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Level k theory
Haruvy:
Liquid error: wrong number of arguments (given 1, expected 2)
== Level-k Theory ==
Level-k theory is the leading theory in the literature of hierarchical bounded rationality.
In the early nineties, level-k theory emerged in the writings of Dales, Stahl and Wilson. Stahl <ref>Stahl, D. O. (1993). Evolution of Smart<sub>n</sub> Players. [[Games and Economic Behavior]], 5(4), 604-617.</ref>
proposed that "player types are drawn from a hierarchy of smartness analogous to the levels of iterated rationalizability."
The hierarchy begins with some very naive type. This completely non-strategic "level-zero" player will choose actions without regard to the actions of other players. Such a player is said to have zero-order beliefs.
A one level higher sophisticated type believe the population consists of all naive types. This slightly more sophisticated (the level one) player believes that the other players will act non-strategically; his or her action will be the best response consistent with those first-order beliefs.
The next level believes the population consists of the first level. This more sophisticated (level two) player acts on the belief that the other players are level one. This pattern continues for higher-level players, but each player has only a finite depth of reasoning, meaning that individual players have a limit to the depth to which they can reason strategically.
As a motivating example, consider the "guessing game" investigated in Nagel [1995]. In that game, players simultaneously state a number between 0 and 100. The player who is closest to 2/3 of the average wins a prize. A person is defined to be of hierarchy level n if he chooses 50(2/3)^n. So a level-1 should choose 33.33, a level-2 is 22.2, etc. The optimal choice in the Nagel [1995] experiments, given the observed empirical frequency, was 25, corresponding to about level-2. Nagel [1995] found that the largest modes were at level-1 and level-2 choices, with a much smaller mode at level-3 and very little past that.
To accommodate that theory using econometric methods, Stahl and collaborators <ref>Stahl II, D. O., & Wilson, P. W. (1994). Experimental evidence on players' models of other players. [[Journal of Economic Behavior & Organization]], 25(3), 309-327.</ref> proposed a Mixture Model. A mixture model is an econometric approach wherein sub-populations exist representing each type, and these subpopulations can be identified in some proportions.
Level-k theory assumes that players in strategic games base their decisions on their predictions about the likely actions of other players. According to level-k, players in strategic games can be categorized by the "depth" of their strategic thought.<ref name="Nagel">Nagel, Rosemarie. "Unraveling in Guessing Games: An Experimental Study". ''[[The American Economic Review]]'', Vol. 85, Issue 5. December 1995</ref> It is thus heavily focused on [[bounded rationality]].
In its basic form, level-k theory implies that each player believes that he or she is the most sophisticated person in the game. Players at some level k will neglect the fact that other players could also be level-k, or even higher. This has been attributed to many factors, such as "maintenance costs" or simply overconfidence.<ref name="StahlDale">Stahl, Dale and Wilson, Paul. "On Players' Models of Other Players: Theory and Experimental Evidence". ''[[Games and Economic Behavior]]''. 10, 1995</ref>
An important element of the econometric modeling of level-k is the distribution of choices within each level-k type. Players within each type make choices that don't conform precisely to the prescribed behavior corresponding to their type. The degree and pattern of deviation from their prescribed choices determines the classification of a player as one type or another. Alternative behavioral econometric models for the characterization of player heterogeneity, both between and within subpopulations of players, include using a model of computational errors and the allowing for diversity in prior beliefs around a modal prior for the subpopulation<ref>Liquid error: wrong number of arguments (given 1, expected 2)</ref>.
December 12, 2019 at 08:54AM
