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Cognitive Hierarchy Theory (Insert redirect from "level-k" and "level-k game theory")

Cognitive Hierarchy Theory is a theory in (link) behavioral economics and (link) game theory that has been offered (by whom?) to explain the deviation of empirical results in games from the predictions offered by standard analytic methods, such as (link) backwards induction and (link) iterated elimination of dominated strategies. According to Cognitive Hierarchy Theory, players can be categorized according to "levels" of strategic behavior; this explains the observed pattern of opportunistic cooperation found in many games, whereas other theories will resort to guessing about the level of intelligence or altruism, which are descriptive and plausible but also non-predictive and non-falsifiable.

Contents Definitions Example Significance See Also References

Definition

Players are categorized in "levels" according to the degree to which they exhibit strategic thinking and behavior. A "level-0" thinker has no strategic behaviors, and is usually modeled as a person who will act either randomly or cooperatively at all times. A "level-1" thinker is one who behaves as if his or her opponents are all level-0. Similarly, a "level-2" thinker is one who behaves as if his or her opponents are all level-1.

As an empirical matter, there are very few people who exhibit level-0, level-1, and even level-2 strategic behavior. Observations tend to indicate that most players are either level-3 or level-4.

Example: The Centipede Game

In many games, such as the (link) centipede game, traditional analytic methods do not accurately predict the behaviors of the players. For example, the use of backwards induction to find the (link) Nash equilibrium in the centipede game predicts that all players will defect as soon as they have the opportunity, despite the higher payoffs that would accrue to more cooperative play. Empirically, cooperative behavior is observed, but only for a limited number of rounds. While the benefits to cooperation persist (and in fact grow), most games end prematurely, with the defection of a player who had previously been cooperative. Explanations of this temporarily-cooperative behavior have included (link) altruism and either error or the anticipation of errors. In the case of altruism, a player opposed by an altruist (someone who will always cooperate; a level-0 thinker) will cooperate with the intention of defecting later, since the payoff for defection increases the longer cooperative play has lasted. In the case of error, a player is merely not thinking "rationally", and does not appreciate the vulnerabilities created by cooperative play. If a player anticipates that his opponent is prone to making such errors, it will be in that player's interest to cooperate until the opponent recognizes his error.

According to Cognitive Hierarchy Theory, a level-0 player will always cooperate in this game. That means two level-0 players will proceed to the final round, and the net benefit to both will be maximized.

A level-1 player will expect that the opponent is a level-0 player, and will thus plan to cooperate until just before the opponent's last move, thereby exploiting the opponent's cooperative nature to the maximum extent possible.

A level-2 player will expect that the opponent is a level-1 player. Knowing this, the level-2 player will expect that the opponent will defect on just before the player's last round, and the level-2 player will defect just before this happens.

Players exhibiting a very high level of strategic thinking, such as expert (link) chess players, will defect extremely early. In Palacios-Huerta and Volij (2009), all (link) Grandmasters observed defected on the first round.

Significance

Cognitive Hierarchy Theory represents a strong effort to incorporate the ideas of (link) bounded rationality ("behavior that is intendedly rational, but only limitedly so") and (link) opportunism ("self-interest with guile") into economic and game theoretic analysis. Unlike methods such as backwards induction, it does not assume that players possess an unrealistically developed ability to process information, especially under conditions of uncertainty, dependence on other players, and time constraints. Furthermore, by incorporating assumptions of opportunism, it is able to explain why a player will cooperate and then defect. Unlike the explanation that the outcomes of some games are the result of errors and learning, or assumptions that opponents will err, Cognitive Hierarchy Theory notes that these outcomes are planned upon, so that neither error nor learning is present in the games. Similarly, the eventual defection of most players signifies that most players are not altruistic (or alternatively, level-0 players). Rather, players cooperate because they are seeking their own self-interest, but with more guile than predicted even by the assumptions of hyperrationality implicit in more traditional analytic methods. As such, the Cognitive Hierarchy Theory preserves an important assumption in economics (that individuals act in ways that advance their self-interest, as they see it).

Most importantly, Cognitive Hierarchy Theory is able to accurately depict and predict human behavior in strategic settings.

See Also

References

See Also