Nash Equilibrium and Dynamics
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1 Nash Equilibrium and Dynamics Sergiu Hart June 2008 Conference in Honor of John Nash s 80th Birthday Opening Panel SERGIU HART c 2008 p. 1
2 NASH EQUILIBRIUM AND DYNAMICS Sergiu Hart Center for the Study of Rationality Dept of Economics Dept of Mathematics The Hebrew University of Jerusalem SERGIU HART c 2008 p. 2
3 Nash equilibrium SERGIU HART c 2008 p. 3
4 nash equilibrium SERGIU HART c 2008 p. 4
5 Nash equilibrium SERGIU HART c 2008 p. 5
6 Nash equilibrium John Nash, Ph.D. Dissertation, Princeton 1950 SERGIU HART c 2008 p. 5
7 Nash equilibrium EQUILIBRIUM POINT: John Nash, Ph.D. Dissertation, Princeton 1950 SERGIU HART c 2008 p. 5
8 Nash equilibrium EQUILIBRIUM POINT: "Each player s strategy is optimal against those of the others." John Nash, Ph.D. Dissertation, Princeton 1950 SERGIU HART c 2008 p. 5
9 Nash equilibrium SERGIU HART c 2008 p. 6
10 Nash equilibrium NON-COOPERATIVE SERGIU HART c 2008 p. 6
11 Nash equilibrium NON-COOPERATIVE "absence of coalitions, communication, and side-payments" SERGIU HART c 2008 p. 6
12 Nash equilibrium NON-COOPERATIVE "absence of coalitions, communication, and side-payments" "Nash Program": non-cooperative foundation and implementation of cooperative approaches SERGIU HART c 2008 p. 6
13 Nash equilibrium NON-COOPERATIVE SERGIU HART c 2008 p. 6
14 Nash equilibrium NON-COOPERATIVE "MASS-ACTION" INTERPRETATION SERGIU HART c 2008 p. 6
15 Nash equilibrium NON-COOPERATIVE "MASS-ACTION" INTERPRETATION "RATIONAL" INTERPRETATION SERGIU HART c 2008 p. 6
16 Nash equilibrium NON-COOPERATIVE "MASS-ACTION" INTERPRETATION "RATIONAL" INTERPRETATION "prediction of the behavior to be expected of rational playing the game" SERGIU HART c 2008 p. 6
17 Nash equilibrium NON-COOPERATIVE "MASS-ACTION" INTERPRETATION "RATIONAL" INTERPRETATION "prediction of the behavior to be expected of rational playing the game" "we need to assume the players know the full structure of the game SERGIU HART c 2008 p. 6
18 Nash equilibrium NON-COOPERATIVE "MASS-ACTION" INTERPRETATION "RATIONAL" INTERPRETATION "prediction of the behavior to be expected of rational playing the game" "we need to assume the players know the full structure of the game... quite strongly a rationalistic and idealising interpretation" SERGIU HART c 2008 p. 6
19 Nash equilibrium SERGIU HART c 2008 p. 7
20 Nash equilibrium If each player SERGIU HART c 2008 p. 7
21 Nash equilibrium If each player knows his own payoff function SERGIU HART c 2008 p. 7
22 Nash equilibrium If each player knows his own payoff function is rational SERGIU HART c 2008 p. 7
23 Nash equilibrium If each player knows his own payoff function is rational knows the (pure) strategy choices of the others SERGIU HART c 2008 p. 7
24 Nash equilibrium If each player knows his own payoff function is rational knows the (pure) strategy choices of the others Then these choices constitute a (pure) NASH EQUILIBRIUM SERGIU HART c 2008 p. 7
25 Nash equilibrium If each player knows his own payoff function is rational knows the (pure) strategy choices of the others Then these choices constitute a (pure) NASH EQUILIBRIUM Aumann and Brandenburger 1995 SERGIU HART c 2008 p. 7
26 Dynamics SERGIU HART c 2008 p. 8
27 Dynamics FACT: SERGIU HART c 2008 p. 8
28 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium SERGIU HART c 2008 p. 8
29 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" SERGIU HART c 2008 p. 8
30 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games SERGIU HART c 2008 p. 8
31 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games (rather than: for specific classes of games) SERGIU HART c 2008 p. 8
32 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" SERGIU HART c 2008 p. 8
33 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" : at a Nash equilibrium (or close to it) from some time on SERGIU HART c 2008 p. 8
34 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" : at a Nash equilibrium (or close to it) from some time on "natural" SERGIU HART c 2008 p. 8
35 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" : at a Nash equilibrium (or close to it) from some time on "natural" : not of the "exhaustive search" variety SERGIU HART c 2008 p. 8
36 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" : at a Nash equilibrium (or close to it) from some time on "natural" : not of the "exhaustive search" variety simple, efficient (time, computation,...) SERGIU HART c 2008 p. 8
37 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium "general" : in all games "leading to Nash equilibrium" : at a Nash equilibrium (or close to it) from some time on "natural" : not of the "exhaustive search" variety simple, efficient (time, computation,...) "uncoupled" SERGIU HART c 2008 p. 8
38 Uncoupled dynamics UNCOUPLED DYNAMICS SERGIU HART c 2008 p. 9
39 Uncoupled dynamics UNCOUPLED DYNAMICS : Each player knows only his own payoff function Hart and Mas-Colell 2003 SERGIU HART c 2008 p. 9
40 Uncoupled dynamics UNCOUPLED DYNAMICS : Each player knows only his own payoff function (does not know the others payoff functions) Hart and Mas-Colell 2003 SERGIU HART c 2008 p. 9
41 Uncoupled dynamics UNCOUPLED DYNAMICS : Each player knows only his own payoff function (does not know the others payoff functions) impossibility results Hart and Mas-Colell 2003, 2006 SERGIU HART c 2008 p. 9
42 Uncoupled dynamics UNCOUPLED DYNAMICS : Each player knows only his own payoff function (does not know the others payoff functions) impossibility results how long? exponential time Hart and Mansour 2008 SERGIU HART c 2008 p. 9
43 Dynamics SERGIU HART c 2008 p. 10
44 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium SERGIU HART c 2008 p. 10
45 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium RESULT: SERGIU HART c 2008 p. 10
46 Dynamics FACT: There are no general, natural dynamics leading to Nash equilibrium RESULT: There cannot be general, natural dynamics leading to Nash equilibrium SERGIU HART c 2008 p. 10
47 Correlated equilibrium SERGIU HART c 2008 p. 11
48 Correlated equilibrium CORRELATED EQUILIBRIUM Aumann 1974 SERGIU HART c 2008 p. 11
49 Correlated equilibrium CORRELATED EQUILIBRIUM : Nash equilibrium when players receive payoff-irrelevant information before the game Aumann 1974 SERGIU HART c 2008 p. 11
50 Correlated equilibrium CORRELATED EQUILIBRIUM : Nash equilibrium when players receive payoff-irrelevant information before the game There are general, natural dynamics leading to correlated equilibria SERGIU HART c 2008 p. 11
51 Correlated equilibrium CORRELATED EQUILIBRIUM : Nash equilibrium when players receive payoff-irrelevant information before the game There are general, natural dynamics leading to correlated equilibria "Law of Conservation of Coordination" SERGIU HART c 2008 p. 11
52 Correlated equilibrium CORRELATED EQUILIBRIUM : Nash equilibrium when players receive payoff-irrelevant information before the game There are general, natural dynamics leading to correlated equilibria "Law of Conservation of Coordination": There must be some "coordination" either in the solution concept, or in the dynamic SERGIU HART c 2008 p. 11
53 HAPPY BIRTHDAY, JOHN! SERGIU HART c 2008 p. 12
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