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Attainability and Stability of Equilibria in Social Dilemmas: An Experimental Exploration

Attainability and Stability of Equilibria in Social Dilemmas: An Experimental Exploration Eser Sekercioglu Ph.D Candidate, Political Science Stony Brook University EITM 2006 , University of Michigan Ann Arbor. A long time ago in an Academia far, far away….

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Attainability and Stability of Equilibria in Social Dilemmas: An Experimental Exploration

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  1. Attainability and Stability of Equilibria in Social Dilemmas: An Experimental Exploration Eser Sekercioglu Ph.D Candidate, Political Science Stony Brook University EITM 2006 , University of Michigan Ann Arbor

  2. A long time ago in an Academia far, far away… • There were institutions, and there was institutionalism… • We may have forgotten those good old days before the Behavioral revolution, but there was really a time when unit of analysis was institutions…

  3. Then came the Skinner Box…errr Behavioral Revolution! • Now, the attention was on the individual. Days of old, and the ways of old, all but forgotten. Unit of analysis was now the individual and even when the effects of institutions on behavior were implied they were never analyzed but merely taken for granted.

  4. Neo-institutionalism • Institutions were meant to return, and they did. In style… • New institutionalists managed to combine institutions and individual behavior. The result, as we know, proved fruitful.

  5. A few recurrent themes… • -Self-enforcement • -Endogenous institutions • -Institutional change • -Institutional stability • -Institution-as-equilibrium • -Path (Phat?) dependence

  6. INDIVIDUAL INSTITUTION Two major lines of thought.. • Institution as constraint • Institution as equilibrium

  7. Institution as Equilibrium • Institution as the equilibrium strategy of an underlying societal game. • Calvert (1995) treats the strategic setting as the environment and institution as a strategy of that game. • -Institutions are not fixed environments in which individuals make decisions • - They do constrain individual behavior, it is true, but they are determined within the system, which is the underlying societal game. • -Hence the focus on self-enforcement and equilibrium

  8. But…. • Characterizing an institution as equilibrium (existence criteria) is something, explaining the existence of such equilibrium is something else. • -What, on earth, does self-enforcement precisely mean? • -Are all equilibrium institutions self-enforcing? • -Are all equilibrium institutions attainable? • -Are all equilibrium institutions stable?

  9. The path…. • Model institutional change as an evolutionary game ….individuals as norm guided players capable of adaptation (learning, and/or imitation) ….strategies as the heritable (imitable, learnable) characteristics. • Define the institutional change as a dynamic evolutionary game… • Characterize the set of all possible institutions as the strategy space • For attainability and stability, use Evolutionary Stability criteria • For the path of institutional change, define replicator dynamics and calculate population (proportion of population that adopts the institution) dynamics. • Voila!!!

  10. First victim… • Calvert(1995) proposed an institutional solution to cooperation problems in order to illustrate the use(fulness) of institution-as-equilibrum concept. • Game: • N players play a repeated 2-person PD with a discount rate of δ. Each player is matched randomly with another player each round.

  11. Game… • Then, each player sends a message to any number of players with the following contents: • “My opponent in this round was j and he played the action a (c,d).” • Note that message need not be honest. But it is also easy to see that lying has no benefits in this context at all. • If, a player is reported to have defected he falls into `punishment condition`, meaning that he cannot receive messages. In order to restore good-standing, player in the punishment condition should cooperate in the following round.

  12. Equilibrium… • TFT/MC : Tit-for-Tat with multilateral communication. • Calvert describes a sub-game perfect equilibrium of this game as follows: • Every player starts with C (cooperate), and then sends honest messages to every other player. • If a player defects (for any reason), s/he immediately cooperates in the following round. (TFT/MC players defect against a player in punishment condition). • Therefore, institution has a more effective punishment mechanism than TFT because players in punishment condition will cooperate and get a payoff of –β.

  13. Calvert shows that for reasonable values of the discount factor there is no one-round profitable deviation from TFT/MC. In other words, if you cooperated in the first round you’d better continue doing so. If you defect at any point immediately switch to cooperate in the next round. • In effect, TFT/MC defines a collective TFT-Grim Trigger hybrid. Group immediately responds to defection through messages but after punishment is suffered goes back to cooperating.

  14. For TFT/MC the bell tolls… • TFT/MC can be an equilibrium…but it does not say anything about attainability and very few things about stability. • So, TFT/MC is a perfect candidate for testing my approach.

  15. KISS… • Let’s first see whether TFT/MC is resistant against an upsurge of defectors. • Need justification? Think about defectors as a resurgent revolutionary group which defies the social order. What should be the size of the resurgent group in order to topple the institution and change it?

  16. ESS First, though, a crash course in Evolutionary Stability: • An incumbent strategy x is ESS if, for small enough values of e, • for all y Є S where S is the set of strategies. • ε, then is the invasion barrier for x. • In our case S has two elements only. TFT/MC and D (always defect)

  17. Let’s turn to TFT/MC • Conditions for TFT/MC being an ESS is given by; For values of p that satisfy the above inequality, TFT/MC will resist an invasion by a resurgent group that refuses to play TFT/MC

  18. Which can be simplified and presented as;

  19. FOC

  20. Visualising… • Lets assume α = β and, fix c at c= β/1000 Now we have a function in 3 variables…This function defines a volume (3D object) in a 4 dimensional space…

  21. TM is all right, where is EI ?! First question: Would real human beings adopt new strategies (institutions) as our evolutionary agents? • Go to the Lab!  Experiment • Rob NSF for big $$$  Field Experiments • Revise your thinking about (a) path dependence, thus, refine historical analysis.

  22. Conclusions • Just scratched the surface, • Have not investigated a richer strategy space…How can TFT/MC perform against other cooperative strategies? • No replicator dynamics, no population dynamics yet… • Ultimate goal: A complete and concise theory of Institutional Change…

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