*Conducted in term:*2020Z

*Erasmus code:*14.3

*ISCED code:*0311

*ECTS credits:*4.5

*Language:*English

*Organized by:*Faculty of Economic Sciences

*Related to study programmes:*

# Advanced Microeconomics Game Theory) 2400-ICU1AMI

Game Theory

1. EXPECTED UTILITY THEORY:

Preferences Over Lotteries, Independence, von Neumann-Morgenstern Utility, Expected Utility Theorem, Allais Paradox, Machina's Paradox. (MC, pp. 168-182)

2. MONETARY LOTTERIES AND RISK AVERSION:

Risk Aversion Equivalence Theorems, Coefficient of Absolute Risk Aversion, Comparisons Across Individuals, Coefficient of Relative Risk Aversion. (MC, pp. 183-193)

3. RETURN-RISK COMPARISONS:

1st and 2nd Order Stochastic Dominance, Mean-Preserving Spreads. Exercises. (MC, pp. 193-199)

4. INTRODUCTION AND STRATEGIC FORM GAMES:

TStrategic (Normal) Form Games, Dominant Strategy, Iterated Elimination of Dominated Strategies. (FT, pp. 1-22, 45-47; OR, pp. 1-15, 58-62)

5. STRATEGIC FORM GAMES:

Existence of Nash Equilibrium. Correlated Equilibria. (FT, pp. 29-35, 53-59; OR, pp.19-20, 44-48)

6. STRATEGIC FORM GAMES:

Applications: Co-ordination, Oligopoly, Auctions.

7. BAYESIAN GAMES

Bayesian Nash Equilibrium, First-price Auction, Double Auction. (FT, pp. 207-215; OR, pp. 24-29)

8. MECHANISM DESIGN

Static Mechanism Design Problems. Example: Principal-Agent, Revenue Equivalency Theorem, Inefficiency Theorem (FT, pp. 243-292; OR, pp. 177-191)

9. EXTENSIVE FORM GAMES:

Constructing a Game Tree. Extensive vs. Normal Form. (FT, pp. 67-82, 85-87; OR, pp. 89-97)

10. EXTENSIVE FORM GAMES:

Subgame Perfect Nash Equilibrium. Applications: Entry Deterrence, Pre-Commitment, Non-cooperative Bargaining. Centipede. (FT, pp. 92-10, 107-114; OR, pp. 97-131)

11. REPEATED GAMES:

Finitely repeated games. Infinitely Repeated Games. Application: Tacit Collusion. Folk Theorems. (FT, pp. 145-168; OR, pp. 133-161)

12. REPEATED GAMES:

Pareto Perfection, Renegotiation Proofness, Markov-perfection. (FT, pp.174-182, 501-513)

13. COOPERATIVE GAME THEORY AND GENERAL EQUILIBRIUM THEORY

Core, Shapley Value and Other Solutions, Walrasian Equilibrium Allocation (OR, pp. 255-297, MC, pp. 652-659, 846-848; V, pp.387-392)

14. AXIOMATIC BARGAINING:

Nash Solution, Kalai-Smorodinsky Solution, Egalitarian Solution (OR, pp. 299-310;

MC, pp. 838-846)

15. EVOLUTIONARY GAME THEORY:

Replicator Dynamics (FT, pp. 23-29; OR, pp. 48-51)

General Equilibrium Theory

1-2. DUALITY APPROACH TO DEMAND PROPERTIES

Money metric utility function, Roy's identity, Walrasian Demand, Welfare measures (MC, pp. 40-95; V, pp. 94-113)

2-3. NEO-WALRASIAN THEORY OF PRODUCTION

Free disposability in production, Axioms of production, Efficient production

5. Midterm exam

6. 2x2 PURE EXCHANGE MODEL

Nonwasteful Feasible Allocation, Endowment, Offer Curve, Pareto Set, Contract Curve (V, pp.313-316, 323-329; MC, pp. 515-525, 538-540)

7-8. 1x1x2x1 ROBINSON CRUSOE MODEL. 2X2X2X2 SMALL OPEN ECONOMY

Excess Demand, Intermediate Goods, Production Possibility Set, Interior Equilibrium, Rybczynski Tehorem, Stolper-Samuelson Theorem, Factor Price Equalization Theorem (MC, pp. 525-538)

9-10.GENERAL MODEL

Private Ownership Economy, Walrasian (quasi)equilibrium, (Quasi)equilibrium with transfers, Fundamental Theorems of Welfare Economics, Locally nonsatiation preferences, Walras' Law (V, pp.317-322, 329-332; MC, pp. 545-557, 578-583)

COMPUTABLE GENERAL EQUILIBRIUM MODELING (classes in a computer lab.):

11 GAMS software, i/o table, simple exercises

12. A pure exchange model in GAMS

13. A 2x2x1 production model

14. Open economy model

15. Alternative production functions. Endogeneous labour supply

## Type of course

## Course coordinators

## Mode

## Learning outcomes

Knowledge and skills

1. Students know and understand the preference relations concept and the concept of utility maximization. Students understand the duality in consumer theory.

2. Students know and understand the producer behaviour. They are aware of the duality of producer problem

3. Students know and understand the methods of economic welfare evaluation.

4. Students are able to solve and analyze the following general equilibrium models: the pure exchange model, the Robinson Crusoe model, and the small open economy model.

5. Students understand the basic theorems of welfare economics. They are able to distinguish competitive equilibrium from the Pareto optimum allocation/social planner allocation.

6. Students know how to implement a simple GE model in GAMS software

7. Students know how to evaluate changes in economic environment with the use of simple GE model

General skills

1. Students understand that microeconomics can be applied to real economic and social issues and that the analysis can be performed using economic models

2. Students can interpret reality based on simple GE models and they are able to combine the micro and macro view.

3. Students are able to undertake employment in entreprises or public organizations that deal with design and assessment of economic policy

4. Students are able to formulate and present their views based on their knowledge and engage in discussion concerning these views.

5. Students are able to fulfill their duties and plan the work schedule on their own.

SW01, SW02, SW03, SW04, SU01, SU02, SU03, SU04, SU05, SU06, SU07, SK01, SK02, SK03

## Assessment criteria

• Completing Advanced Microeconomics requires completing the two separate parts:

o Game Theory –prof. Tomasz Żylicz

o General Equilibrium Theory– dr Jan Hagemejer

• In order to complete each of the parts students need to:

o Collect at least 50% combined points from the two following components:

midterm exam (weighted 50%);

final exam (50%).

• The final grade will be average of the grades from the two separate parts (rounded up), with the restriction of both of them being at least 3 (otherwise the final grade becomes 2).

• All exams are to be taken by all students at the same time (only one date for everyone).

• There will be only one possibility to retake any of the failed exams for all students at the same time.

• Absence from any of the exams is equivalent to failing it.

• There will be no other possibilities of completing the course.

• ‘0 tolerance for cheating’.

## Bibliography

• (MC) Mas-Colell, A., M. D. Whinston, J. R. Green, Microeconomic Theory, Oxford University Press, 1995

• (V) Varian, H. R., Microeconomic Analysis, W. W. Norton & Co., ed. 3′

• Varian, H. R., Intermediate Microeconomics, ed. 7

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