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   Course Title    Game Theory and Political Theory
Lecturer    Serguei Kokovin
Institution    Novosibirsk State University
Country    Russia


This obligatory course will be delivered at Novosibirsk State University (NSU) in 1999, February-May semester, for 3-rd year economists. It should be a methodological course, teaching standards and tools of analysis rather than empirical facts. It relies on basic cooperative games theory included in the "Mathematical economy" course studied during the 2-nd year, and it provides a base for "Advanced microeconomics: imperfect markets" of the 4-th year, in respect of rationality concepts, game concepts, of understanding political process, governmental failures, etc. Students should be able to formalize and solve (if solvable) most typical politico-economical games.

Accordingly, it has been decided to organize the course in two parts: method-oriented "Game Theory", and empirics-oriented "Political Theory", though most examples of the former are political ones, and very little of the pure non-stylized empirics is included into the latter.



Currently, due to the limitations of the overall teaching schedule, it is decided to restrict the course to 18 lectures (36 academic hours), with no seminars, concluding with a final exam. At the same time, game theory teaching should be based primarily on exercises. This will be implemented through extensive homework tasks, small tasks during some lectures, and one or two written control tests during the semester. In addition, I have positive experience of solving during a lecture typical problems right on the blackbord with the help of the audience, in interactive communication.



Part I: Basic Game Concepts

Lecture 1

0. Game as any situation with rational agents. Game classification by various features: by admissible sets (finite or infinite), by the goal structure (antagonistic or non-zero-sum games), by information and behavior (cooperative and non-cooperative games, different game concepts among both types), by the way of formalization (strategic form and extensive form). Solution notions.

1. Strategic (normal) Form Games

1.1. Dominating and dominated strategies, dominant equilibrium (DE).

Examples of dominant strategies in finite and infinite games (Original prisonerís dilemma and the dilemma in disarmament, dominant strategies in Vickrey auction, in price competition for commodities-substitutes). Equivalency of DEi and DE.

1.2. Maximin.

Maximin (MM) as cautious solution when moves are unobservable. Examples: prisonerís dilemma, "polite drivers", voting for 3 candidates.

Maximin as strategic behavior in antagonistic (zero sum) games. Voting for property redistribution as a zero sum game, Condorset paradox. DEŐ MM.

Lecture 2

1.3. Nash equilibrium (NE).

NE under observable moves and myopic behavior (prisonerís dilemma). NE in extensive form game: "polite drivers" ("chicken game"), connection between extensive and normal forms. NE in continuous-strategy examples: spatial competition of political parties, price competition for commodities-substitutes. Geometry: reply functions or mappings.

1.4. Pareto-efficiency. C-core. Interpretation of NE as an enforced agreement (prisonerís dilemma). DEŐ NE.

Lecture 3

1.5. Nash equilibrium in mixed strategies (NEm.)

Coin game and NEm . Solution rule and geometry: reply functions or mappings. Full characterization of solutions to 2x2 games (1,3 or continuum, Pareto-efficiency or inefficiency). Nash theorem of existence (proof) and its consequences: NEm??. Brown-Jackson theorem for computing NEm. ?Saddle points: Sad=NE« MM , their existence.

1.4. Strategic behavior: reduction of weakly dominated strategies under common knowledge: Sophisticated Equilibrium (SE). Voting example. DEŐ SE.

Leadership and Stackelberg equilibrium. Multiple equilibria and struggle for leadership ("chicken game").

Lecture 4

2.3. Incomplete information: Bayesian equilibria (BE).

Lotteries and preferences over lotteries. Neumann-Morgenstern expected utility function and its existence for a given preference. Risk aversion and its measures.

Incomplete information about partnerís type, Bayesian equilibrium: trespassers and inspectors, educational signalling game, advertising game. BE as NE in extended game, its existence.

Lecture 5

2. Extensive Form Games and incomplete information

2.1. Subgame perfect equilibrium (SPE).

"Pilot and terrorist" game. Backward induction for finding SPE. Connection between extensive and normal forms again. Examples: Condorset winners, voting agendas, matches game, finite and infinite bargaining procedures. Relation of SPE to NE, to SE, and existence theorems: SPE??, SE??.

2.2. Informational sets. SPE in imperfect information case: "pilot and terrorist" again, passing the bill. Possible inexistence.

2.3 Centipede game; trembling hand perfection.

Homework: Pirattes game.

Lecture 6

2.3. Perfect Bayesian equilibria.

Perfect Bayesian equilibrium: a thief and a policeman, Caribean crises.

2.4. Dynamic games with symmetric information.

Creadible threats, sunk costs ("game of nuisance suits"). Recoordination of Pareto-dominant equilibria. Discounting. Evolutionary equilibrium: hawk-dove game (evolutionary stable strategies).

Lecture 7

2.5. Reputation and repeated games with symmetric information.

Finite gaims and Chainstore paradox.

The repeated Prisonerís dilemma: troops shirking in World War I, absteining from gas attacks in World War II.

Infinitely repeated games, minimax punishments and the Folk theorem. Product quality in an infinitely repeated game.

Bargining: splitting a pie. Nash bargaining solutions in finite time and infinite time. Incomplete information.

2.6. Dynamic games with asymmetric information.

Entry deterrence game. Incomplete information in the repeated prisonerís dilemma.

2.7. Additional cooperative concepts: N-M-solution, a -core, b -core.

Part II: Political and economico-political games

Lecture 8

Goals of the following lectures. General notion of governmental failure.

3. Voting, elections and public choice under full rationality

3.0. Some empirics; different constitutions: Westminster model and presidential model. Separation of powers and cabinet formation.

Idea of non-manipulation and incentive compatibility. Example: Franklinís constitutional design: electing Judges by lawyers.

3.1. Positive approach to public choice problem.

Majority rule (Condorset tournament): Pareto efficient, non-manipulable, but non-transitive.

Analysis of widely used voting rules: simple plurality and two stage majority.

Can Condorset looser win elections? Manipulating an election compaign: monotonicity and participation properties violated. Mayís theorem. Manipulation by unsincere preference revealation and by irrelevant alternative.

Lecture 9

3.2. Normative approach to public choice problem.

Representative democracy problem (Arrowís impossibility theorem for preference aggregation) and direct democracy problem (Gibbard-Satterthwait impossibility theorem). Solution for restricted preference set (single-peakedness in "left-right" choice): median voter rule gives transitivity and the Condorset winner.

3.3 Direct voting for tax level: general equilibrium can be efficient or inefficient. Voting in two or more dimensions: possible intransitivity.

Tiebout tax-competition feet-voting model of federalism: efficient clusters ("clubs"), willingness-to-pay taxes.

Lecture 10

3.4. Representative democracy; political enterprenership.

Two-party presidential compaign: setting a platform (spatial competition in "left-right" choice); convergence of platforms and equivalence to direct democracy median voter rule, solution in multi-modal case. Multi-party compaign: no Nash equilibrium. Electoral blocks.

Electoral blocks in multi-party parliamentary campaign; division of seats and cabinet formation under different constitutions: Italian instability.

3.5. USA presidential two-candidate elections within the electoral college: president vs. states redistribution game: policy distortion by college. Candidates allocating time (money) game: no Nash equilibria; stimuli for Watergate.

Why presidential constitution and college supress small parties.

Lecture 11

4. Elections as games with incomplete information

4.1. Elections with uninformed voters, rational uninformedness, the game with revealing candidatís positions through opinion polls: equivalence to full-information median voter case. Poll manipulation.

4.2. Rational unparticipation (rational behavior can not explain participation). Low voting turnout and responsible political parties; does abstention from voting bias the policy?

4.3. Money-driven elections. Simple money-driven elections as Groves-Clark mechanism among oligarchies competing; non-manipulation and constrained efficiency. Oligarchies bargaining. Organizational power to form pressure groups: Olsonís model; small groups have unproportionally big power. Countervailing effect: long-living parties in reputation game. Political cycle under bounded rationality.

Lecture 12

5. Voting and other games within legislature

5.1. Committee formation: single-transferrable-vote rule. Relative power of fractions: Shapley vector. Bargaining. The paradox of power: the weakest win in 3-fraction "Condorset paradox" game.

5.2. Agendas and Condorset winners: the agenda predetermines the result.

5.3. Bayesian (perfect) equilibria. Legislator-lobbyst game. A game with two-sided incomplete information: BPE in strategic voting of fractions.

Politician- lobbyst game of bribing (Ital.model).

5.4. Agendas reconsidered: passing the bill as BPE.

5.5. Electoral model of redistribution within the budget: redistribution from future generations, budget deficit (national debt).

5.6. Pressure groups and log-rolling in parlimentary budget voting: budget deficit reconsidered. Bargaining.

Lecture 13

6. Regimes and their change

6.1. Empirics on regimes: Traditional and modern classification of regimes: totalitarian, authoritarian, democratic, liberal- democratic, etc., examples.

Regime as equilibrium of institutions and their performance.

6.2. Regimes: Public choice by rational dictator, monarchy, oligarchy: comparative efficiency. Model of nationís choice between democracy and autocracy.

6.3. Redistribution: Roemerís model of social revolution (Lenin and Tzar), connecting equity and stability. Voting against the rich and against the future; progressive taxation. Money-driven elections countervailing redistribution.

Lecture 14

7. Some irrational politics

7.1. Ideologies: liberalism, conservatism, socialism, communism, moslem fundamentalism.

Enthusiasm and a model of harismatic politician. How much sionists and antisemits need each other. Makkiavellyís conventional wisdom. Setting bridges on fire. Establishing a behavioral norm: model of altruists, conformists and egoists; possibility of honest parliment.

7.2. Multi-party election game within ideological constraints.

7.3. Regime changes: Roemerís model again: Hitler. Other models of revolutions and coups; power resources, tolerance thresholds.

7.4. Model of would-be-dictator and the people.

Lecture 15

8. Intragovernmental games: bureaucracy and corruption.

8.1. Loss of control in bureaucracies: basic principle-agent problem, informational problem. Soviet case.

8.2. Corruption 1. Bureaucratic enterprenership in incomplete-information games and governmental failure: Indian case.

8.3. Corruption 2. Knights, conformists and egoists: how much samurays you need for making the hierarchy working (modelling collaps of communism)?

Bribes as Groves-Clark mechanism reconsidered.

8.4. Corruption 3. Rent-seeking or productive activity: low and high equilibria.

Lecture 16

9. Several international games: conflict and cooperation

9.1. Kingdom formation: Shumer and Egypt.

9.2. Superpowers struggle: Athens - Sparta, Rome - Karthagen, USA ó USSR.

9.3. Small country: to resist or to capitulate?

9.4. Does nuclear threat support peace? Caribean crisis model.

9.5. Collective defence: "European equilibrium".

2.3. Elections with several candidates.

Lectures 17, 18 should be used for written tests.



A. Mandatory readings:

1. David M. Kreps. 1990. A Course in Microeconomic Theory.- Princeton University Press, Princeton. .

2. V.Busygin, S.Kokovin, A.Tsyplakov. 1996. Lectures on microeconomic methods.- TEMPUS(TACIS), NSU, Novosibirsk.

3. Peter C. Ordeshook. 1992. A Political Theory Primer.- Routledge, N.-Y., London.

Use of readings:

Lectures 1,2 (DE, MM, NE): D.Kreps - Sections 11.1-3, V.Busygin - Section 1.

Lecture 3 (NEm,SE, StE): D.Kreps - Sections 12.4-7, 12.2, V.Busygin - Section 1, _P.Ordeshook - Section 3.2-3.6.

Lecture 4 (BE). , D.Kreps - Section 13.1, P.Ordeshook - Section 5.4-5.5.

Lecture 5 (SPE??, SE??). , D.Kreps - Sections 11.4, 12.7., P.Ordeshook - _Sections 2.2-2.5, 5.6.

Lecture 6 (PBE, Evolutionary equilibrium) D.Kreps - Sections 13.1-2, P.Ordeshook - Sections 4.9, 5.8.

Lecture 7 (Repeated games, reputation) D.Kreps - Sections 14.1-6, _P.Ordeshook - Sections 5.10, 6.3.

Part II

Lecture 8 A.Heywood - Ch.2, P.Ordeshook - Sections 2.4, 3.3., H.Moulin - Ch. 6.

Lecture 9 H.Moulin - Ch. 6., D.Kreps - Section 18.4, J.Green & J.-J.Laffont - Ch.?.

Lecture 10 P.Ordeshook - Sections 4.1-5.

Lecture 11 P.Ordeshook - Sections 5.1-10.

Lecture 12 P.Ordeshook - Sections 4.4-6, -10.

Lecture 13 A.Heywood - Ch.2, P.Ordeshook - Sections 6.3-7.

Lecture 14 A.Heywood - Ch.3, D.Kreps - Section 13.3.

Lecture 15 A.Heywood - Ch.17, D.Kreps - Sections 16, 18.1-3., I., Eshel et all.

Lecture 16 P.Ordeshook - Sections 4.8, 5.8, 6.9.


B. Recommended readings:

1. H.Varian. Microeconomic Analysis.

2. A.Mas-Colell, M.D.Winston & J.Green. 1995. Microeconomic Theory.- N.Y. Oxford University Press.

3. R.B.Myerson. 1991. Game Theory (Analysis of Conflict).- Harvard U.P., Camridge, London.

4. Fudenberg, Drew & Jean Tirole. 1991. Game theory.- MIT Press. Cambridge, Massachusets.

5. Andrew Heywood. 1997. Politics.- London, Macmillan.

6. J.-E.Lane & S.Ersson. 1994. Comparative politics.- Cambridge, Blackwell.

7. R.Hague, M.Harrop, S.Breslin. 1992. Comparative Government and Politics.- London, Macmillan.

8. Herve Moulin. 1988. Axioms of Cooperative Decision Making.- Cambridge U. Press, Cambridge.

9. J.Green & J.-J.Laffont. 1981. Public Choice.

10. I.Eshel, L.Samuelson & A.Shaked. 1998. Altruists, Egoists and Hooligans in a Local Interaction Model.- The Amer.Ec.Review v.88, N 1.



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