Landscape Dynamics
Articles by Dan Friedman

  • 5. Castles in Tuscany: The Dynamics of Rank Dependent Consumption
    June, 2000. With Joel Yellin
    We apply gradient dynamics to population games in which consumers interact via rank dependent preferences. Rank dependent consumption leads to a payoff landscape that changes shape in response to the nonlinearity inherent in non-price interactions. The nonlinearity causes the spontaneous formation of moving accreting clusters in action space. We study the structure and development of these clusters in deterministic models and also in the presence of stochastic uncertainty about the shape of the local landscape. We discuss extensions that may shed light on the dynamics of asset price bubbles.
  • 11. Evolving Landscapes for Population Games
    February, 1997. With Joel Yellin
    We consider population games where the possible actions of each player are labeled by a real number that ranges over a finite interval. The adjustment dynamics of such games can be visualized in terms of the ``landscape'' - the graph of the payoff (or fitness) function. A leading example is gradient dynamics, in which the speed with which a player changes action is proportional to the gradient (or slope) of the landscape at his current action. The time behavior of the action distribution in gradient dynamics is described by a class of nonlinear partial differential equations. Cases are exhibited in which the distribution of actions develops compressive and rarefaction shock waves. We discuss connections to the learning in games literature and to replicator and other monotone (or order compatible) dynamics. Applications are suggested in economics and population biology.
  • 18. On Economic Applications of Evolutionary Games
    Journal of Evolutionary Economics, 1998
    This paper exposits the specification of evolutionary game models, and classifies asymptotic behavior in one and two dimensional models.
  • 20. Towards Evolutionary Game Models of Financial Markets
    August 2000
    Evolutionary game models analyze strategic interaction over time; equilibrium emerges (or fails to emerge) as players/traders adjust their actions in response to the payoffs they earn. This paper sketches some early and some recent evolutionary game models that contain ideas useful in modeling financial markets. It spotlights recent work on adaptive landscapes. In an extended example, the distribution of player/trader behavior obeys a variant of Burgers' partial differential equation, and solutions involve travelling shock waves. It is conjectured that financial market crashes might insightfully be modeled in a similar fashion. A slightly modified version appears in Quantitative Finance 1:1 (Jan 2001)pp. 177-185.
  • Papers of Dan Friedman
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  • Revised 10 October 2004 by Ralph Abraham