., firms competing for business,bidders competing in auctions, joint ventures)
Political games (e.g., political candidates competing forvotes, international trade agreements)
Biological games (e.g., animals fighting over preys andterritories)
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What is not a game?
Two cases: Isolated or insignificant decision maker
. (Isolation) Your decisions affect only yourself- Personal issues like whether to go jogging or not, how many
movies to watch in a week, what to build in a sand-box.- Price-setting behavior of a monopolistic firm
. (Insignificance) Because there so many decision-makersinvolved, your decision does not (really) affect others’decisions.
- Buying foreign exchanges or stocks.- Price-taking behavior of a firm (assumption of perfect
competition)
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Let’s play a game: The Guessing Game
The rules of this game are as follows:
. Each of you secretly submits a number from interval[0,100]. The winner is the person whose submitted numberis the closest to the two-third of the mean of all submittednumbers.
. The winner receives a prize. If there are several winners theprize will be divided equally among them.
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Interaction in the Guessing Game
As its name suggests, the GUESSING GAME induces a situationof interaction:
The success of a player’s guess depends essentially on thenumbers guessed by the other players.
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Game-theoretic models
Like other sciences, game theory consists of a variety of models.A game-theoretic model is an abstract representation of real-lifesituations of interaction.
Such abstractions allow us to study a wide range of social andbiological phenomena and to improve our understanding of theworld.
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Rules of a game
A game is a detailed description of a situation of interaction. Itdescribes the rules under which this interaction takes place.
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Rules of a game
For example, a game specifies
the set of participants (which are referred to as players)
the set of actions available by the players
the set of outcomes resulting from the available actions
the sequence of the players’ moves
the information the players have about the past moves ofthe other players
the information the players have about the goals pursuedby the other players
. . .
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Classes of games
A class of games is a set of games which have certain rules incommon. Following classifications of games are popular ingame theory.
- Cooperative and noncooperative games
- Strategic and extensive games
- Games with complete and with incomplete information
- Games with perfect and with imperfect information
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Cooperative and noncooperative games
Noncooperative games are games in which the players chooseindependently their actions. The players are not able to enforcea binding agreement on their actions.
Cooperative games (also called coalitional games) are games inwhich the players can form coalitions and engage in a bindingagreement on their actions.
REMARK: In this course, we only deal with noncooperativegames.
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Strategic games and extensive games
Strategic games (also known as simultaneous move games)describe situations of interactions in which each player movesonly ones and the players’ decisions are made simultaneously(i.e, when choosing an action each player is not informed ofactions chosen by the other players)
EXAMPLES: ROCK-PAPER-SCISSORS, MATCHING PENNIES,presidential election
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Strategic games and extensive games
Extensive games (also known as dynamic games) describesituations of interactions in which the players movesequentially.
EXAMPLE: TIC-TAC-TOE, MARIENBAD GAME, poker, eBayauction
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Tic-Tac-Toe
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Marienbad Game
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Complete and incomplete information
A game takes place under complete information if there iscommon knowledge about the preferences the players have (i.e.,every player knows the preferences of every player, everyplayer knows that every player knows the preferences of everyplayer, and so on ad infinitum) .
A game takes place under incomplete information if someplayer is uncertain about the preferences of some other player.
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Perfect and imperfect information
A game takes place under perfect information if each playerwhen she is deciding is informed about the past moves of heropponents.
A game takes place under imperfect information if some playeris uncertain about the past moves of her opponents.
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Game-theoretic solution concepts
A game describes the set of actions a player can do, but does notspecify the actions that the player do take.
A solution of a game determines the set of actions that may berealized by the players and a solution concept for a class gamesdetermines for each game of this class the set of actions that maybe realized by the players.
Game theory aims to provide reasonable solutions for classes ofgames and to examine their properties.
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The Nash equilibrium concept
The most prominent solution concept of game theory is thesolution concept introduced by John F. Nash (1950), which isknown nowadays as the Nash equilibrium concept.
John F. Nash (born on June 13, 1928) received,together with John C. Harsanyi and ReinhardSelten, the Sveriges Riksbank Prize in EconomicSciences in Memory of Alfred Nobel in 1994 fortheir “pioneering analysis of equilibria in thetheory of noncooperative games”.
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The Nash equilibrium concept
The actions chosen by the players constitute a Nash equilibriumif they satisfy following property of stability: None of theplayers has an incentive to deviate from her action providedthat the other players have already realized these actions.
QUESTION: What’s the Nash equilibrium of the GUESSING
GAME? Is it reasonable?
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Positive and normative game theory
Game theory is used to address
positive issues of situations of interaction.- Why do interacting decision-maker behave as they do?
(explanation)- How will decision-makers behave in situations of
interaction? (prediction)
normative issues of situations of interaction.- How should interacting decision-maker behave?
(recommendation)
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Positive applications of game theory
For example, game theory allows us to understand
- why public goods (e.g., defense or flood protection) areoften provided by state.
- why arrangements of production cartels are often brokenby their members.
- how the size of sunk costs will affect the price setting of amonopolistic firm.
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Normative applications of game theory
For example, game theory helps us to figure out
- the winning (or at least non-losing) strategies for simplerecreational games (e.g., TIC-TAC-TOE, MARIENBAD
GAME).
- the profit-maximizing bids in auctions.
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Outline of this course
I The theory of rational choice
(a) Preferences and utility function(b) Expected utility function
II Simultaneous move games with complete information
(a) Nash equilibrium in pure strategies(b) Nash equilibrium in mixed strategies
III Simultaneous move games with incomplete information
(a) Bayesian games and Bayes-Nash equilibrium(b) Auctions
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Outline of this course
IV Dynamic games with complete information
(a) Extensive form games and subgame perfect equilibrium(b) Bargaining games
V Dynamic games with imperfect information
(a) Repeated games and the Folk Theorems(b) Signalling games and sequential equilibrium
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Lectures
DATE: The two-hour lectures game theory start on October 25and take place on Fridays, 8:30 a.m., room LG 2/213.
ANNOUNCEMENTS: An additional two-hour lecture (instead ofa tutorial) is given on October 25, Friday, 10:15 a.m., room LG2/213. In the last week of lectures a mock exam will bediscussed.
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Tutorials to the lectures
In addition to the lecture tutorials are offered.
DATE: The two-hour tutorials start on November 1 and takeplace on Fridays, 10:15 a.m., room LG 2/213.
EXERCISES: Exercise sheets for tutorials will be uploaded aweek before. We advise you to go carefully through theseexercises before we will discuss them in tutorials. The formationof learning groups is highly recommended.
REMARK: There are no extra credits for the tutorials.
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Literature
Main textbook for this course:
Osborne, M. (2009), An Introduction to Game Theory, 2ndedition, Oxford University Press, Oxford.)
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Literature
Further possible readings:
Heifetz, A. (2012), Game Theory: Interactive Strategies inEconomics and Management, Cambridge University Press,Cambridge. (Introductory textbook)
McCarty N. and Meirowitz, A. (2007), Political Game Theory:An Introduction, Cambridge University Press, Cambridge.(Advanced textbook)
Osborne, M. and Rubinstein, A. (1994), A Course in GameTheory, MIT Press, Cambridge. (Advanced textbook)
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Acknowledgments
I am indebted to Ozgur Gurerk and Manfred Konigstein fortheir permission to paste parts of their teaching materials intothese lecture notes.
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