Learning rules, matching and frequency dependence

https://doi.org/10.1016/S0022-5193(87)80236-9Get rights and content

We believe that Harley (1981, 1983) confuses various issues that are important in the application of optimality and game theory principles to behaviour. This paper attempts to clarify these issues, using examples based on various studies of foraging behaviour. We argue that it is important to distinguish between two meanings of “frequency dependent”. One meaning is concerned with how the payoff to a given action in an animal's repertoire depends on the frequency with which the animal uses the action. The other meaning is concerned with how the payoff to a strategy depends on the frequency with which the strategy is present in the population. A confusion between these levels seems to underlie an incorrect proof that the matching law is optimal.

References (48)

  • CharnovE.C.

    Theor. Pop. Biol.

    (1976)
  • HarleyC.B.

    J. theor. Biol.

    (1981)
  • HarleyC.B.

    J. theor. Biol.

    (1983)
  • HerrnsteinR.J. et al.
  • HoustonA.I.

    J. theor. Biol.

    (1983)
  • McNamaraJ.M. et al.

    J. theor. Biol.

    (1985)
  • Maynard SmithJ.

    J. theor. Biol.

    (1974)
  • MilinskiM.

    Anim. Behav.

    (1984)
  • RegelmannK.

    Anim. Behav.

    (1984)
  • WilliamsB.A.

    Learn. and Mot.

    (1985)
  • BaumW.M.

    J. exp. Anal. Behav.

    (1974)
  • BaumW.M.

    J. exp. Anal. Behav.

    (1979)
  • BaumW.M.

    Learn. and Mot.

    (1985)
  • CataniaA.C.

    Concurrent operants

  • DawkinsR.
  • FellerW.F.

    An Introduction to Probability Theory and its Applications

    (1968)
  • FindleyJ.D.

    J. exp. Anal. Behav.

    (1958)
  • FretwellS.D. et al.

    Acta. Biotheor.

    (1970)
  • GreenL. et al.

    J. exp. Anal. Behav.

    (1983)
  • HerrnsteinR.J.

    J. exp. Anal. Behav.

    (1961)
  • HerrnsteinR.J.

    J. exp. Anal. Behav.

    (1970)
  • HerrnsteinR.J. et al.

    J. exp. Anal. Biol.

    (1979)
  • HeymanG.M.

    J. exp. Anal. Behav.

    (1979)
  • HeymanG.M. et al.

    Anim. Learn. and Behav.

    (1979)
  • Cited by (107)

    • Matching Behaviours and Rewards

      2021, Trends in Cognitive Sciences
      Citation Excerpt :

      An alternative approach has been to search for rules that predict moment to moment decisions on the basis of experience. Given suitable parameters, many sorts of rule result in matching [27,45,46,58,92,95,96]; for the generality of this result see [16]. Since the formulation of the GML, there have been two interesting lines of research into mechanisms.

    • On learning dynamics underlying the evolution of learning rules

      2014, Theoretical Population Biology
      Citation Excerpt :

      All these features taken together make the analysis of the evolution of learning rules more challenging to analyze than standard evolutionary game theory models focusing on actions or strategies for constant environments (e.g., Axelrod and Hamilton, 1981; Maynard Smith, 1982; Binmore and Samuelson, 1992; Leimar and Hammerstein, 2001; McElreath and Boyd, 2007; André, 2010). Although there has been some early studies on evolutionarily stable learning rules (Harley, 1981; Houston, 1983; Houston and Sumida, 1987; Tracy and Seaman, 1995), this research field has only recently been reignited by the use of agent-based simulations (Großet al., 2008; Josephson, 2008; Hamblin and Giraldeau, 2009; Arbilly et al., 2010, 2011a,b; Katsnelson et al., 2011). It is noteworthy that during the gap in time in the study of learning in behavioral ecology, the fields of game theory and economics have witnessed an explosion of theoretical studies of learning dynamics (e.g., Jordan, 1991; Erev and Roth, 1998; Fudenberg and Levine, 1998; Camerer and Ho, 1999; Hopkins, 2002; Hofbauer and Sandholm, 2002; Foster and Young, 2003; Young, 2004; Sandholm, 2011).

    • Co-evolution of learning complexity and social foraging strategies

      2010, Journal of Theoretical Biology
      Citation Excerpt :

      Interestingly, this prediction has not been tested theoretically or empirically. There has been extensive research on the producer–scrounger game (reviewed by Giraldeau and Caraco, 2000; Giraldeau and Dubois, 2008), on the evolution of social versus individual learning (Boyd and Richerson, 1985, 1988, 1995; Rogers, 1988; Feldman et al., 1996; Wakano et al., 2004; Aoki et al., 2005; Borenstein et al., 2008), and on evolutionarily stable learning rules for choosing among strategies in a game (Harley, 1981; Houston and Sumida, 1987; Tracy and Seaman, 1995; Beauchamp, 2000; Hamblin and Giraldeau, 2009). There is also increasing interest in the evolution of individual learning in stochastic and stable environments (Stephens, 1991; Bergman and Feldman, 1995; Kerr and Feldman, 2003; Groß et al., 2008).

    • Chapter 2 Social Foraging and the Study of Exploitative Behavior

      2008, Advances in the Study of Behavior
      Citation Excerpt :

      One approach to the study of learning has been to evaluate the performance of so-called “learning rules,” an algorithm that specifies how information is collected, processed, and then used in deciding among alternatives (Harley, 1981). While many studies have explored how different learning rules perform against each other in a game context (Beauchamp, 2000; Harley, 1981; Houston and Sumida, 1987), few have explored how these rules may evolve within a game context. From a theoretical point of view, this question has been recently addressed by Dubois et al. (MS) who asked whether flexible strategy use could evolve in a background of fixed strategists in a frequency-dependent game such as the PS game.

    View all citing articles on Scopus
    View full text