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Unformatted text preview: Unit III: The Evolution of Cooperation • Can Selfishness Save the Environment? • Repeated Games: the Folk Theorem • Evolutionary Games • A Tournament • How to Promote Cooperation/Unit Review 4/14 7/28 7/21 • We saw that the indefinitely repeated prisoner’s dilemma (IRPD) gives rise to a very large set of (subgame perfect) Nash equilibria – Folk Theorem. • In this context, evolution can be seen as a process that selects for repeated game strategies with efficient payoffs. “Survival of the Fittest” Last Time The Folk Theorem ( R,R ) ( T,S ) ( S,T ) ( P,P ) In other words, in the repeated game, if the future matters “enough” i.e., ( δ > δ * ), there are zillions of equilibria! The white line is the set of “collectively stable” strategies Evolutionary Games Fifteen months after I had begun my systematic enquiry, I happened to read for amusement ‘Malthus on Population’ . . . It at once struck me that . . . favorable variations would tend to be preserved, and unfavorable ones to be destroyed. Here then I had at last got a theory by which to work. Charles Darwin Evolutionary Games • Evolutionary Stability (ESS) • HawkDove: an example • The Replicator Dynamic • The Trouble with TIT FOR TAT • Designing Repeated Game Strategies • Finite Automata Evolutionary Games Biological Evolution : Under the pressure of natural selection, any population (capable of reproduction and variation) will evolve so as to become better adapted to its environment, i.e., will develop in the direction of increasing “fitness.” Economic Evolution : Firms that adopt efficient “routines” will survive, expand, and multiply; whereas others will be “weeded out” (Nelson and Winters, 1982). Evolutionary Stability Evolutionary Stable Strategy (ESS) : A strategy is evolutionarily stable if it cannot be invaded by a mutant strategy. (Maynard Smith & Price, 1973) A strategy, A, is ESS, if i) V(A/A) > V(B/A), for all B ii) either V(A/A) > V(B/A) or V(A/B) > V(B/B), for all B HawkDove: an example Imagine a population of Hawks and Doves competing over a scarce resource (say food in a given area). The share of each type in the population changes according to the payoff matrix, so that payoffs determine the number of offspring left to the next generation. v = value of the resource c = cost of fighting H/D: Hawk gets resource; Dove flees ( v , 0) D/D: Share resource ( v /2, v /2) H/H: Share resource less cost of fighting (( vc )/2, ( vc )/2) (See HargreaveHeap and Varoufakis: 195214; Casti: 7175.) HawkDove: an example H D H 1,1 4 ,0 D ,4 2, 2 NE = {(1,0);(0,1); (2/3,2/3) } unstable stable The mixed NE corresponds to a population that is 2/3 Hawks and 1/3 Doves H D H D1,1 4,0 0,4 2,2 A strategy, A, is ESS, if i) V(A/A) > V(B/A), for all B In other words, to be ESS, a strategy must be a NE with itself....
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This note was uploaded on 03/21/2010 for the course ECON 1050 taught by Professor Neugeboren during the Summer '09 term at Harvard.
 Summer '09
 NEUGEBOREN
 Game Theory

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