Introduccin a la Teora No Cooperativa de Juegos

Juegos en forma estratgica

El Dilema del Prisionero

DelatarNo Delatar

Delatar-10 -100 -15No Delatar-15 0-1 -1

El equilibrio de NashM. Davis (1986). Introduccin a la teora de juegos. Alianza Editorial.R. Gibbons (1992). Un primer curso de teora de juegos. Antoni Bosch. (www.antonibosch.com).M.J. Osborne and A. Rubinstein (1994). A course in game theory. The MIT Press.

Much of the modern literature in economics (and related disciplines) takes the following form: A social situation is modelled, as a non-cooperative game, the Nash equilibria of the game are computed, and their properties are translated into insights into the original problem.

H.W. Kuhn, J.C. Harsanyi, R. Selten, J.W. Weibull, E. van Damme, J.F. Nash and P. Hammerstein (1996). The work of John Nash in game theory. Journal of Economic Theory 69, 153-185.

During the past two decades non-cooperative game theory has become a central topic in economic theory. Many scholars have contributed to this revolution, none more than John Nash.

A. Rubinstein (1995). John Nash: The master of economic modeling. Scandinavian Journal of Economics 97, 9-13.

La Batalla de los Sexos

CineTeatroCine4 32 2Teatro1 13 4

No tiene equilibrios de Nash(L,L) es un equilibrio de NashEdgar Allan PoeLa carta robadaMatching Pennies

PIP-1 1 1 -1I 1 -1-1 1

PILP-1 1 1 -10 0I 1 -1-1 10 0L 0 0 0 00 0

Teorema de NashTodo juego finito en forma estratgica en el que los jugadores pueden elegir loteras sobre sus conjuntos de estrategias tiene al menos un equilibrio de Nash.

B=BotnC=CrcelLa Paradoja de la InstigacinS=SiestaP=ParoM=MedallaEl nico equilibrio de Nash de este juego es: (S/(S+P+M),(P+M) /(S+P+M))(C/(C+B),B/(C+B))

LADRN (L)RobaV DuermeBV No Duerme-CNo Roba0

VIGILANTE (V)DuermeL No RobaSL Roba-PNo DuermeL No Roba0L RobaM

DNDRB -P-C MNR0 S 0 0

(S/(S+P+M),C/(C+B)) es el nico equilibrio de Nash.

INSTIGACINCONSECUENCIAC ms grandeL roba lo mismoV duerme msP, M ms grandesL roba menosV duerme lo mismo

((2/5,3/5),(1/5,4/5))V=86El lanzamiento del sistema exafnicoPEQUEO 1/2GRANDE 1/2

868095

MAM60 20 20 60A 70 1050 30

MAM160 40 140 60A 70 130 130 70

MAM110 30 80 60A 70 7090 50

MMMAAMAAM110 30 110 30 80 60 80 60A 70 7090 5070 7090 50

MMMAAMAAMM110 30 110 30 80 60 80 60MA 75 65 95 45 45 9575 65AM 115 25105 35105 3595 45AA 70 70 90 50 70 7090 50

R. Selten (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4, 25-55.E. Van Damme (1991). Stability and Perfection of Nash Equilibria. Springer Verlag.Refinamientos del equilibrio de NashAaID(2,2)(3,1)(0,0)AaaA12(a,D) es el nico equilibrio de Nash razonable.(a,A) es el nico equilibrio de Nash razonable.

10 10 0 1010 01 1

El modelo de duopolio de CournotEn un monopolio...

El Modelo de Duopolio de Stackelberg

Al contrario que en el lanzamiento del sistema exafnico, aqu es bueno ser el lder. R. Gibbons (1992). Un primer curso de teora de juegos. Antoni Bosch. (www.antonibosch.com).

MONOPOLIOCOURNOTSTACKELBERG

F. Patrone, I. Garca-Jurado and S. Tijs (2000). Game Practice: Contributions from Applied Game Theory. Kluwer Academic Publishers.P. Borm and B. van der Genutgen. On the exploitation of casino games: how to distinguish between games of chance and games of skill?A. Roth. Game theory as a tool for market design.E. van Damme. The Dutch DCS-1800 auction.

...it is not allowed to: exploit games with monetary prizes if the participants in general do not have a dominant influence on the probability to win, unless in compliance to this act, a license is granted...Dutch Gaming ActIn practice the Dutch state only grants such a license to its own Holland Casinos foundation.The formulation of the Gaming Act clearly implies that skill should be considered relatively with respect to chance.If it would be possible to rank a broad class of games with chance elements by means of an operational and objective criterium which quantifies the level of skill relatively to chance, e.g. on a scale from zero to one, the legislator would be able to decide on a certain bound on the level of skill, below which a game should be considered as a game of chance.Game of chance: it needs a license according to the Gaming Act. Game of skill: all the other games.

P. Borm and B. van der Genutgen. On the exploitation of casino games: how to distinguish between games of chance and games of skill?

Jugador principiante: juega el juego de un modo ingenuo, del modo en que lo jugara alguien que acaba de conocer las reglas.Jugador avanzado real: juega el juego de un modo ptimo.Jugador avanzado virtual: juega el juego de un modo ptimo y conoce de antemano el resultado de todos los elementos del juego en los que interviene el azar. La legislacin se refiere nicamente a la explotacin de juegos con premios en metlico. Efecto del aprendizaje: Es el resultado esperado de un jugador avanzado real (AR), menos el resultado esperado de un jugador principiante (P). Efecto del azar: Es el resultado esperado de un jugador avanzado virtual (AV), menos el resultado esperado de un jugador avanzado real (AR).

Market design concerns the creation of a venue for buyers and sellers, and a format for transactions.Game theorists have taken the lead in designing a number of different kinds of markets. Perhaps the three best known of these are auction markets for radio spectrum licenses, spot markets for electric power, and labor market clearinghouses.My own experience in market design has been with entry-level professional labor markets. Since 1998, the vast majority of jobs for new physicians in the US (about 20,000 per year) are filled by a clearinghouse whose design I directed.A. Roth. Game theory as a tool for market design.

Problema Bsico de Asignacin

En un problema bsico de asignacin siempre existe una asignacin estable. Algoritmo de Gale y Shapley (1962).Complejidades del mercado mdico:Plazas con prerrequisitos.Asignacin en problemas con parejas.

E. van Damme. The Dutch DCS-1800 auction.In the case of radio spectrum auctions in the United States, the federal government used to give away licenses, but was ordered by Congress to sell them, both to raise revenue and to promote efficient use. A. Roth.In February 1998 the Dutch government auctioned licenses to operate mobile telecommunications networks according to the DCS-1800 technology. Two national licenses and sixteen regional ones were auctioned by using a variant of the simultaneous, multiple round auction that was proposed by US-economists and that had been tested in the US. This paper describes how the decision to auction came about, it details the auction rules, and it analizes the resulting outcomes. E. van Damme.

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Introduccin a la Teora No Cooperativa de Juegos

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