Evolution and Learning in Spatial Models/TITLE> </HEAD> <BODY BACKGROUND="Sand.jpeg"> <A HREF="http://www.informatik.uni-bonn.de/unibo-en.html">Uni-Bonn</A> / <A HREF="http://www.informatik.uni-bonn.de/rechtustaatswi-en.html"> Law and Economics</A> / <A HREF="http://hannibal.econ3.uni-bonn.de/"> Economic Theory III</A> / <A HREF="http://witch.econ3.uni-bonn.de/~oliver/homepage.html"> Oliver Kirchkamp</A> <HR> <H1>Evolution and Learning in Spatial Models</H1> <H3><A HREF="http://witch.econ3.uni-bonn.de/~oliver/homepage.html">Oliver Kirchkamp</A></H3> <HR> The text is actually my thesis, which you can read as a <A HREF="http://witch.econ3.uni-bonn.de/~oliver/di.pdf">PDF-File</A> (3523960 bytes, 160 Pages) or as a <A HREF="http://witch.econ3.uni-bonn.de/~oliver/di.ps.zip">with zip compressed PostScript file</A> (2221370 bytes, 160 Pages) <HR> <H2>Abstract</H2> Classical evolutionary game theory studies properties of a dynamic process where a population interacts and evolves <EM>globally</EM>, i.e. each player is equally likely to interact with any other player. Further successful strategies are adopted (through learning or replication) equally likely by<EM>any</EM> member of the population, regardless whether the successful strategy was used far away or nearby. <P> In my dissertation I analyze models with <EM>local</EM> interaction and evolution. I start (in chapter 2) with the analysis of a simple and abstract model of local evolution that can be treated analytically. Standard replicator dynamics can be regarded as a special case of this model. I model <EM>local interaction</EM> assuming that pairs of players are matched permanently. <EM>Local evolution</EM> is introduced as a higher likelihood to switch to strategies that are known from the interaction environment. Despite the simplicity of the model several features of more complex models (like persistence of cooperation and long run exploitation among different strategies) are already present. I try to demonstrate how equity is linked to the assumption of global evolution. I further analyze stability of pure and mixed equilibria under this dynamics and discuss how evolution of repeated game strategies can be introduced. In the second part of my dissertation (chapters 3 and 4) I study a cellular automaton model of local interaction and evolution where players play prisoners' dilemmas and coordination games. Players may use discriminative strategies (automata) and timing can be stochastic. In contrast to models of global evolution I find that payoffs among strategies that survive in the long run may differ (`clever' strategies exploit often and feed sometimes `dumb' strategies). In contrast to undiscriminative behavior cooperation persists even in a stochastic environment. <P> In the above mentioned parts of my dissertation I have always analyzed evolution of <EM>strategies</EM> assuming that the forces of evolution, i.e. <EM>learning rules</EM>, are given exogenously. In the third part of my dissertation (chapters 5 and 6) I analyze evolution of <EM>strategies</EM> together with evolution of <EM>learning rules</EM>. In this context I ask two questions. First I want to find out whether surviving learning rules are similar to the ones assumed in the literature on network evolution. Second I ask whether the surviving learning rules imply a stage game behavior which is similar to the one found with standard learning rules. <P> To answer these questions I study a model where players are distributed on a network, and where they are characterized by three properties: Stage game strategies which are used in various stage games played against neighbors, second a repeated game strategy which determines the above stage game strategy given past behavior of the neighborhood, and third a learning rule that determines from time to time the players' repeated game strategy given success of repeated game strategies in their neighborhood. The players' individual learning rule is determined by an exogenously given rule that is the same for all players in the population. Very rarely players changes their learning rule. To do this they sample other player's learning rules and their respective success in the neighborhood. Given this information a player builds a simple (quadratic) model that explains success of learning rules as a function of the parameters of this rule. Players implement a best learning rule given their individual estimation of the model. This process is repeated over and over again. <P> It turns out that in the long run endogenous learning rules differ from the learning rules assumed in the literature on network evolution in the sense that they are not deterministic and that they are suspicious. Still stage game behavior does not differ substantially from the one analyzed in the literature. We still observe cooperation in prisoners' dilemmas and coordination on non-risk-dominant equilibria in coordination games. <HR> <UL> <LI><I><A HREF="http://witch.econ3.uni-bonn.de/~oliver/homepage.html">Oliver Kirchkamp</A></I> <LI><B>email:</B> <A HREF="mailto:oliver@witch.econ3.uni-bonn.de"> oliver@witch.econ3.uni-bonn.de </A> </A> <LI><B>Paper Address:</B><P> <A HREF="http://www.informatik.uni-bonn.de/unibo-ge.html">Bonn University</A><P> Department of Economic Theory III <A HREF="http://hannibal.econ3.uni-bonn.de">(Wirtschaftstheorie III)</A><P> Adenauerallee 24<P> 53113 Bonn<P> Germany<P> <LI><I>Phone:</I> [49]-228-73-7994 <LI>Financial support from the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn is gratefully acknowledged. </UL> <HR> <A HREF="http://www.informatik.uni-bonn.de/unibo-en.html">Uni-Bonn</A> / <A HREF="http://www.informatik.uni-bonn.de/rechtustaatswi-en.html"> Law and Economics</A> / <A HREF="http://hannibal.econ3.uni-bonn.de/"> Economic Theory III</A> / <A HREF="http://witch.econ3.uni-bonn.de/~oliver/homepage.html"> Oliver Kirchkamp</A> <HR> <ADDRESS>May 2, 1996 <A HREF="mailto:oliver@witch.econ3.uni-bonn.de"> oliver@witch.econ3.uni-bonn.de</A></ADDRESS> </BODY> </HTML>